Random_Variables.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Random Variables",
      "provenance": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/TheHouseOfVermeulens/Financial-Engineering/blob/master/Random_Variables.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "IOcpw5B_Hewu",
        "colab_type": "text"
      },
      "source": [
        "#Libraries and Functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XEcek_CzHa0I",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "\n",
        "\n",
        "# Useful Functions\n",
        "class DiscreteRandomVariable:\n",
        "    def __init__(self, a=0, b=1):\n",
        "        self.variableType = \"\"\n",
        "        self.low = a\n",
        "        self.high = b\n",
        "        return\n",
        "    def draw(self, numberOfSamples):\n",
        "        samples = np.random.randint(self.low, self.high, numberOfSamples)\n",
        "        return samples\n",
        "    \n",
        "class BinomialRandomVariable(DiscreteRandomVariable):\n",
        "    def __init__(self, numberOfTrials = 10, probabilityOfSuccess = 0.5):\n",
        "        self.variableType = \"Binomial\"\n",
        "        self.numberOfTrials = numberOfTrials\n",
        "        self.probabilityOfSuccess = probabilityOfSuccess\n",
        "        return\n",
        "    def draw(self, numberOfSamples):\n",
        "        samples = np.random.binomial(self.numberOfTrials, self.probabilityOfSuccess, numberOfSamples)\n",
        "        return samples\n",
        "    \n",
        "def factorial(n):return reduce(lambda x,y:x*y,[1]+range(1,n+1))\n",
        "\n",
        "# Useful Libraries\n",
        "import pandas as pd\n",
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "import statsmodels.stats as stats\n",
        "from statsmodels.stats import stattools\n",
        "from __future__ import division\n",
        "\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "WKxOq-cfK1Jy",
        "colab_type": "text"
      },
      "source": [
        "#1 : Uniform Distribution\n",
        "\n",
        "    Plot the histogram of 10 tosses with a fair coin (let 1 be heads and 2 be tails).\n",
        "    Plot the histogram of 1000000 tosses of a fair coin\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "m4SavO8dKpTO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "12fe54be-2d04-4504-85b4-0fc89e55596d"
      },
      "source": [
        "# Histograms with 10 tosses. \n",
        "cointoss = DiscreteRandomVariable(1, 3)\n",
        "plt.hist(cointoss.draw(10), align = 'mid')\n",
        "\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Occurences')\n",
        "plt.legend(['Coin Tosses']);"
      ],
      "execution_count": 2,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DSZXWTaIK9wO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 279
        },
        "outputId": "a01c734d-d8b6-4d6f-a2e7-dd48a5d99c84"
      },
      "source": [
        "# Histograms with 1000000 tosses. \n",
        "cointoss = DiscreteRandomVariable(1, 3)\n",
        "plt.hist(cointoss.draw(1000000), align = 'mid')\n",
        "\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Occurences')\n",
        "plt.legend(['Coin Tosses']);"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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llPolSjMzs5I5XMzMLHMOFzMzy5zDxczMMudwMTOzzDlczMwscw4XMzPLnMPFzMwy53Ax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\nmXO4mJlZ5hwuZmaWOYeLmZll7v8D+DnOlXWXRDIAAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "9bD8n3wiLQDq",
        "colab_type": "text"
      },
      "source": [
        "#2 : Binomial Distributions.\n",
        "\n",
        "    Graph the histogram of 1000000 samples from a binomial distribution of probability 0.25 and n=20\n",
        "\n",
        "Find the value that occurs the most often\n",
        "Calculate the probability of the value that occurs the most often occurring. Use the factorial(x) function to find factorials"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OMMS-WA6LLKO",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "e5694cd0-f205-4cf7-f957-9615e4f1c6b2"
      },
      "source": [
        "# Binomial distribution with p=0.25 and n=20\n",
        "binomialdistribution = BinomialRandomVariable(20, 0.25)\n",
        "bins = np.arange(0,21,1)\n",
        "n, bins, patches = plt.hist(binomialdistribution.draw(1000000), bins=bins)\n",
        "\n",
        "plt.title('Binomial Distribution with p=0.25 and n=20')\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Occurrences')\n",
        "plt.legend(['Die Rolls']);"
