option pricing active.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Collect stock and option data, price with BSM, compare accuracy"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "import pandas as pd\n",
    "\n",
    "from math import sqrt\n",
    "import numpy as np\n",
    "from scipy.stats import norm\n",
    "\n",
    "import seaborn as sns\n",
    "\n",
    "from datetime import datetime, timezone, timedelta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# initial parameters\n",
    "\n",
    "ticker = 'GOOG'\n",
    "risk_free_rate = 0.08\n",
    "option_type = 'put'\n",
    "\n",
    "# 2 weeks, 1m, 3m, 6m\n",
    "# expiration_datetime = datetime(2020, 12, 4, 0, 0, tzinfo=timezone.utc)\n",
    "# expiration_datetime = datetime(2020, 12, 11, 0, 0, tzinfo=timezone.utc)\n",
    "# expiration_datetime = datetime(2020, 12, 24, 0, 0, tzinfo=timezone.utc)\n",
    "# expiration_datetime = datetime(2021, 2, 19, 0, 0, tzinfo=timezone.utc)\n",
    "expiration_datetime = datetime(2021, 6, 18, 0, 0, tzinfo=timezone.utc)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1623974400\n",
      "2021-06-18 00:00:00\n"
     ]
    }
   ],
   "source": [
    "# get a UTC timestamp from a date. This is used to scrape data from Yahoo Finance.\n",
    "\n",
    "expiration_timestamp = int(expiration_datetime.timestamp())\n",
    "\n",
    "print(expiration_timestamp)\n",
    "print(datetime.fromtimestamp(expiration_timestamp)) # this is in UTC, add 5 hours to this to get EST\n",
    "\n",
    "# feb 19 2021"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# !pip install lxml"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Download historical stock price data for Google (GOOG). I get a past year's worth from (https://finance.yahoo.com/quote/GOOG/history?p=GOOG)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "           Date         Open         High          Low        Close  \\\n",
      "0    2019-12-02  1301.000000  1305.829956  1281.000000  1289.920044   \n",
      "1    2019-12-03  1279.569946  1298.461060  1279.000000  1295.280029   \n",
      "2    2019-12-04  1307.010010  1325.800049  1304.869995  1320.540039   \n",
      "3    2019-12-05  1328.000000  1329.358032  1316.439941  1328.130005   \n",
      "4    2019-12-06  1333.439941  1344.000000  1333.439941  1340.619995   \n",
      "..          ...          ...          ...          ...          ...   \n",
      "249  2020-11-25  1772.890015  1778.540039  1756.540039  1771.430054   \n",
      "250  2020-11-27  1773.089966  1804.000000  1772.439941  1793.189941   \n",
      "251  2020-11-30  1781.183960  1788.064941  1755.000000  1760.739990   \n",
      "252  2020-12-01  1774.369995  1824.829956  1769.369995  1798.099976   \n",
      "253  2020-12-02  1798.099976  1835.650024  1789.472534  1827.949951   \n",
      "\n",
      "       Adj Close   Volume  close_day_before   returns  \n",
      "0    1289.920044  1510900               NaN       NaN  \n",
      "1    1295.280029  1143800       1289.920044  0.004155  \n",
      "2    1320.540039  1537500       1295.280029  0.019502  \n",
      "3    1328.130005  1212700       1320.540039  0.005748  \n",
      "4    1340.619995  1314800       1328.130005  0.009404  \n",
      "..           ...      ...               ...       ...  \n",
      "249  1771.430054  1045800       1768.880005  0.001442  \n",
      "250  1793.189941   884900       1771.430054  0.012284  \n",
      "251  1760.739990  1823800       1793.189941 -0.018096  \n",
      "252  1798.099976  1736900       1760.739990  0.021218  \n",
      "253  1827.949951  1179809       1798.099976  0.016601  \n",
      "\n",
      "[254 rows x 9 columns]\n",
      "           Contract Name         Last Trade Date  Strike  Last Price     Bid  \\\n",
      "0    GOOG210618P00520000  2020-12-02 11:32AM EST   520.0        0.15    0.05   \n",
      "1    GOOG210618P00540000  2020-12-01 12:29PM EST   540.0        0.20    0.00   \n",
      "2    GOOG210618P00560000  2020-10-29 11:18AM EST   560.0        1.25    0.00   \n",
      "3    GOOG210618P00580000   2020-07-01 8:54AM EST   580.0        5.50    3.00   \n",
      "4    GOOG210618P00600000   2020-11-25 1:39PM EST   600.0        0.24    0.05   \n",
      "..                   ...                     ...     ...         ...     ...   \n",
      "134  GOOG210618P01860000  2020-11-16 12:56PM EST  1860.0      205.00  171.90   \n",
      "135  GOOG210618P01900000   2020-10-12 8:47AM EST  1900.0      407.40  215.50   \n",
      "136  GOOG210618P02000000   2020-10-30 2:57PM EST  2000.0      436.00  275.90   \n",
      "137  GOOG210618P02100000   2020-06-24 2:02PM EST  2100.0      673.60  602.00   \n",
      "138  GOOG210618P02200000   2020-11-06 2:29PM EST  2200.0      469.60  405.70   \n",
      "\n",
      "        Ask  Change % Change Volume  Open Interest Implied Volatility  \n",
      "0      0.20   -0.15  -50.00%    111            899             55.96%  \n",
      "1      0.35    0.00        -      1            164             55.86%  \n",
      "2      0.85    0.00        -      1            217             59.01%  \n",
      "3      4.50    0.00        -      1             31             74.88%  \n",
      "4      0.65    0.00        -      1            228             54.64%  \n",
      "..      ...     ...      ...    ...            ...                ...  \n",
      "134  177.60    0.00        -      4              4             29.80%  \n",
      "135  221.10    0.00        -      1              2             33.48%  \n",
      "136  282.60    0.00        -      1              1             32.82%  \n",
      "137  611.10    0.00        -      2              2             80.63%  \n",
      "138  413.70    0.00        -      1              2             28.06%  \n",
      "\n",
      "[139 rows x 11 columns]\n"
     ]
    }
   ],
   "source": [
    "# download annual historical data for the stock\n",
    "\n",
    "# stock_price_path = \"~/documents/quant_finance/price_data/{}.csv\".format(ticker)\n",
    "stock_price_path = \"price_data/{}.csv\".format(ticker)\n",
    "options_data_path = 'https://finance.yahoo.com/quote/{}/options?date={}&p={}'.format(ticker, expiration_timestamp, ticker)\n",
    "\n",
    "df = pd.read_csv(stock_price_path)\n",
    "df = df.sort_values(by=\"Date\")\n",
    "df = df.dropna()\n",
    "\n",
    "# calculate returns\n",
    "df = df.assign(close_day_before=df['Adj Close'].shift(1))\n",
    "df['returns'] = ((df['Adj Close'] - df.close_day_before)/df.close_day_before)\n",
    "\n",
    "# get options data\n",
    "options_data = pd.read_html(options_data_path) # returns two dataframes, for calls and puts\n",
    "\n",
    "if option_type == 'call':\n",
    "    r = options_data[0]\n",
    "elif option_type == 'put':\n",
    "    r = options_data[1]\n",
    "\n",
    "print(df)\n",
    "print(r)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Date</th>\n",
       "      <th>1 mo</th>\n",
       "      <th>2 mo</th>\n",
       "      <th>3 mo</th>\n",
       "      <th>6 mo</th>\n",
       "      <th>1 yr</th>\n",
       "      <th>2 yr</th>\n",
       "      <th>3 yr</th>\n",
       "      <th>5 yr</th>\n",
       "      <th>7 yr</th>\n",
       "      <th>10 yr</th>\n",
       "      <th>20 yr</th>\n",
       "      <th>30 yr</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>12/01/20</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.12</td>\n",
       "      <td>0.17</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.68</td>\n",
       "      <td>0.92</td>\n",
       "      <td>1.46</td>\n",
       "      <td>1.66</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>12/02/20</td>\n",
       "      <td>0.07</td>\n",
       "      <td>0.08</td>\n",
       "      <td>0.09</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.11</td>\n",
       "      <td>0.16</td>\n",
       "      <td>0.22</td>\n",
       "      <td>0.42</td>\n",
       "      <td>0.69</td>\n",
       "      <td>0.95</td>\n",
       "      <td>1.50</td>\n",
       "      <td>1.70</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
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      ],
      "text/plain": [
       "       Date  1 mo  2 mo  3 mo  6 mo  1 yr  2 yr  3 yr  5 yr  7 yr  10 yr  \\\n",
       "0  12/01/20  0.07  0.07  0.09   0.1  0.12  0.17  0.22  0.42  0.68   0.92   \n",
       "1  12/02/20  0.07  0.08  0.09   0.1  0.11  0.16  0.22  0.42  0.69   0.95   \n",
       "\n",
       "   20 yr  30 yr  \n",
       "0   1.46   1.66  \n",
       "1   1.50   1.70  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# get risk free rate data\n",
    "\n",
    "rfr_data_path = 'https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield'\n",
    "rfr_df = pd.read_html(rfr_data_path)[1] # returns two dataframes, for calls and puts\n",
    "rfr_df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f84291e1b38>"
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot the rfr\n",
    "rfr_date = rfr_df.iloc[-1][0]\n",
    "\n",
    "cur_rfr = rfr_df.iloc[-1][1:].astype(float)\n",
    "cur_rfr.plot(title=\"Treasury Curve for {}\".format(rfr_date))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [],
   "source": [
    "# BSM model\n",
    "\n",
    "# S is the spot price \n",
    "# K is the strike price \n",
    "# T is the fraction of days to strike date divided by 252 (stock market days)\n",
    "# r is the risk free rate\n",
    "# sigma is the annual volatility of the returns of the stock \n",
    "\n",
    "def black_scholes(S, K, T, r, sigma, option_type='call'):\n",
    "    \n",
    "    d1 = (np.log(S/K) + (r + sigma**2/2)*T)/(sigma * sqrt(T))\n",
    "    d2 = d1 - sigma * np.sqrt(T)\n",
    "    \n",
    "    if option_type=='call':\n",
    "        return S * norm.cdf(d1) - K*np.exp(-r*T) * norm.cdf(d2)\n",
    "    elif option_type=='put':\n",
    "        return K*np.exp(-r*T) * norm.cdf(-d2) - S * norm.cdf(-d1)\n",
    "    \n",
    "        \n",
    "# get the (num days to expiration) / (trading days in a year)\n",
    "def get_time_to_expiration(expiration_datetime_utc):\n",
    "    return (expiration_datetime_utc - datetime.now(timezone.utc)).days / 252\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "6.401407649076464\n"
     ]
    }
   ],
   "source": [
    "value_s = black_scholes(S = 69, \n",
    "                        K = 70, \n",
    "                        T = 6/12, \n",
    "                        r = .05, \n",
    "                        sigma = .35,\n",
    "                        option_type='put')\n",
    "print(value_s)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cur_stock_price: 1827.949951, time to expiration: 0.7777777777777778, rfr: 0.08, vol: 0.38212781123440914\n"
     ]
    }
   ],
   "source": [
    "# the rfr should vary with time, not be constant.\n",
    "\n",
    "cur_stock_price = df.iloc[-1]['Adj Close']\n",
    "time_to_expiration = get_time_to_expiration(expiration_datetime)\n",
    "\n",
    "# Calculate the volatility as the annualized standard deviation of the stock returns\n",
    "sigma = np.sqrt(252) * df['returns'].std()\n",
    "\n",
    "print('cur_stock_price: {}, time to expiration: {}, rfr: {}, vol: {}'.format(cur_stock_price, time_to_expiration, risk_free_rate, sigma))\n",
    "list_estimates = []\n",
    "\n",
    "strike_start_idx, strike_end_idx = 0, r.shape[0]\n",
    "# strike_start_idx, strike_end_idx = 0, 21\n",
    "\n",
    "# run BSM for different strikes\n",
    "for x in range(strike_start_idx,strike_end_idx):\n",
    "    value_s = black_scholes(S = cur_stock_price, \n",
    "                            K = r['Strike'][x], \n",
    "                            T = time_to_expiration, \n",
    "                            r = risk_free_rate, \n",
    "                            sigma = sigma,\n",
    "                            option_type = option_type)\n",
    "    list_estimates.append(value_s)\n",
    "    \n",
