simulating_trading_volume.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Simulating Equity Trading Volume with Pareto Distribution"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "**Extreme value theory (EVT)** is employed for evaluating the risk associated with rare and severe natural and human-made events. These events often involve clusters of extreme observations that cannot be effectively modeled using a Gaussian distribution. The **Generalised Pareto distribution (GPD)** has demonstrated its effectiveness in modeling such events, particularly when dealing with extreme values surpassing a predefined threshold [1]. The GPD has uniform, triangular, exponential, and Pareto distribution as special cases. Halder and Das, through graphical analysis, validate the applicability of the GPD in modeling stock volume data [1].\n",
    "\n",
    "We employ a **Pareto distribution** to model non-negative trading **volume** data for equities. It's important to note that this simulation does not have any correlation with any actual asset prices, as it might in real-world scenarios [2].\n",
    "\n",
    "To generate volume data, we use a vectorised approach to sample from a Pareto distribution, which mimics the daily trading volume for a stock. Since the Pareto distribution yields floating point values, we must **scale** them and cast them to integers to prevent the simulation of 'fractional shares.' The values obtained from the Pareto distribution are multiplied by a scalar factor of $10^6$ to represent typical large-cap equity daily volume figures. It's worth mentioning that this volume data does **not** exhibit any **autocorrelation** and is not correlated to any asset prices [2]."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "# import relevant packages\n",
    "import os\n",
    "import random\n",
    "import numpy as np\n",
    "import pandas as pd\n",
    "import matplotlib.pyplot as plt"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "# define Trading Volume Simulator class\n",
    "\n",
    "class TradingVolumeSimulator:\n",
    "    \"\"\"\n",
    "    Trading Volume Simulator.\n",
    "    \n",
    "    This callable class will generate a DataFrame with daily volume \n",
    "    data. The generator uses a Pareto distribution to simulate the \n",
    "    volume data.\n",
    "    \n",
    "    Parameters\n",
    "    ----------\n",
    "    start_date : `str`\n",
    "        The starting date in YYYY-MM-DD format.\n",
    "    end_date : `str`\n",
    "        The ending date in YYYY-MM-DD format.\n",
    "    pareto_shape : `float`\n",
    "        The parameter used to govern the Pareto distribution\n",
    "        shape for the generation of volume data.\n",
    "    \"\"\"\n",
    "\n",
    "    def __init__(self, start_date, end_date, pareto_shape):\n",
    "        self.start_date = start_date\n",
    "        self.end_date = end_date\n",
    "        self.pareto_shape = pareto_shape\n",
    "    \n",
    "\n",
    "    def _create_empty_frame(self):\n",
    "        \"\"\"\n",
    "        Creates the empty Pandas DataFrame with a date column using\n",
    "        business days between two dates. Each of the volume columns \n",
    "        are set to zero [2].\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        `pd.DataFrame`\n",
    "            The empty DataFrame for subsequent population.\n",
    "        \"\"\"\n",
    "        date_range = pd.date_range(\n",
    "            self.start_date,\n",
    "            self.end_date,\n",
    "            freq='B'\n",
    "        )\n",
    "\n",
    "        zeros = pd.Series(np.zeros(len(date_range)))\n",
    "\n",
    "        return pd.DataFrame(\n",
    "            {\n",
    "                'date': date_range,\n",
    "                'volume': zeros\n",
    "            }\n",
    "        )[['date', 'volume']]\n",
    "\n",
    "\n",
    "    def _append_volume_to_data(self, data):\n",
    "        \"\"\"\n",
    "        Utilises a Pareto distribution to simulate non-negative\n",
    "        volume data. Note that this is not correlated to any\n",
    "        underlying asset price, as may likely be the case for\n",
    "        real world data [2].\n",
    "\n",
    "        Parameters\n",
    "        ----------\n",
    "        data : `pd.DataFrame`\n",
    "            The DataFrame to append volume data to, in place.\n",
    "\n",
    "        Returns\n",
    "        -------\n",
    "        `pd.DataFrame`\n",
    "            The DataFrame with volume data populated.\n",
    "        \"\"\"\n",
    "        data['volume'] = np.array(\n",
    "            list(\n",
    "                map(\n",
    "                    int,\n",
    "                    np.random.pareto(\n",
    "                        self.pareto_shape,\n",
    "                        size=len(data)\n",
    "                    ) * 1000000.0\n",
    "                )\n",
    "            )\n",
    "        )\n",
    "        \n",
    "        return data\n",
    "\n",
    "\n",
    "    def simulate(self):\n",
    "        \"\"\"\n",
    "        Runs the trading volume simulation \n",
    "        step-by-step.\n",
    "        \n",
    "        Returns\n",
    "        -------\n",
    "        `pd.DataFrame`\n",
    "            The DataFrame with simulated volume data.\n",
    "        \"\"\"\n",
    "        data = self._create_empty_frame()\n",
    "        data = self._append_volume_to_data(data)\n",
    "        return data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "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>date</th>\n",
       "      <th>volume</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1970-01-01</td>\n",
       "      <td>498093</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1970-01-02</td>\n",
       "      <td>12365772</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1970-01-05</td>\n",
       "      <td>2108523</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1970-01-06</td>\n",
       "      <td>1195350</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1970-01-07</td>\n",
       "      <td>157314</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        date    volume\n",
       "0 1970-01-01    498093\n",
       "1 1970-01-02  12365772\n",
       "2 1970-01-05   2108523\n",
       "3 1970-01-06   1195350\n",
       "4 1970-01-07    157314"
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# run simulation\n",
    "\n",
    "# set parameters\n",
    "random_seed = 42\n",
    "start_date='1970-01-01'\n",
    "end_date='2070-12-31'\n",
    "pareto_shape = 1.161\n",
    "\n",
    "# need to seed both Python and NumPy separately\n",
    "random.seed(random_seed)\n",
    "np.random.seed(seed=random_seed)\n",
    "\n",
    "# simulate\n",
    "simulator = TradingVolumeSimulator(start_date, end_date, pareto_shape)\n",
    "data = simulator.simulate()\n",
    "\n",
    "# display simulated data\n",
    "data.head()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# visualise simulated data\n",
    "df = data.set_index('date')\n",
    "df[['volume']].plot(color='teal')\n",
    "plt.xlabel('Date')\n",
    "plt.ylabel('Daily Trading Volume')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## References  \n",
    "\n",
    "[1] Das, Kumer and Halder, Shaymal, “Understanding Extreme Stock Trading Volume by Generalized Pareto Distribution.” North Carolina Journal of Mathematics and Statistics, vol. 2, pp. 45-60, 2016. Available: https://libjournal.uncg.edu/ncjms/article/view/1356/0. [Accessed: 03-Nov-2023].  \n",
    "  \n",
    "[2] “Geometric Brownian Motion Simulation with Python,” QuantStart, 2013. Available: https://www.quantstart.com/articles/geometric-brownian-motion-simulation-with-python/. [Accessed: 03-Nov-2023].  "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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