    "# merge the real and computed dataframes to compare results\n",
    "df_list = pd.DataFrame(data=list_estimates, index=r.index[strike_start_idx:strike_end_idx])\n",
    "df_list['estimate'] = df_list[0]\n",
    "del df_list[0]\n",
    "df_estimate = r.merge(df_list, right_index = True, left_index = True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Contract Name</th>\n",
       "      <th>Last Trade Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Ask</th>\n",
       "      <th>Change</th>\n",
       "      <th>% Change</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Open Interest</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>estimate</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>GOOG210618P00520000</td>\n",
       "      <td>2020-12-02 11:32AM EST</td>\n",
       "      <td>520.0</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>-50.00%</td>\n",
       "      <td>111</td>\n",
       "      <td>899</td>\n",
       "      <td>55.96%</td>\n",
       "      <td>0.003265</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>GOOG210618P00540000</td>\n",
       "      <td>2020-12-01 12:29PM EST</td>\n",
       "      <td>540.0</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>164</td>\n",
       "      <td>55.86%</td>\n",
       "      <td>0.005388</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>GOOG210618P00560000</td>\n",
       "      <td>2020-10-29 11:18AM EST</td>\n",
       "      <td>560.0</td>\n",
       "      <td>1.25</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.85</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>217</td>\n",
       "      <td>59.01%</td>\n",
       "      <td>0.008636</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>GOOG210618P00580000</td>\n",
       "      <td>2020-07-01 8:54AM EST</td>\n",
       "      <td>580.0</td>\n",
       "      <td>5.50</td>\n",
       "      <td>3.00</td>\n",
       "      <td>4.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>31</td>\n",
       "      <td>74.88%</td>\n",
       "      <td>0.013480</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>GOOG210618P00600000</td>\n",
       "      <td>2020-11-25 1:39PM EST</td>\n",
       "      <td>600.0</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>228</td>\n",
       "      <td>54.64%</td>\n",
       "      <td>0.020534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>GOOG210618P00620000</td>\n",
       "      <td>2020-08-19 1:00PM EST</td>\n",
       "      <td>620.0</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>5.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>32</td>\n",
       "      <td>66.75%</td>\n",
       "      <td>0.030584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>GOOG210618P00640000</td>\n",
       "      <td>2020-08-18 2:48PM EST</td>\n",
       "      <td>640.0</td>\n",
       "      <td>3.24</td>\n",
       "      <td>1.50</td>\n",
       "      <td>2.65</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>22</td>\n",
       "      <td>63.27%</td>\n",
       "      <td>0.044617</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>GOOG210618P00660000</td>\n",
       "      <td>2020-08-10 12:02PM EST</td>\n",
       "      <td>660.0</td>\n",
       "      <td>5.65</td>\n",
       "      <td>3.80</td>\n",
       "      <td>5.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>15</td>\n",
       "      <td>28</td>\n",
       "      <td>68.85%</td>\n",
       "      <td>0.063853</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>GOOG210618P00680000</td>\n",
       "      <td>2020-11-06 11:21AM EST</td>\n",
       "      <td>680.0</td>\n",
       "      <td>1.30</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.85</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>153</td>\n",
       "      <td>50.00%</td>\n",
       "      <td>0.089771</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>GOOG210618P00700000</td>\n",
       "      <td>2020-12-02 3:15PM EST</td>\n",
       "      <td>700.0</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.17</td>\n",
       "      <td>-24.29%</td>\n",
       "      <td>1</td>\n",
       "      <td>71</td>\n",
       "      <td>52.76%</td>\n",
       "      <td>0.124141</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>GOOG210618P00720000</td>\n",
       "      <td>2020-10-15 12:42PM EST</td>\n",
       "      <td>720.0</td>\n",
       "      <td>3.29</td>\n",
       "      <td>0.50</td>\n",
       "      <td>1.95</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>107</td>\n",
       "      <td>52.88%</td>\n",
       "      <td>0.169050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>GOOG210618P00740000</td>\n",
       "      <td>2020-10-12 8:36AM EST</td>\n",
       "      <td>740.0</td>\n",
       "      <td>3.35</td>\n",
       "      <td>0.70</td>\n",
       "      <td>2.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>91</td>\n",
       "      <td>52.41%</td>\n",
       "      <td>0.226926</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>GOOG210618P00760000</td>\n",
       "      <td>2020-10-28 2:01PM EST</td>\n",
       "      <td>760.0</td>\n",
       "      <td>5.30</td>\n",
       "      <td>0.45</td>\n",
       "      <td>1.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>74</td>\n",
       "      <td>52.12%</td>\n",
       "      <td>0.300563</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GOOG210618P00780000</td>\n",
       "      <td>2020-10-08 11:04AM EST</td>\n",
       "      <td>780.0</td>\n",
       "      <td>5.60</td>\n",
       "      <td>1.85</td>\n",
       "      <td>2.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>38</td>\n",
       "      <td>52.72%</td>\n",
       "      <td>0.393135</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GOOG210618P00800000</td>\n",
       "      <td>2020-11-24 3:54PM EST</td>\n",
       "      <td>800.0</td>\n",
       "      <td>1.65</td>\n",
       "      <td>0.75</td>\n",
       "      <td>1.55</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>79</td>\n",
       "      <td>48.70%</td>\n",
       "      <td>0.508215</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GOOG210618P00820000</td>\n",
       "      <td>2020-10-20 10:11AM EST</td>\n",
       "      <td>820.0</td>\n",
       "      <td>5.10</td>\n",
       "      <td>1.00</td>\n",
       "      <td>3.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>52.39%</td>\n",
       "      <td>0.649779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>GOOG210618P00840000</td>\n",
       "      <td>2020-11-18 10:28AM EST</td>\n",
       "      <td>840.0</td>\n",
       "      <td>2.40</td>\n",
       "      <td>1.10</td>\n",
       "      <td>1.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>26</td>\n",
       "      <td>47.30%</td>\n",
       "      <td>0.822214</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>GOOG210618P00860000</td>\n",
       "      <td>2020-11-17 11:49AM EST</td>\n",
       "      <td>860.0</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1.30</td>\n",
       "      <td>2.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>5</td>\n",
       "      <td>35</td>\n",
       "      <td>46.77%</td>\n",
       "      <td>1.030318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>GOOG210618P00880000</td>\n",
       "      <td>2020-09-21 11:11AM EST</td>\n",
       "      <td>880.0</td>\n",
       "      <td>12.50</td>\n",
       "      <td>5.80</td>\n",
       "      <td>7.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>24</td>\n",
       "      <td>53.94%</td>\n",
       "      <td>1.279290</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>GOOG210618P00900000</td>\n",
       "      <td>2020-11-06 1:55PM EST</td>\n",
       "      <td>900.0</td>\n",
       "      <td>3.50</td>\n",
       "      <td>1.75</td>\n",
       "      <td>2.65</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>6</td>\n",
       "      <td>38</td>\n",
       "      <td>45.52%</td>\n",
       "      <td>1.574725</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>GOOG210618P00920000</td>\n",
       "      <td>2020-11-19 10:43AM EST</td>\n",
       "      <td>920.0</td>\n",
       "      <td>3.80</td>\n",
       "      <td>2.05</td>\n",
       "      <td>2.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>26</td>\n",
       "      <td>44.83%</td>\n",
       "      <td>1.922596</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>GOOG210618P00940000</td>\n",
       "      <td>2020-10-13 11:21AM EST</td>\n",
       "      <td>940.0</td>\n",
       "      <td>10.70</td>\n",
       "      <td>3.80</td>\n",
       "      <td>5.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>33</td>\n",
       "      <td>48.29%</td>\n",
       "      <td>2.329232</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>GOOG210618P00960000</td>\n",
       "      <td>2020-11-23 10:40AM EST</td>\n",
       "      <td>960.0</td>\n",
       "      <td>4.80</td>\n",
       "      <td>2.70</td>\n",
       "      <td>3.60</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>6</td>\n",
       "      <td>71</td>\n",
       "      <td>43.75%</td>\n",
       "      <td>2.801297</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>GOOG210618P00980000</td>\n",
       "      <td>2020-11-04 9:59AM EST</td>\n",
       "      <td>980.0</td>\n",
       "      <td>5.75</td>\n",
       "      <td>3.00</td>\n",
       "      <td>4.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>130</td>\n",
       "      <td>43.22%</td>\n",
       "      <td>3.345760</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GOOG210618P01000000</td>\n",
       "      <td>2020-12-02 3:20PM EST</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>3.81</td>\n",
       "      <td>3.40</td>\n",
       "      <td>4.40</td>\n",
       "      <td>-1.94</td>\n",
       "      <td>-33.74%</td>\n",
       "      <td>1</td>\n",
       "      <td>586</td>\n",
       "      <td>42.63%</td>\n",
       "      <td>3.969864</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GOOG210618P01020000</td>\n",
       "      <td>2020-10-28 8:49AM EST</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>19.70</td>\n",
       "      <td>4.50</td>\n",
       "      <td>5.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>26</td>\n",
       "      <td>43.55%</td>\n",
       "      <td>4.681093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GOOG210618P01040000</td>\n",
       "      <td>2020-11-05 12:35PM EST</td>\n",
       "      <td>1040.0</td>\n",
       "      <td>10.37</td>\n",
       "      <td>4.40</td>\n",
       "      <td>5.40</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>53</td>\n",
       "      <td>41.61%</td>\n",
       "      <td>5.487132</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>GOOG210618P01060000</td>\n",
       "      <td>2020-10-20 11:13AM EST</td>\n",
       "      <td>1060.0</td>\n",
       "      <td>21.40</td>\n",
       "      <td>6.60</td>\n",
       "      <td>9.30</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>21</td>\n",
       "      <td>40</td>\n",
       "      <td>44.75%</td>\n",
       "      <td>6.395833</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>GOOG210618P01080000</td>\n",
       "      <td>2020-11-04 10:05AM EST</td>\n",
       "      <td>1080.0</td>\n",
       "      <td>12.40</td>\n",
       "      <td>5.50</td>\n",
       "      <td>6.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>385</td>\n",
       "      <td>40.52%</td>\n",
       "      <td>7.415170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>GOOG210618P01100000</td>\n",
       "      <td>2020-11-30 11:38AM EST</td>\n",
       "      <td>1100.0</td>\n",
       "      <td>8.30</td>\n",
       "      <td>6.10</td>\n",
       "      <td>7.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>300</td>\n",
       "      <td>40.06%</td>\n",
       "      <td>8.553204</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>GOOG210618P01600000</td>\n",
       "      <td>2020-12-02 12:04PM EST</td>\n",
       "      <td>1600.0</td>\n",
       "      <td>67.73</td>\n",
       "      <td>67.70</td>\n",
       "      <td>71.30</td>\n",
       "      <td>-4.47</td>\n",
       "      <td>-6.19%</td>\n",
       "      <td>1</td>\n",
       "      <td>239</td>\n",
       "      <td>31.92%</td>\n",
       "      <td>96.626534</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>GOOG210618P01605000</td>\n",
       "      <td>2020-11-24 10:28AM EST</td>\n",
       "      <td>1605.0</td>\n",
       "      <td>96.30</td>\n",
       "      <td>69.10</td>\n",
       "      <td>72.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>31.86%</td>\n",
       "      <td>98.233881</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>GOOG210618P01610000</td>\n",
       "      <td>2020-11-20 10:18AM EST</td>\n",
       "      <td>1610.0</td>\n",
       "      <td>93.60</td>\n",
       "      <td>70.50</td>\n",
       "      <td>74.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>31.83%</td>\n",
       "      <td>99.857210</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>GOOG210618P01615000</td>\n",
       "      <td>2020-11-24 2:36PM EST</td>\n",
       "      <td>1615.0</td>\n",
       "      <td>90.40</td>\n",
       "      <td>72.00</td>\n",
       "      <td>75.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>28</td>\n",
       "      <td>31.78%</td>\n",
       "      <td>101.496528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>GOOG210618P01620000</td>\n",
       "      <td>2020-12-02 3:49PM EST</td>\n",
       "      <td>1620.0</td>\n",
       "      <td>76.20</td>\n",
       "      <td>73.50</td>\n",
       "      <td>77.20</td>\n",
       "      <td>-16.00</td>\n",
       "      <td>-17.35%</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>31.73%</td>\n",
       "      <td>103.151844</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114</th>\n",
       "      <td>GOOG210618P01625000</td>\n",
       "      <td>2020-11-18 11:18AM EST</td>\n",
       "      <td>1625.0</td>\n",
       "      <td>99.00</td>\n",
       "      <td>75.00</td>\n",
       "      <td>78.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>31.68%</td>\n",
       "      <td>104.823164</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>GOOG210618P01630000</td>\n",
       "      <td>2020-11-20 10:18AM EST</td>\n",
       "      <td>1630.0</td>\n",
       "      <td>100.60</td>\n",
       "      <td>76.50</td>\n",
       "      <td>80.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>31.62%</td>\n",
       "      <td>106.510492</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>116</th>\n",
       "      <td>GOOG210618P01635000</td>\n",
       "      <td>2020-11-17 11:18AM EST</td>\n",
       "      <td>1635.0</td>\n",
       "      <td>98.40</td>\n",
       "      <td>78.00</td>\n",
       "      <td>81.80</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>31.58%</td>\n",
       "      <td>108.213832</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>GOOG210618P01640000</td>\n",
       "      <td>2020-12-02 3:49PM EST</td>\n",
       "      <td>1640.0</td>\n",
       "      <td>80.90</td>\n",
       "      <td>79.60</td>\n",
       "      <td>83.40</td>\n",
       "      <td>-23.50</td>\n",
       "      <td>-22.51%</td>\n",
       "      <td>1</td>\n",
       "      <td>33</td>\n",
       "      <td>31.54%</td>\n",
       "      <td>109.933186</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>GOOG210618P01645000</td>\n",
       "      <td>2020-11-16 1:01PM EST</td>\n",
       "      <td>1645.0</td>\n",
       "      <td>103.40</td>\n",
       "      <td>81.10</td>\n",
       "      <td>85.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>31.49%</td>\n",
       "      <td>111.668555</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>119</th>\n",
       "      <td>GOOG210618P01650000</td>\n",
       "      <td>2020-10-21 12:32PM EST</td>\n",
       "      <td>1650.0</td>\n",
       "      <td>205.20</td>\n",
       "      <td>106.70</td>\n",
       "      <td>118.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>38.31%</td>\n",
       "      <td>113.419938</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>120</th>\n",
       "      <td>GOOG210618P01655000</td>\n",
       "      <td>2020-11-23 10:06AM EST</td>\n",
       "      <td>1655.0</td>\n",
       "      <td>115.70</td>\n",
       "      <td>84.40</td>\n",
       "      <td>88.30</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>14</td>\n",
       "      <td>31.40%</td>\n",
       "      <td>115.187334</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>121</th>\n",
       "      <td>GOOG210618P01660000</td>\n",
       "      <td>2020-11-19 9:47AM EST</td>\n",
       "      <td>1660.0</td>\n",
       "      <td>118.40</td>\n",
       "      <td>86.00</td>\n",
       "      <td>90.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>31.36%</td>\n",
       "      <td>116.970740</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>122</th>\n",
       "      <td>GOOG210618P01665000</td>\n",
       "      <td>2020-11-20 3:32PM EST</td>\n",
       "      <td>1665.0</td>\n",
       "      <td>116.90</td>\n",
       "      <td>87.70</td>\n",
       "      <td>91.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>31.31%</td>\n",
       "      <td>118.770151</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>123</th>\n",
       "      <td>GOOG210618P01670000</td>\n",
       "      <td>2020-12-01 12:25PM EST</td>\n",
       "      <td>1670.0</td>\n",
       "      <td>93.59</td>\n",
       "      <td>89.40</td>\n",
       "      <td>93.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>17</td>\n",
       "      <td>31.28%</td>\n",
       "      <td>120.585561</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>GOOG210618P01675000</td>\n",
       "      <td>2020-11-24 2:36PM EST</td>\n",
       "      <td>1675.0</td>\n",
       "      <td>112.90</td>\n",
       "      <td>91.00</td>\n",
       "      <td>95.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>31.22%</td>\n",
       "      <td>122.416964</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125</th>\n",
       "      <td>GOOG210618P01680000</td>\n",
       "      <td>2020-12-02 11:51AM EST</td>\n",
       "      <td>1680.0</td>\n",
       "      <td>94.00</td>\n",
       "      <td>92.70</td>\n",
       "      <td>97.00</td>\n",
       "      <td>-6.99</td>\n",
       "      <td>-6.92%</td>\n",
       "      <td>1</td>\n",
       "      <td>17</td>\n",
       "      <td>31.18%</td>\n",
       "      <td>124.264352</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>126</th>\n",
       "      <td>GOOG210618P01700000</td>\n",
       "      <td>2020-12-02 3:03PM EST</td>\n",
       "      <td>1700.0</td>\n",
       "      <td>100.10</td>\n",
       "      <td>100.30</td>\n",
       "      <td>104.40</td>\n",
       "      <td>-8.00</td>\n",
       "      <td>-7.40%</td>\n",
       "      <td>11</td>\n",
       "      <td>54</td>\n",
       "      <td>31.02%</td>\n",
       "      <td>131.813543</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>GOOG210618P01720000</td>\n",
       "      <td>2020-11-30 10:51AM EST</td>\n",
       "      <td>1720.0</td>\n",
       "      <td>132.70</td>\n",
       "      <td>107.70</td>\n",
       "      <td>112.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>39</td>\n",
       "      <td>30.84%</td>\n",
       "      <td>139.617528</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>128</th>\n",
       "      <td>GOOG210618P01740000</td>\n",
       "      <td>2020-12-02 3:14PM EST</td>\n",
       "      <td>1740.0</td>\n",
       "      <td>115.91</td>\n",
       "      <td>115.60</td>\n",
       "      <td>120.30</td>\n",
       "      <td>-27.29</td>\n",
       "      <td>-19.06%</td>\n",
       "      <td>3</td>\n",
       "      <td>67</td>\n",
       "      <td>30.69%</td>\n",
       "      <td>147.675221</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>GOOG210618P01760000</td>\n",
       "      <td>2020-12-02 2:06PM EST</td>\n",
       "      <td>1760.0</td>\n",
       "      <td>125.21</td>\n",
       "      <td>124.00</td>\n",
       "      <td>128.80</td>\n",
       "      <td>-23.89</td>\n",
       "      <td>-16.02%</td>\n",
       "      <td>2</td>\n",
       "      <td>88</td>\n",
       "      <td>30.52%</td>\n",
       "      <td>155.985258</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>130</th>\n",
       "      <td>GOOG210618P01780000</td>\n",
       "      <td>2020-11-25 10:13AM EST</td>\n",
       "      <td>1780.0</td>\n",
       "      <td>164.30</td>\n",
       "      <td>132.70</td>\n",
       "      <td>137.80</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>47</td>\n",
       "      <td>30.38%</td>\n",
       "      <td>164.546007</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131</th>\n",
       "      <td>GOOG210618P01800000</td>\n",
       "      <td>2020-12-02 3:58PM EST</td>\n",
       "      <td>1800.0</td>\n",
       "      <td>144.70</td>\n",
       "      <td>142.00</td>\n",
       "      <td>147.20</td>\n",
       "      <td>-3.80</td>\n",
       "      <td>-2.56%</td>\n",
       "      <td>5</td>\n",
       "      <td>25</td>\n",
       "      <td>30.24%</td>\n",
       "      <td>173.355582</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>132</th>\n",
       "      <td>GOOG210618P01820000</td>\n",
       "      <td>2020-12-01 3:19PM EST</td>\n",
       "      <td>1820.0</td>\n",
       "      <td>166.50</td>\n",
       "      <td>151.60</td>\n",
       "      <td>156.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>22</td>\n",
       "      <td>30.08%</td>\n",
       "      <td>182.411860</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>133</th>\n",
       "      <td>GOOG210618P01840000</td>\n",
       "      <td>2020-11-05 10:32AM EST</td>\n",
       "      <td>1840.0</td>\n",
       "      <td>210.60</td>\n",
       "      <td>161.40</td>\n",
       "      <td>167.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>29.93%</td>\n",
       "      <td>191.712495</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>134</th>\n",
       "      <td>GOOG210618P01860000</td>\n",
       "      <td>2020-11-16 12:56PM EST</td>\n",
       "      <td>1860.0</td>\n",
       "      <td>205.00</td>\n",
       "      <td>171.90</td>\n",
       "      <td>177.60</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>29.80%</td>\n",
       "      <td>201.254934</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>GOOG210618P01900000</td>\n",
       "      <td>2020-10-12 8:47AM EST</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>407.40</td>\n",
       "      <td>215.50</td>\n",
       "      <td>221.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>33.48%</td>\n",
       "      <td>221.054049</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>GOOG210618P02000000</td>\n",
       "      <td>2020-10-30 2:57PM EST</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>436.00</td>\n",
       "      <td>275.90</td>\n",
       "      <td>282.60</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>32.82%</td>\n",
       "      <td>274.570866</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>137</th>\n",
       "      <td>GOOG210618P02100000</td>\n",
       "      <td>2020-06-24 2:02PM EST</td>\n",
       "      <td>2100.0</td>\n",
       "      <td>673.60</td>\n",
       "      <td>602.00</td>\n",
       "      <td>611.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>80.63%</td>\n",
       "      <td>333.472840</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>138</th>\n",
       "      <td>GOOG210618P02200000</td>\n",
       "      <td>2020-11-06 2:29PM EST</td>\n",
       "      <td>2200.0</td>\n",
       "      <td>469.60</td>\n",
       "      <td>405.70</td>\n",
       "      <td>413.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>28.06%</td>\n",
       "      <td>397.271434</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>139 rows × 12 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Contract Name         Last Trade Date  Strike  Last Price     Bid  \\\n",
       "0    GOOG210618P00520000  2020-12-02 11:32AM EST   520.0        0.15    0.05   \n",
       "1    GOOG210618P00540000  2020-12-01 12:29PM EST   540.0        0.20    0.00   \n",
       "2    GOOG210618P00560000  2020-10-29 11:18AM EST   560.0        1.25    0.00   \n",
       "3    GOOG210618P00580000   2020-07-01 8:54AM EST   580.0        5.50    3.00   \n",
       "4    GOOG210618P00600000   2020-11-25 1:39PM EST   600.0        0.24    0.05   \n",
       "..                   ...                     ...     ...         ...     ...   \n",
       "134  GOOG210618P01860000  2020-11-16 12:56PM EST  1860.0      205.00  171.90   \n",
       "135  GOOG210618P01900000   2020-10-12 8:47AM EST  1900.0      407.40  215.50   \n",
       "136  GOOG210618P02000000   2020-10-30 2:57PM EST  2000.0      436.00  275.90   \n",
       "137  GOOG210618P02100000   2020-06-24 2:02PM EST  2100.0      673.60  602.00   \n",
       "138  GOOG210618P02200000   2020-11-06 2:29PM EST  2200.0      469.60  405.70   \n",
       "\n",
       "        Ask  Change % Change Volume  Open Interest Implied Volatility  \\\n",
       "0      0.20   -0.15  -50.00%    111            899             55.96%   \n",
       "1      0.35    0.00        -      1            164             55.86%   \n",
       "2      0.85    0.00        -      1            217             59.01%   \n",
       "3      4.50    0.00        -      1             31             74.88%   \n",
       "4      0.65    0.00        -      1            228             54.64%   \n",
       "..      ...     ...      ...    ...            ...                ...   \n",
       "134  177.60    0.00        -      4              4             29.80%   \n",
       "135  221.10    0.00        -      1              2             33.48%   \n",
       "136  282.60    0.00        -      1              1             32.82%   \n",
       "137  611.10    0.00        -      2              2             80.63%   \n",
       "138  413.70    0.00        -      1              2             28.06%   \n",
       "\n",
       "       estimate  \n",
       "0      0.003265  \n",
       "1      0.005388  \n",
       "2      0.008636  \n",
       "3      0.013480  \n",
       "4      0.020534  \n",
       "..          ...  \n",
       "134  201.254934  \n",
       "135  221.054049  \n",
       "136  274.570866  \n",
       "137  333.472840  \n",
       "138  397.271434  \n",
       "\n",
       "[139 rows x 12 columns]"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "df_estimate"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f8428cb1390>"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# plot option prices across strikes\n",
    "\n",
    "df_estimate.plot(x='Strike',y=['Last Price','estimate'], title='Computed v Market prices for {}, Expiry {}'.format(ticker, expiration_datetime.date()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count      139.000000\n",
      "mean       730.263463\n",
      "std       3862.921848\n",
      "min        -38.260741\n",
      "25%        -21.539273\n",
      "50%         -7.774220\n",
      "75%         71.604271\n",
      "max      40700.062332\n",
      "Name: estimate_error, dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f840a299208>"
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_estimate['estimate_error'] = ((df_estimate['Last Price'] - df_estimate['estimate'])/df_estimate['estimate'])*100\n",
    "ax = sns.distplot(df_estimate['estimate_error'])\n",
    "print(df_estimate['estimate_error'].describe())\n",
    "\n",
    "# across strikes, the median error is 34%, but there is a huge spread and outliers, \n",
    "# which mainly seem to be due to the higher strikes being very close to 0.\n",
    "\n",
    "# plot the error across strikes\n",
    "\n",
    "df_estimate.plot(x='Strike',y='estimate_error',title='estimate error across strikes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "1555.921413793013 39.44516971433908\n"
     ]
    }
   ],
   "source": [
    "# what is a measure of error?\n",
    "# MSE: average of the sum of squared errors\n",
    "\n",
    "mse = np.sum((df_estimate['Last Price'] - df_estimate['estimate'])**2) / df_estimate.shape[0]\n",
    "rmse = np.sqrt(mse)\n",
    "\n",
    "print(mse, rmse)\n",
    "# could also try MAD"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Contract Name</th>\n",
       "      <th>Last Trade Date</th>\n",
       "      <th>Strike</th>\n",
       "      <th>Last Price</th>\n",
       "      <th>Bid</th>\n",
       "      <th>Ask</th>\n",
       "      <th>Change</th>\n",
       "      <th>% Change</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Open Interest</th>\n",
       "      <th>Implied Volatility</th>\n",
       "      <th>estimate</th>\n",
       "      <th>estimate_error</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>GOOG210618P00520000</td>\n",
       "      <td>2020-12-02 11:32AM EST</td>\n",
       "      <td>520.0</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.20</td>\n",
       "      <td>-0.15</td>\n",
       "      <td>-50.00%</td>\n",
       "      <td>111</td>\n",
       "      <td>899</td>\n",
       "      <td>55.96%</td>\n",
       "      <td>0.003265</td>\n",
       "      <td>4494.040577</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>GOOG210618P00540000</td>\n",
       "      <td>2020-12-01 12:29PM EST</td>\n",
       "      <td>540.0</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.35</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>164</td>\n",
       "      <td>55.86%</td>\n",
       "      <td>0.005388</td>\n",
       "      <td>3612.055727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>GOOG210618P00560000</td>\n",
       "      <td>2020-10-29 11:18AM EST</td>\n",
       "      <td>560.0</td>\n",
       "      <td>1.25</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.85</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>217</td>\n",
       "      <td>59.01%</td>\n",
       "      <td>0.008636</td>\n",
       "      <td>14373.731205</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>GOOG210618P00580000</td>\n",
       "      <td>2020-07-01 8:54AM EST</td>\n",
       "      <td>580.0</td>\n",
       "      <td>5.50</td>\n",
       "      <td>3.00</td>\n",
       "      <td>4.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>31</td>\n",
       "      <td>74.88%</td>\n",
       "      <td>0.013480</td>\n",
       "      <td>40700.062332</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>GOOG210618P00600000</td>\n",
       "      <td>2020-11-25 1:39PM EST</td>\n",
       "      <td>600.0</td>\n",
       "      <td>0.24</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.65</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>228</td>\n",
       "      <td>54.64%</td>\n",
       "      <td>0.020534</td>\n",
       "      <td>1068.786308</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>GOOG210618P00620000</td>\n",
       "      <td>2020-08-19 1:00PM EST</td>\n",
       "      <td>620.0</td>\n",
       "      <td>3.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>5.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>32</td>\n",
       "      <td>66.75%</td>\n",
       "      <td>0.030584</td>\n",
       "      <td>9709.082805</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>GOOG210618P00640000</td>\n",
       "      <td>2020-08-18 2:48PM EST</td>\n",
       "      <td>640.0</td>\n",
       "      <td>3.24</td>\n",
       "      <td>1.50</td>\n",
       "      <td>2.65</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>22</td>\n",
       "      <td>63.27%</td>\n",
       "      <td>0.044617</td>\n",
       "      <td>7161.751414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>GOOG210618P00660000</td>\n",
       "      <td>2020-08-10 12:02PM EST</td>\n",
       "      <td>660.0</td>\n",
       "      <td>5.65</td>\n",
       "      <td>3.80</td>\n",
       "      <td>5.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>15</td>\n",
       "      <td>28</td>\n",
       "      <td>68.85%</td>\n",
       "      <td>0.063853</td>\n",
       "      <td>8748.417437</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>GOOG210618P00680000</td>\n",
       "      <td>2020-11-06 11:21AM EST</td>\n",
       "      <td>680.0</td>\n",
       "      <td>1.30</td>\n",
       "      <td>0.05</td>\n",
       "      <td>0.85</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>153</td>\n",
       "      <td>50.00%</td>\n",
       "      <td>0.089771</td>\n",
       "      <td>1348.124059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>GOOG210618P00700000</td>\n",
       "      <td>2020-12-02 3:15PM EST</td>\n",
       "      <td>700.0</td>\n",
       "      <td>0.53</td>\n",
       "      <td>0.15</td>\n",
       "      <td>0.95</td>\n",
       "      <td>-0.17</td>\n",
       "      <td>-24.29%</td>\n",
       "      <td>1</td>\n",
       "      <td>71</td>\n",
       "      <td>52.76%</td>\n",
       "      <td>0.124141</td>\n",
       "      <td>326.933101</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>GOOG210618P00720000</td>\n",
       "      <td>2020-10-15 12:42PM EST</td>\n",
       "      <td>720.0</td>\n",
       "      <td>3.29</td>\n",
       "      <td>0.50</td>\n",
       "      <td>1.95</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>107</td>\n",
       "      <td>52.88%</td>\n",
       "      <td>0.169050</td>\n",
       "      <td>1846.172059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>GOOG210618P00740000</td>\n",
       "      <td>2020-10-12 8:36AM EST</td>\n",
       "      <td>740.0</td>\n",
       "      <td>3.35</td>\n",
       "      <td>0.70</td>\n",
       "      <td>2.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>91</td>\n",
       "      <td>52.41%</td>\n",
       "      <td>0.226926</td>\n",
       "      <td>1376.252176</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>GOOG210618P00760000</td>\n",
       "      <td>2020-10-28 2:01PM EST</td>\n",
       "      <td>760.0</td>\n",
       "      <td>5.30</td>\n",
       "      <td>0.45</td>\n",
       "      <td>1.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>74</td>\n",
       "      <td>52.12%</td>\n",
       "      <td>0.300563</td>\n",
       "      <td>1663.358584</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>GOOG210618P00780000</td>\n",
       "      <td>2020-10-08 11:04AM EST</td>\n",
       "      <td>780.0</td>\n",
       "      <td>5.60</td>\n",
       "      <td>1.85</td>\n",
       "      <td>2.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>38</td>\n",
       "      <td>52.72%</td>\n",
       "      <td>0.393135</td>\n",
       "      <td>1324.445620</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>GOOG210618P00800000</td>\n",
       "      <td>2020-11-24 3:54PM EST</td>\n",
       "      <td>800.0</td>\n",
       "      <td>1.65</td>\n",
       "      <td>0.75</td>\n",
       "      <td>1.55</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>79</td>\n",
       "      <td>48.70%</td>\n",
       "      <td>0.508215</td>\n",
       "      <td>224.665625</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>GOOG210618P00820000</td>\n",
       "      <td>2020-10-20 10:11AM EST</td>\n",
       "      <td>820.0</td>\n",
       "      <td>5.10</td>\n",
       "      <td>1.00</td>\n",
       "      <td>3.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>5</td>\n",
       "      <td>52.39%</td>\n",
       "      <td>0.649779</td>\n",
       "      <td>684.882061</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>GOOG210618P00840000</td>\n",
       "      <td>2020-11-18 10:28AM EST</td>\n",
       "      <td>840.0</td>\n",
       "      <td>2.40</td>\n",
       "      <td>1.10</td>\n",
       "      <td>1.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>26</td>\n",
       "      <td>47.30%</td>\n",
       "      <td>0.822214</td>\n",
       "      <td>191.894651</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>GOOG210618P00860000</td>\n",
       "      <td>2020-11-17 11:49AM EST</td>\n",
       "      <td>860.0</td>\n",
       "      <td>3.00</td>\n",
       "      <td>1.30</td>\n",
       "      <td>2.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>5</td>\n",
       "      <td>35</td>\n",
       "      <td>46.77%</td>\n",
       "      <td>1.030318</td>\n",
       "      <td>191.172284</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>GOOG210618P00880000</td>\n",
       "      <td>2020-09-21 11:11AM EST</td>\n",
       "      <td>880.0</td>\n",
       "      <td>12.50</td>\n",
       "      <td>5.80</td>\n",
       "      <td>7.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>24</td>\n",
       "      <td>53.94%</td>\n",
       "      <td>1.279290</td>\n",
       "      <td>877.104393</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>GOOG210618P00900000</td>\n",
       "      <td>2020-11-06 1:55PM EST</td>\n",
       "      <td>900.0</td>\n",
       "      <td>3.50</td>\n",
       "      <td>1.75</td>\n",
       "      <td>2.65</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>6</td>\n",
       "      <td>38</td>\n",
       "      <td>45.52%</td>\n",
       "      <td>1.574725</td>\n",
       "      <td>122.260961</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>GOOG210618P00920000</td>\n",
       "      <td>2020-11-19 10:43AM EST</td>\n",
       "      <td>920.0</td>\n",
       "      <td>3.80</td>\n",
       "      <td>2.05</td>\n",
       "      <td>2.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>26</td>\n",
       "      <td>44.83%</td>\n",
       "      <td>1.922596</td>\n",
       "      <td>97.649421</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>GOOG210618P00940000</td>\n",
       "      <td>2020-10-13 11:21AM EST</td>\n",
       "      <td>940.0</td>\n",
       "      <td>10.70</td>\n",
       "      <td>3.80</td>\n",
       "      <td>5.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>33</td>\n",
       "      <td>48.29%</td>\n",
       "      <td>2.329232</td>\n",
       "      <td>359.378901</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>GOOG210618P00960000</td>\n",
       "      <td>2020-11-23 10:40AM EST</td>\n",
       "      <td>960.0</td>\n",
       "      <td>4.80</td>\n",
       "      <td>2.70</td>\n",
       "      <td>3.60</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>6</td>\n",
       "      <td>71</td>\n",
       "      <td>43.75%</td>\n",
       "      <td>2.801297</td>\n",
       "      <td>71.349217</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>GOOG210618P00980000</td>\n",
       "      <td>2020-11-04 9:59AM EST</td>\n",
       "      <td>980.0</td>\n",
       "      <td>5.75</td>\n",
       "      <td>3.00</td>\n",
       "      <td>4.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>130</td>\n",
       "      <td>43.22%</td>\n",
       "      <td>3.345760</td>\n",
       "      <td>71.859325</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>GOOG210618P01000000</td>\n",
       "      <td>2020-12-02 3:20PM EST</td>\n",
       "      <td>1000.0</td>\n",
       "      <td>3.81</td>\n",
       "      <td>3.40</td>\n",
       "      <td>4.40</td>\n",
       "      <td>-1.94</td>\n",
       "      <td>-33.74%</td>\n",
       "      <td>1</td>\n",
       "      <td>586</td>\n",
       "      <td>42.63%</td>\n",
       "      <td>3.969864</td>\n",
       "      <td>-4.026941</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>GOOG210618P01020000</td>\n",
       "      <td>2020-10-28 8:49AM EST</td>\n",
       "      <td>1020.0</td>\n",
       "      <td>19.70</td>\n",
       "      <td>4.50</td>\n",
       "      <td>5.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>26</td>\n",
       "      <td>43.55%</td>\n",
       "      <td>4.681093</td>\n",
       "      <td>320.841889</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>GOOG210618P01040000</td>\n",
       "      <td>2020-11-05 12:35PM EST</td>\n",
       "      <td>1040.0</td>\n",
       "      <td>10.37</td>\n",
       "      <td>4.40</td>\n",
       "      <td>5.40</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>53</td>\n",
       "      <td>41.61%</td>\n",
       "      <td>5.487132</td>\n",
       "      <td>88.987604</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>GOOG210618P01060000</td>\n",
       "      <td>2020-10-20 11:13AM EST</td>\n",
       "      <td>1060.0</td>\n",
       "      <td>21.40</td>\n",
       "      <td>6.60</td>\n",
       "      <td>9.30</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>21</td>\n",
       "      <td>40</td>\n",
       "      <td>44.75%</td>\n",
       "      <td>6.395833</td>\n",
       "      <td>234.592852</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>GOOG210618P01080000</td>\n",
       "      <td>2020-11-04 10:05AM EST</td>\n",
       "      <td>1080.0</td>\n",
       "      <td>12.40</td>\n",
       "      <td>5.50</td>\n",
       "      <td>6.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>385</td>\n",
       "      <td>40.52%</td>\n",
       "      <td>7.415170</td>\n",
       "      <td>67.224751</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>GOOG210618P01100000</td>\n",
       "      <td>2020-11-30 11:38AM EST</td>\n",
       "      <td>1100.0</td>\n",
       "      <td>8.30</td>\n",
       "      <td>6.10</td>\n",
       "      <td>7.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>300</td>\n",
       "      <td>40.06%</td>\n",
       "      <td>8.553204</td>\n",
       "      <td>-2.960340</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>...</th>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "      <td>...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>107</th>\n",
       "      <td>GOOG210618P01590000</td>\n",
       "      <td>2020-11-24 2:36PM EST</td>\n",
       "      <td>1590.0</td>\n",
       "      <td>82.00</td>\n",
       "      <td>65.10</td>\n",
       "      <td>68.40</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>4</td>\n",
       "      <td>32.00%</td>\n",
       "      <td>93.459739</td>\n",
       "      <td>-12.261685</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>108</th>\n",
       "      <td>GOOG210618P01595000</td>\n",
       "      <td>2020-12-01 10:00AM EST</td>\n",
       "      <td>1595.0</td>\n",
       "      <td>78.00</td>\n",
       "      <td>66.30</td>\n",
       "      <td>69.80</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>31.95%</td>\n",
       "      <td>95.035157</td>\n",
       "      <td>-17.925110</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>109</th>\n",
       "      <td>GOOG210618P01600000</td>\n",
       "      <td>2020-12-02 12:04PM EST</td>\n",
       "      <td>1600.0</td>\n",
       "      <td>67.73</td>\n",
       "      <td>67.70</td>\n",
       "      <td>71.30</td>\n",
       "      <td>-4.47</td>\n",
       "      <td>-6.19%</td>\n",
       "      <td>1</td>\n",
       "      <td>239</td>\n",
       "      <td>31.92%</td>\n",
       "      <td>96.626534</td>\n",
       "      <td>-29.905382</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>110</th>\n",
       "      <td>GOOG210618P01605000</td>\n",
       "      <td>2020-11-24 10:28AM EST</td>\n",
       "      <td>1605.0</td>\n",
       "      <td>96.30</td>\n",
       "      <td>69.10</td>\n",
       "      <td>72.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>6</td>\n",
       "      <td>31.86%</td>\n",
       "      <td>98.233881</td>\n",
       "      <td>-1.968650</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>111</th>\n",
       "      <td>GOOG210618P01610000</td>\n",
       "      <td>2020-11-20 10:18AM EST</td>\n",
       "      <td>1610.0</td>\n",
       "      <td>93.60</td>\n",
       "      <td>70.50</td>\n",
       "      <td>74.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>31.83%</td>\n",
       "      <td>99.857210</td>\n",
       "      <td>-6.266157</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>112</th>\n",
       "      <td>GOOG210618P01615000</td>\n",
       "      <td>2020-11-24 2:36PM EST</td>\n",
       "      <td>1615.0</td>\n",
       "      <td>90.40</td>\n",
       "      <td>72.00</td>\n",
       "      <td>75.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>28</td>\n",
       "      <td>31.78%</td>\n",
       "      <td>101.496528</td>\n",
       "      <td>-10.932914</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>113</th>\n",
       "      <td>GOOG210618P01620000</td>\n",
       "      <td>2020-12-02 3:49PM EST</td>\n",
       "      <td>1620.0</td>\n",
       "      <td>76.20</td>\n",
       "      <td>73.50</td>\n",
       "      <td>77.20</td>\n",
       "      <td>-16.00</td>\n",
       "      <td>-17.35%</td>\n",
       "      <td>3</td>\n",
       "      <td>2</td>\n",
       "      <td>31.73%</td>\n",
       "      <td>103.151844</td>\n",
       "      <td>-26.128320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>114</th>\n",
       "      <td>GOOG210618P01625000</td>\n",
       "      <td>2020-11-18 11:18AM EST</td>\n",
       "      <td>1625.0</td>\n",
       "      <td>99.00</td>\n",
       "      <td>75.00</td>\n",
       "      <td>78.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>31.68%</td>\n",
       "      <td>104.823164</td>\n",
       "      <td>-5.555226</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>115</th>\n",
       "      <td>GOOG210618P01630000</td>\n",
       "      <td>2020-11-20 10:18AM EST</td>\n",
       "      <td>1630.0</td>\n",
       "      <td>100.60</td>\n",
       "      <td>76.50</td>\n",
       "      <td>80.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>31.62%</td>\n",
       "      <td>106.510492</td>\n",
       "      <td>-5.549211</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>116</th>\n",
       "      <td>GOOG210618P01635000</td>\n",
       "      <td>2020-11-17 11:18AM EST</td>\n",
       "      <td>1635.0</td>\n",
       "      <td>98.40</td>\n",
       "      <td>78.00</td>\n",
       "      <td>81.80</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>31.58%</td>\n",
       "      <td>108.213832</td>\n",
       "      <td>-9.068925</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>117</th>\n",
       "      <td>GOOG210618P01640000</td>\n",
       "      <td>2020-12-02 3:49PM EST</td>\n",
       "      <td>1640.0</td>\n",
       "      <td>80.90</td>\n",
       "      <td>79.60</td>\n",
       "      <td>83.40</td>\n",
       "      <td>-23.50</td>\n",
       "      <td>-22.51%</td>\n",
       "      <td>1</td>\n",
       "      <td>33</td>\n",
       "      <td>31.54%</td>\n",
       "      <td>109.933186</td>\n",
       "      <td>-26.409847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>118</th>\n",
       "      <td>GOOG210618P01645000</td>\n",
       "      <td>2020-11-16 1:01PM EST</td>\n",
       "      <td>1645.0</td>\n",
       "      <td>103.40</td>\n",
       "      <td>81.10</td>\n",
       "      <td>85.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>3</td>\n",
       "      <td>31.49%</td>\n",
       "      <td>111.668555</td>\n",
       "      <td>-7.404551</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>119</th>\n",
       "      <td>GOOG210618P01650000</td>\n",
       "      <td>2020-10-21 12:32PM EST</td>\n",
       "      <td>1650.0</td>\n",
       "      <td>205.20</td>\n",
       "      <td>106.70</td>\n",
       "      <td>118.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>38.31%</td>\n",
       "      <td>113.419938</td>\n",
       "      <td>80.920571</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>121</th>\n",
       "      <td>GOOG210618P01660000</td>\n",
       "      <td>2020-11-19 9:47AM EST</td>\n",
       "      <td>1660.0</td>\n",
       "      <td>118.40</td>\n",
       "      <td>86.00</td>\n",
       "      <td>90.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>7</td>\n",
       "      <td>31.36%</td>\n",
       "      <td>116.970740</td>\n",
       "      <td>1.221895</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>122</th>\n",
       "      <td>GOOG210618P01665000</td>\n",
       "      <td>2020-11-20 3:32PM EST</td>\n",
       "      <td>1665.0</td>\n",
       "      <td>116.90</td>\n",
       "      <td>87.70</td>\n",
       "      <td>91.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>8</td>\n",
       "      <td>31.31%</td>\n",
       "      <td>118.770151</td>\n",
       "      <td>-1.574597</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>123</th>\n",
       "      <td>GOOG210618P01670000</td>\n",
       "      <td>2020-12-01 12:25PM EST</td>\n",
       "      <td>1670.0</td>\n",
       "      <td>93.59</td>\n",
       "      <td>89.40</td>\n",
       "      <td>93.50</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>17</td>\n",
       "      <td>31.28%</td>\n",
       "      <td>120.585561</td>\n",
       "      <td>-22.387059</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>124</th>\n",
       "      <td>GOOG210618P01675000</td>\n",
       "      <td>2020-11-24 2:36PM EST</td>\n",
       "      <td>1675.0</td>\n",
       "      <td>112.90</td>\n",
       "      <td>91.00</td>\n",
       "      <td>95.20</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>7</td>\n",
       "      <td>31.22%</td>\n",
       "      <td>122.416964</td>\n",
       "      <td>-7.774220</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>125</th>\n",
       "      <td>GOOG210618P01680000</td>\n",
       "      <td>2020-12-02 11:51AM EST</td>\n",
       "      <td>1680.0</td>\n",
       "      <td>94.00</td>\n",
       "      <td>92.70</td>\n",
       "      <td>97.00</td>\n",
       "      <td>-6.99</td>\n",
       "      <td>-6.92%</td>\n",
       "      <td>1</td>\n",
       "      <td>17</td>\n",
       "      <td>31.18%</td>\n",
       "      <td>124.264352</td>\n",
       "      <td>-24.354814</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>126</th>\n",
       "      <td>GOOG210618P01700000</td>\n",
       "      <td>2020-12-02 3:03PM EST</td>\n",
       "      <td>1700.0</td>\n",
       "      <td>100.10</td>\n",
       "      <td>100.30</td>\n",
       "      <td>104.40</td>\n",
       "      <td>-8.00</td>\n",
       "      <td>-7.40%</td>\n",
       "      <td>11</td>\n",
       "      <td>54</td>\n",
       "      <td>31.02%</td>\n",
       "      <td>131.813543</td>\n",
       "      <td>-24.059397</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>127</th>\n",
       "      <td>GOOG210618P01720000</td>\n",
       "      <td>2020-11-30 10:51AM EST</td>\n",
       "      <td>1720.0</td>\n",
       "      <td>132.70</td>\n",
       "      <td>107.70</td>\n",
       "      <td>112.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>39</td>\n",
       "      <td>30.84%</td>\n",
       "      <td>139.617528</td>\n",
       "      <td>-4.954627</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>128</th>\n",
       "      <td>GOOG210618P01740000</td>\n",
       "      <td>2020-12-02 3:14PM EST</td>\n",
       "      <td>1740.0</td>\n",
       "      <td>115.91</td>\n",
       "      <td>115.60</td>\n",
       "      <td>120.30</td>\n",
       "      <td>-27.29</td>\n",
       "      <td>-19.06%</td>\n",
       "      <td>3</td>\n",
       "      <td>67</td>\n",
       "      <td>30.69%</td>\n",
       "      <td>147.675221</td>\n",
       "      <td>-21.510190</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>129</th>\n",
       "      <td>GOOG210618P01760000</td>\n",
       "      <td>2020-12-02 2:06PM EST</td>\n",
       "      <td>1760.0</td>\n",
       "      <td>125.21</td>\n",
       "      <td>124.00</td>\n",
       "      <td>128.80</td>\n",
       "      <td>-23.89</td>\n",
       "      <td>-16.02%</td>\n",
       "      <td>2</td>\n",
       "      <td>88</td>\n",
       "      <td>30.52%</td>\n",
       "      <td>155.985258</td>\n",
       "      <td>-19.729594</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>131</th>\n",
       "      <td>GOOG210618P01800000</td>\n",
       "      <td>2020-12-02 3:58PM EST</td>\n",
       "      <td>1800.0</td>\n",
       "      <td>144.70</td>\n",
       "      <td>142.00</td>\n",
       "      <td>147.20</td>\n",
       "      <td>-3.80</td>\n",
       "      <td>-2.56%</td>\n",
       "      <td>5</td>\n",
       "      <td>25</td>\n",
       "      <td>30.24%</td>\n",
       "      <td>173.355582</td>\n",
       "      <td>-16.529945</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>132</th>\n",
       "      <td>GOOG210618P01820000</td>\n",
       "      <td>2020-12-01 3:19PM EST</td>\n",
       "      <td>1820.0</td>\n",
       "      <td>166.50</td>\n",
       "      <td>151.60</td>\n",
       "      <td>156.90</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>22</td>\n",
       "      <td>30.08%</td>\n",
       "      <td>182.411860</td>\n",
       "      <td>-8.723040</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>133</th>\n",
       "      <td>GOOG210618P01840000</td>\n",
       "      <td>2020-11-05 10:32AM EST</td>\n",
       "      <td>1840.0</td>\n",
       "      <td>210.60</td>\n",
       "      <td>161.40</td>\n",
       "      <td>167.00</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>3</td>\n",
       "      <td>4</td>\n",
       "      <td>29.93%</td>\n",
       "      <td>191.712495</td>\n",
       "      <td>9.851995</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>134</th>\n",
       "      <td>GOOG210618P01860000</td>\n",
       "      <td>2020-11-16 12:56PM EST</td>\n",
       "      <td>1860.0</td>\n",
       "      <td>205.00</td>\n",
       "      <td>171.90</td>\n",
       "      <td>177.60</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>4</td>\n",
       "      <td>4</td>\n",
       "      <td>29.80%</td>\n",
       "      <td>201.254934</td>\n",
       "      <td>1.860857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>135</th>\n",
       "      <td>GOOG210618P01900000</td>\n",
       "      <td>2020-10-12 8:47AM EST</td>\n",
       "      <td>1900.0</td>\n",
       "      <td>407.40</td>\n",
       "      <td>215.50</td>\n",
       "      <td>221.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>33.48%</td>\n",
       "      <td>221.054049</td>\n",
       "      <td>84.298818</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>136</th>\n",
       "      <td>GOOG210618P02000000</td>\n",
       "      <td>2020-10-30 2:57PM EST</td>\n",
       "      <td>2000.0</td>\n",
       "      <td>436.00</td>\n",
       "      <td>275.90</td>\n",
       "      <td>282.60</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>1</td>\n",
       "      <td>32.82%</td>\n",
       "      <td>274.570866</td>\n",
       "      <td>58.793249</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>137</th>\n",
       "      <td>GOOG210618P02100000</td>\n",
       "      <td>2020-06-24 2:02PM EST</td>\n",
       "      <td>2100.0</td>\n",
       "      <td>673.60</td>\n",
       "      <td>602.00</td>\n",
       "      <td>611.10</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>2</td>\n",
       "      <td>2</td>\n",
       "      <td>80.63%</td>\n",
       "      <td>333.472840</td>\n",
       "      <td>101.995461</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>138</th>\n",
       "      <td>GOOG210618P02200000</td>\n",
       "      <td>2020-11-06 2:29PM EST</td>\n",
       "      <td>2200.0</td>\n",
       "      <td>469.60</td>\n",
       "      <td>405.70</td>\n",
       "      <td>413.70</td>\n",
       "      <td>0.00</td>\n",
       "      <td>-</td>\n",
       "      <td>1</td>\n",
       "      <td>2</td>\n",
       "      <td>28.06%</td>\n",
       "      <td>397.271434</td>\n",
       "      <td>18.206334</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>136 rows × 13 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "           Contract Name         Last Trade Date  Strike  Last Price     Bid  \\\n",
       "0    GOOG210618P00520000  2020-12-02 11:32AM EST   520.0        0.15    0.05   \n",
       "1    GOOG210618P00540000  2020-12-01 12:29PM EST   540.0        0.20    0.00   \n",
       "2    GOOG210618P00560000  2020-10-29 11:18AM EST   560.0        1.25    0.00   \n",
       "3    GOOG210618P00580000   2020-07-01 8:54AM EST   580.0        5.50    3.00   \n",
       "4    GOOG210618P00600000   2020-11-25 1:39PM EST   600.0        0.24    0.05   \n",
       "..                   ...                     ...     ...         ...     ...   \n",
       "134  GOOG210618P01860000  2020-11-16 12:56PM EST  1860.0      205.00  171.90   \n",
       "135  GOOG210618P01900000   2020-10-12 8:47AM EST  1900.0      407.40  215.50   \n",
       "136  GOOG210618P02000000   2020-10-30 2:57PM EST  2000.0      436.00  275.90   \n",
       "137  GOOG210618P02100000   2020-06-24 2:02PM EST  2100.0      673.60  602.00   \n",
       "138  GOOG210618P02200000   2020-11-06 2:29PM EST  2200.0      469.60  405.70   \n",
       "\n",
       "        Ask  Change % Change Volume  Open Interest Implied Volatility  \\\n",
       "0      0.20   -0.15  -50.00%    111            899             55.96%   \n",
       "1      0.35    0.00        -      1            164             55.86%   \n",
       "2      0.85    0.00        -      1            217             59.01%   \n",
       "3      4.50    0.00        -      1             31             74.88%   \n",
       "4      0.65    0.00        -      1            228             54.64%   \n",
       "..      ...     ...      ...    ...            ...                ...   \n",
       "134  177.60    0.00        -      4              4             29.80%   \n",
       "135  221.10    0.00        -      1              2             33.48%   \n",
       "136  282.60    0.00        -      1              1             32.82%   \n",
       "137  611.10    0.00        -      2              2             80.63%   \n",
       "138  413.70    0.00        -      1              2             28.06%   \n",
       "\n",
       "       estimate  estimate_error  \n",
       "0      0.003265     4494.040577  \n",
       "1      0.005388     3612.055727  \n",
       "2      0.008636    14373.731205  \n",
       "3      0.013480    40700.062332  \n",
       "4      0.020534     1068.786308  \n",
       "..          ...             ...  \n",
       "134  201.254934        1.860857  \n",
       "135  221.054049       84.298818  \n",
       "136  274.570866       58.793249  \n",
       "137  333.472840      101.995461  \n",
       "138  397.271434       18.206334  \n",
       "\n",
       "[136 rows x 13 columns]"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# examine outliers\n",
    "\n",
    "df_estimate[df_estimate['estimate_error'].abs() > 1]\n",
    "\n",
    "# the model tends to undervalue puts especially at high strikes (deep out of the money)."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# how accurate are our vol estimates?\n",
    "\n",
    "df_estimate['Implied Volatility'] = df_estimate['Implied Volatility'].str.replace(',','').str.slice(stop=-1).astype('float') / 100\n",
    "\n",
    "df_estimate['Historical Vol'] = sigma\n",
    "ax = df_estimate.plot(x='Strike',y=['Implied Volatility','Historical Vol'],title='volatility across strikes')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f840a1c1208>"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "df_estimate['Volume'] = df_estimate['Volume'].replace(to_replace='-',value=0)\n",
    "df_estimate['Volume'] = df_estimate['Volume'].astype('int')\n",
    "\n",
    "df_estimate['Open Interest'] = df_estimate['Open Interest'].replace(to_replace='-',value=0)\n",
    "df_estimate['Open Interest'] = df_estimate['Open Interest'].astype('int')\n",
    "\n",
    "df_estimate.plot(x='Strike',y=['Volume','Open Interest'],title='volume and open interest')"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count    139.000000\n",
      "mean      64.633094\n",
      "std      137.448760\n",
      "min        1.000000\n",
      "25%        6.000000\n",
      "50%       23.000000\n",
      "75%       54.500000\n",
      "max      899.000000\n",
      "Name: Open Interest, dtype: float64\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "sns.distplot(df_estimate['Open Interest'])\n",
    "print(df_estimate['Open Interest'].describe())"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "count       83.000000\n",
      "mean      1208.392351\n",
      "std       4952.807073\n",
      "min        -38.260741\n",
      "25%        -23.859948\n",
      "50%         -4.954627\n",
      "75%        191.533467\n",
      "max      40700.062332\n",
      "Name: estimate_error, dtype: float64\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f8409fc8d68>"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# filter out low volume options\n",
    "\n",
    "# lower_bound, upper_bound = cur_stock_price * .5, cur_stock_price * 1.5\n",
    "# price_estimate_filtered = df_estimate[(df_estimate['Strike'] > lower_bound) & (df_estimate['Strike'] < upper_bound)].reset_index()\n",
    "\n",
    "price_estimate_filtered = df_estimate[(df_estimate['Open Interest'] > 15)].reset_index()\n",
    "ax = sns.distplot(price_estimate_filtered['estimate_error'])\n",
    "print(price_estimate_filtered['estimate_error'].describe())\n",
    "\n",
    "price_estimate_filtered.plot(x='Strike',y=['Last Price','estimate'], title='Option prices for {}, Expiry {} (Filtered Strikes)'.format(ticker, expiration_datetime.date()))\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cur_stock_price: 1827.949951, time to expiration: 0.7777777777777778, rfr: 0.08, vol: 0.38212781123440914\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:34: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:35: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f840a077b38>"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# if we use implied vol instead of historical vol, our estimate should improve\n",
    "\n",
    "def calculate_prices_across_strikes(options_df, cur_stock_price, time_to_expiration, risk_free_rate, sigma, option_type):\n",
    "\n",
    "    print('cur_stock_price: {}, time to expiration: {}, rfr: {}, vol: {}'.format(cur_stock_price, time_to_expiration, risk_free_rate, sigma))\n",
    "    list_estimates = []\n",
    "    estimates_with_implied = []\n",
    "\n",
    "    strike_start_idx, strike_end_idx = 0, options_df.shape[0]\n",
    "\n",
    "    # run BSM for different strikes\n",
    "    for x in range(strike_start_idx,strike_end_idx):\n",
    "#         print(options_df['Strike'][x])\n",
    "        value_s = black_scholes(S = cur_stock_price, \n",
    "                                K = options_df['Strike'][x], \n",
    "                                T = time_to_expiration, \n",
    "                                r = risk_free_rate, \n",
    "                                sigma = sigma,\n",
    "                                option_type = option_type)\n",
    "        list_estimates.append(value_s)\n",
    "        \n",
    "    for x in range(strike_start_idx,strike_end_idx):\n",
    "#         print(options_df['Strike'][x])\n",
    "        value_s = black_scholes(S = cur_stock_price, \n",
    "                                K = options_df['Strike'][x], \n",
    "                                T = time_to_expiration, \n",
    "                                r = risk_free_rate, \n",
    "                                sigma = options_df['Implied Volatility'][x],\n",
    "                                option_type = option_type)\n",
    "        estimates_with_implied.append(value_s)\n",
    "\n",
    "    # merge the real and computed dataframes to compare results\n",
    "    df_estimate = options_df[['Strike','Last Price']]\n",
    "    df_estimate['estimate'] = list_estimates\n",
    "    df_estimate['estimate_with_implied'] = estimates_with_implied\n",
    "\n",
    "    return df_estimate\n",
    "\n",
    "df_estimate_european = calculate_prices_across_strikes(price_estimate_filtered, cur_stock_price, time_to_expiration, risk_free_rate, sigma, option_type)\n",
    "df_estimate_european.plot(x='Strike',y=['Last Price','estimate','estimate_with_implied'], title='Option Prices for {}, Expiry {}, with Implied Vol'.format(ticker, expiration_datetime.date()))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "ename": "KeyError",
     "evalue": "'estimate_with_implied'",
     "output_type": "error",
     "traceback": [
      "\u001b[0;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m/opt/conda/lib/python3.7/site-packages/pandas/core/indexes/base.py\u001b[0m in \u001b[0;36mget_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m   2889\u001b[0m             \u001b[0;32mtry\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2890\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2891\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 'estimate_with_implied'",
      "\nDuring handling of the above exception, another exception occurred:\n",
      "\u001b[0;31mKeyError\u001b[0m                                  Traceback (most recent call last)",
      "\u001b[0;32m<ipython-input-21-597d0da53774>\u001b[0m in \u001b[0;36m<module>\u001b[0;34m\u001b[0m\n\u001b[0;32m----> 1\u001b[0;31m \u001b[0mdf_estimate\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'estimate_with_implied_error'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m(\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf_estimate\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'Last Price'\u001b[0m\u001b[0;34m]\u001b[0m \u001b[0;34m-\u001b[0m \u001b[0mdf_estimate\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'estimate_with_implied'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m/\u001b[0m\u001b[0mdf_estimate\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'estimate_with_implied'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m*\u001b[0m\u001b[0;36m100\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m      2\u001b[0m \u001b[0max\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0msns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdistplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf_estimate\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'estimate_with_implied_error'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      3\u001b[0m \u001b[0mprint\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mdf_estimate\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0;34m'estimate_with_implied_error'\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mdescribe\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      4\u001b[0m \u001b[0mdf_estimate\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mplot\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mx\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Strike'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0my\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'estimate_with_implied_error'\u001b[0m\u001b[0;34m,\u001b[0m\u001b[0mtitle\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0;34m'Estimate Percent Error Across Strikes (Filtered Strikes)'\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m      5\u001b[0m \u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.7/site-packages/pandas/core/frame.py\u001b[0m in \u001b[0;36m__getitem__\u001b[0;34m(self, key)\u001b[0m\n\u001b[1;32m   2973\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mnlevels\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2974\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_getitem_multilevel\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2975\u001b[0;31m             \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mcolumns\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2976\u001b[0m             \u001b[0;32mif\u001b[0m \u001b[0mis_integer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2977\u001b[0m                 \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0;34m[\u001b[0m\u001b[0mindexer\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32m/opt/conda/lib/python3.7/site-packages/pandas/core/indexes/base.py\u001b[0m in \u001b[0;36mget_loc\u001b[0;34m(self, key, method, tolerance)\u001b[0m\n\u001b[1;32m   2890\u001b[0m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2891\u001b[0m             \u001b[0;32mexcept\u001b[0m \u001b[0mKeyError\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0;32m-> 2892\u001b[0;31m                 \u001b[0;32mreturn\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_engine\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_loc\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0m_maybe_cast_indexer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[0m\u001b[1;32m   2893\u001b[0m         \u001b[0mindexer\u001b[0m \u001b[0;34m=\u001b[0m \u001b[0mself\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mget_indexer\u001b[0m\u001b[0;34m(\u001b[0m\u001b[0;34m[\u001b[0m\u001b[0mkey\u001b[0m\u001b[0;34m]\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mmethod\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mmethod\u001b[0m\u001b[0;34m,\u001b[0m \u001b[0mtolerance\u001b[0m\u001b[0;34m=\u001b[0m\u001b[0mtolerance\u001b[0m\u001b[0;34m)\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n\u001b[1;32m   2894\u001b[0m         \u001b[0;32mif\u001b[0m \u001b[0mindexer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0mndim\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m \u001b[0;32mor\u001b[0m \u001b[0mindexer\u001b[0m\u001b[0;34m.\u001b[0m\u001b[0msize\u001b[0m \u001b[0;34m>\u001b[0m \u001b[0;36m1\u001b[0m\u001b[0;34m:\u001b[0m\u001b[0;34m\u001b[0m\u001b[0;34m\u001b[0m\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/index.pyx\u001b[0m in \u001b[0;36mpandas._libs.index.IndexEngine.get_loc\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;32mpandas/_libs/hashtable_class_helper.pxi\u001b[0m in \u001b[0;36mpandas._libs.hashtable.PyObjectHashTable.get_item\u001b[0;34m()\u001b[0m\n",
      "\u001b[0;31mKeyError\u001b[0m: 'estimate_with_implied'"
     ]
    }
   ],
   "source": [
    "\n",
    "df_estimate_european['estimate_with_implied_error'] = ((df_estimate_european['Last Price'] - df_estimate_european['estimate_with_implied'])/df_estimate_european['estimate_with_implied'])*100\n",
    "ax = sns.distplot(df_estimate_european['estimate_with_implied_error'])\n",
    "print(df_estimate_european['estimate_with_implied_error'].describe())\n",
    "df_estimate_european.plot(x='Strike',y='estimate_with_implied_error',title='Estimate Percent Error Across Strikes (Filtered Strikes)')\n",
    "\n",
    "mse = np.sum((df_estimate_european['Last Price'] - df_estimate_european['estimate_with_implied'])**2) / df_estimate_european.shape[0]\n",
    "rmse = np.sqrt(mse)\n",
    "\n",
    "print(mse, rmse)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [],
   "source": [
    "# American options\n",
    "\n",
    "from functions.BS_pricer import BS_pricer\n",
    "from functions.Parameters import Option_param\n",
    "from functions.Processes import Diffusion_process\n",
    "from functions.cython.cython_functions import PSOR\n",
    "\n",
    "import numpy as np\n",
    "import scipy.stats as ss\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "%matplotlib inline\n",
    "from IPython.display import display\n",
    "import sympy; sympy.init_printing()\n",
    "\n",
    "def display_matrix(m):\n",
    "    display(sympy.Matrix(m))\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Longstaff Schwartz Method\n",
    "\n",
    "def price_american(S0, K, T, r, sigma, payoff='call'):\n",
    "    \n",
    "    # Creates the object with the parameters of the option\n",
    "    opt_param = Option_param(S0=S0, K=K, T=T, exercise=\"American\", payoff=payoff )\n",
    "    # Creates the object with the parameters of the process\n",
    "    diff_param = Diffusion_process(r=r, sig=sigma)\n",
    "    # Creates the pricer object\n",
    "    BS = BS_pricer(opt_param, diff_param)\n",
    "    \n",
    "#     return BS.LSM(N=1000, paths=1000, order=2)  # Longstaff Schwartz Method\n",
    "    N_space = 8000\n",
    "    N_time = 5000\n",
    "    return BS.PDE_price((N_space,N_time))\n",
    "\n",
    "# def plot_american(BS, x_start, x_end, y_start, y_end):\n",
    "    \n",
    "#     fig = plt.figure(figsize=(9,5))\n",
    "#     BS.plot([x_start,x_end,y_start,y_end])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/latex": [
       "$\\displaystyle 9.559096612544998$"
      ],
      "text/plain": [
       "9.559096612544998"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# price_american(S0=100, K=100, T=1, r=0.1, sigma=0.2, payoff=\"put\" )\n",
    "# 1827.949951 1110.0 0.7817460317460317 0.08 0.38212781123440914 put\n",
    "price_american(S0=1827.949951, K=1110.0, T=0.7817460317460317, r=0.08, sigma=0.38212781123440914, payoff=\"put\" )\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "cur_stock_price: 1827.949951, time to expiration: 0.7777777777777778, rfr: 0.08, vol: 0.2\n",
      "strike 520.0\n",
      "strike 720.0\n",
      "strike 940.0\n",
      "strike 1120.0\n",
      "strike 1200.0\n",
      "strike 1285.0\n",
      "strike 1390.0\n",
      "strike 1560.0\n",
      "strike 1780.0\n",
      "0     8.655832e-13\n",
      "10    2.991858e-07\n",
      "20    9.517629e-04\n",
      "30    6.108268e-02\n",
      "40    2.475580e-01\n",
      "50    8.717275e-01\n",
      "60    3.169869e+00\n",
      "70    1.591410e+01\n",
      "80    6.918282e+01\n",
      "dtype: float64\n",
      "CPU times: user 17.1 s, sys: 348 ms, total: 17.5 s\n",
      "Wall time: 17.4 s\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:39: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.axes._subplots.AxesSubplot at 0x7f8403f6ff60>"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "%%time\n",
    "\n",
    "# if we use implied vol instead of historical vol, our estimate should improve\n",
    "\n",
    "def calculate_prices_across_strikes_american(options_df, cur_stock_price, time_to_expiration, risk_free_rate, sigma, option_type):\n",
    "\n",
    "    print('cur_stock_price: {}, time to expiration: {}, rfr: {}, vol: {}'.format(cur_stock_price, time_to_expiration, risk_free_rate, sigma))\n",
    "    index = []\n",
    "    list_estimates = []\n",
    "#     estimates_with_implied = []\n",
    "\n",
    "    strike_start_idx, strike_end_idx = 0, options_df.shape[0]\n",
    "    step = 10\n",
    "\n",
    "    # run BSM for different strikes\n",
    "    for x in range(strike_start_idx,strike_end_idx, step):\n",
    "        index.append(x)\n",
    "        print('strike', options_df['Strike'][x])\n",
    "        value_s = price_american(S0 = cur_stock_price, \n",
    "                                K = options_df['Strike'][x], \n",
    "                                T = time_to_expiration, \n",
    "                                r = risk_free_rate, \n",
    "                                sigma = sigma,\n",
    "                                payoff = option_type)\n",
    "        list_estimates.append(value_s)\n",
    "        \n",
    "#         print(cur_stock_price, options_df['Strike'][x], time_to_expiration, risk_free_rate, options_df['Implied Volatility'][x], option_type)\n",
    "#         value_s = price_american(S0 = cur_stock_price, \n",
    "#                                 K = options_df['Strike'][x], \n",
    "#                                 T = time_to_expiration, \n",
    "#                                 r = risk_free_rate, \n",
    "#                                 sigma = options_df['Implied Volatility'][x],\n",
    "#                                 payoff = option_type)\n",
    "#         estimates_with_implied.append(value_s)\n",
    "\n",
    "    # merge the real and computed dataframes to compare results\n",
    "    price_estimates = pd.Series(data=list_estimates, index=index)\n",
    "    print(price_estimates)\n",
    "#     df_estimate['estimate_with_implied'] = estimates_with_implied\n",
    "    df_estimate = options_df[['Strike','Last Price']]\n",
    "    df_estimate['estimate'] = price_estimates\n",
    "\n",
    "    return df_estimate\n",
    "\n",
    "df_estimate_american = calculate_prices_across_strikes_american(price_estimate_filtered, cur_stock_price, time_to_expiration, risk_free_rate, sigma, option_type)\n",
    "# df_estimate.plot(x='Strike',y=['Last Price','estimate','estimate_with_implied'], title='Option Prices for {}, Expiry {}, with Implied Vol'.format(ticker, expiration_datetime.date()))\n",
    "# df_estimate.plot(x='Strike',y=['Last Price','estimate'], title='Option Prices for {}, Expiry {}, with Implied Vol'.format(ticker, expiration_datetime.date()))\n",
    "\n",
    "ax1 = df_estimate_american.plot(kind='scatter', x='Strike',y=['Last Price'], title='Option Prices for {}, Expiry {}, with Implied Vol'.format(ticker, expiration_datetime.date()))\n",
    "df_estimate_american.plot(kind='scatter', x='Strike',y=['estimate'], ax=ax1, color='r')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:3: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  This is separate from the ipykernel package so we can avoid doing imports until\n",
      "/opt/conda/lib/python3.7/site-packages/ipykernel_launcher.py:4: SettingWithCopyWarning: \n",
      "A value is trying to be set on a copy of a slice from a DataFrame.\n",
      "Try using .loc[row_indexer,col_indexer] = value instead\n",
      "\n",
      "See the caveats in the documentation: http://pandas.pydata.org/pandas-docs/stable/user_guide/indexing.html#returning-a-view-versus-a-copy\n",
      "  after removing the cwd from sys.path.\n"
     ]
    },
    {
     "data": {
      "text/plain": [
       "<matplotlib.legend.Legend at 0x7f8403cd3978>"
      ]
     },
     "execution_count": 45,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# compare with european\n",
    "\n",
    "df_estimate_american['european_estimate'] = df_estimate_european['estimate']\n",
    "df_estimate_american['european_estimate_with_implied'] = df_estimate_european['estimate_with_implied']\n",
    "\n",
    "ax1 = df_estimate_american.plot(kind='scatter', x='Strike',y=['Last Price'], label='Actual Price')\n",
    "df_estimate_american.plot(kind='scatter', x='Strike',y=['estimate'], ax=ax1, color='r', label='PDE solver')\n",
    "df_estimate_american.plot(kind='scatter', x='Strike',y=['european_estimate'], ax=ax1, color='g', label='European')\n",
    "# df_estimate.plot(kind='scatter', x='Strike',y=['estimate'], ax=ax1, color='r')\n",
    "ax1.set_title('Option Prices for {}, Expiry {}, Collected {}'.format(ticker, expiration_datetime.date(), datetime.now().date()))\n",
    "ax1.legend()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "datetime.date(2020, 12, 3)"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "datetime.now().date()\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "# how accurate is BSM for different expiration dates?\n",
    "\n",
    "# import os \n",
    "\n",
    "# data_path = \"/home/amao/options_data/2020-11-19 17:00:01.568118\"\n",
    "\n",
    "# ticker = 'TSLA'\n",
    "# calls_data, puts_data = dict(), dict()\n",
    "\n",
    "# for filename in os.listdir(data_path):\n",
    "#     if ticker in filename:\n",
    "#         df = pd.read_csv(os.path.join(data_path, filename))\n",
    "#         if 'puts' in filename :\n",
    "#             puts_data[filename] = df\n",
    "#         elif 'calls' in filename:\n",
    "#             calls_data[filename] = df\n",
    "        \n",
    "# print(len(calls_data), len(puts_data))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "# stock_price_df = df\n",
    "\n",
    "# for k,v in calls_data.items():\n",
    "#     print(k, v.head())\n",
    "#     bsm_estimate_df = calculate_prices_across_strikes(v, cur_stock_price, time_to_expiration, risk_free_rate, sigma):\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "u and d: 1.2214027581601699 0.8187307530779818\n",
      "p 0.47512469600943963\n"
     ]
    }
   ],
   "source": [
    "# binomial tree\n",
    "import math\n",
    "\n",
    "sigma = .2\n",
    "rfr = .02\n",
    "delta_t = 1\n",
    "\n",
    "u = math.exp(sigma * math.sqrt(delta_t))\n",
    "d = math.exp(-sigma * math.sqrt(delta_t))\n",
    "print('u and d:',u,d)\n",
    "\n",
    "# a = math.exp(rfr * delta_t)\n",
    "a = math.exp((rfr - .01) * delta_t)\n",
    "p = (a - d)/(u - d)\n",
    "\n",
    "print('p', p)\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price 0\n",
      "price 18.65195571686643\n",
      "price 17.452716560268637\n",
      "price 25.695678025946652\n",
      "price 24.44307753439426\n"
     ]
    }
   ],
   "source": [
    "# N period binomial tree model\n",
    "\n",
    "def price_option_european(S_0, u, d, K, option_type: str, num_periods: int):\n",
    "    \n",
    "    if num_periods == 0:\n",
    "        if option_type == 'call':\n",
    "            return max(S_0-K, 0)\n",
    "        elif option_type == 'put':\n",
    "            return max(K-S_0, 0)\n",
    "    else:\n",
    "        S_u = S_0 * u\n",
    "        S_d = S_0 * d\n",
    "        \n",
    "        f_u = price_option_european(S_0 * u,u,d,K,option_type,num_periods-1)\n",
    "        f_d = price_option_european(S_0 * d,u,d,K,option_type,num_periods-1)\n",
    "        \n",
    "#         print('f_u and f_d:', f_u, f_d)\n",
    "\n",
    "        return math.exp(-rfr*delta_t) * (p*f_u + (1-p)*f_d)\n",
    "\n",
    "S_0 = 200\n",
    "K = 200\n",
    "option_type = 'put'\n",
    "\n",
    "for i in range(5):\n",
    "    price = price_option_european(S_0, u, d, K, option_type, num_periods=i)\n",
    "    print('price',price)\n",
    "    "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "price 0\n",
      "price 18.65195571686643\n",
      "price 18.65195571686643\n",
      "price 18.65195571686643\n",
      "price 18.65195571686643\n"
     ]
    }
   ],
   "source": [
    "def price_option_american(S_0, u, d, K, option_type: str, num_periods: int):\n",
    "    \n",
    "    if num_periods == 0:\n",
    "        if option_type == 'call':\n",
    "            return max(S_0-K, 0)\n",
    "        elif option_type == 'put':\n",
    "            return max(K-S_0, 0)\n",
    "    else:\n",
    "        S_u = S_0 * u\n",
    "        S_d = S_0 * d\n",
    "        \n",
    "        f_u = price_option_american(S_0 * u,u,d,K,option_type,num_periods-1)\n",
    "        f_d = price_option_american(S_0 * d,u,d,K,option_type,num_periods-1)\n",
    "        \n",
    "        if option_type == 'call':\n",
    "            f_u_early = max(S_u-K, 0)\n",
    "            f_d_early = max(S_d-K, 0)\n",
    "        elif option_type == 'put':\n",
    "            f_u_early = max(K-S_u, 0)\n",
    "            f_d_early = max(K-S_d, 0)\n",
    "#         print('f_u,f_d,f_u_early,f_d_early:',f_u,f_d,f_u_early,f_d_early)\n",
    "        f_u = max(f_u,f_u_early)\n",
    "        f_d = max(f_u,f_d_early)\n",
    "        \n",
    "#         print('f_u and f_d:', f_u, f_d)\n",
    "\n",
    "        return math.exp(-rfr*delta_t) * (p*f_u + (1-p)*f_d)\n",
    "\n",
    "S_0 = 200\n",
    "K = 200\n",
    "option_type = 'put'\n",
    "\n",
    "for i in range(5):\n",
    "    price = price_option_american(S_0, u, d, K, option_type, num_periods=i)\n",
    "    print('price',price)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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