      ],
      "execution_count": 4,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MbOO1rgRzPNkIspdKgTT9BbK7T5qZmVW0rgQT6U6T5cHVvHt/mHaRtKekWbnH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\n4QRjZmaFcIIxM7NC/H9MwbfVz0FYHAAAAABJRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "tPAItLX5LYCJ",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        },
        "outputId": "b2ef2f46-ee03-4d54-db14-a14a461c5444"
      },
      "source": [
        "# Finding x which occurs most often\n",
        "elem = np.argmax(n)\n",
        "print ('Maximum occurance for x =', elem)"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Maximum occurance for x = 5\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "DETpUdlbLdEi",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Calculating the probability of finding x. \n",
        "n = 20\n",
        "p = 0.5\n",
        "x = elem\n",
        "n_factorial = factorial(n)\n",
        "x_factorial = factorial(x)\n",
        "n_x_factorial = factorial(n-x)\n",
        "fact = n_factorial / (n_x_factorial * x_factorial)\n",
        "probability = fact * (p**x) * ((1-p)**(n-x))\n",
        "print ('proabability of x = %d' % x, probability)\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Fd6ki8UcLqLg",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "```\n",
        "proabability of x = 5 0.0147857666016\n",
        "```\n",
        "\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5-TB_CJULwDW",
        "colab_type": "text"
      },
      "source": [
        "#3 : Normal Distributions\n",
        "##a. Graphing\n",
        "\n",
        "Graph a normal distribution using the Probability Density Function bellow, with a mean of 0 and standard deviation of 5."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "-mjYFbamLlKg",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 295
        },
        "outputId": "511fe52d-ca13-4d18-bd03-9539415c5f9d"
      },
      "source": [
        "# Graphing a normal distribution pdf. \n",
        "mu = 0\n",
        "sigma = 5\n",
        "x = np.linspace(-30, 30, 200)\n",
        "y = (1/(sigma * np.sqrt(2 * 3.14159))) * np.exp(-(x - mu)*(x - mu) / (2 * sigma * sigma))\n",
        "plt.plot(x, y)\n",
        "plt.title('Graph of PDF with mu = 0 and sigma = 5')\n",
        "plt.xlabel('Value')\n",
        "plt.ylabel('Probability');"
      ],
      "execution_count": 8,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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t3s8HZp8QdSh94sjIrtUNXDhzbNThuAyV1GztkgoIqoNmE1xNAGBm/ytNcX0N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\n6P8DjV6MLiXuvH4AAAAASUVORK5CYII=\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Odk-df1GL9jp",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "##b. Confidence Intervals.\n",
        "\n",
        "    Calculate the first, second, and third confidence intervals.\n",
        "    Plot the PDF and the first, second, and third confidence intervals.\n",
        "\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "O5mtiSGEL5K2",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 69
        },
        "outputId": "7f1c06fe-4c84-4d70-fede-10743ba3e040"
      },
      "source": [
        "# finding the 1st, 2nd, and third confidence intervals. \n",
        "first_ci = (-sigma, sigma)\n",
        "second_ci = (-2*sigma, 2*sigma)\n",
        "third_ci = (-3*sigma, 3*sigma)\n",
        "\n",
        "print ('1-sigma -> mu +/-', sigma)\n",
        "print ('2-sigma -> mu +/-', second_ci[1])\n",
        "print ('3-sigma -> mu +/-', third_ci[1])"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "1-sigma -> mu +/- 5\n",
            "2-sigma -> mu +/- 10\n",
            "3-sigma -> mu +/- 15\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VRO_BymxMFHE",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 281
        },
        "outputId": "76eda94a-4741-4959-cef4-12fcb3774a99"
      },
      "source": [
        "plt.axvline(first_ci[0], linestyle='dashdot', label='68% of observations', color = 'blue')\n",
        "plt.axvline(first_ci[1], linestyle='dashdot', label='68% of observations', color = 'blue')\n",
        "plt.axvline(second_ci[0], linestyle='dashdot', label='95% of observations', color = 'red')\n",
        "plt.axvline(second_ci[1],linestyle='dashdot', color = 'red')\n",
        "plt.axvline(third_ci[0],  linestyle='dashdot', label='99% of observations', color = 'green')\n",
        "plt.axvline(third_ci[1], linestyle='dashdot', color = 'green')\n",
        "plt.plot(x,y)\n",
        "plt.title('Graph of PDF with 3 confidence intervals.')\n",
        "\n",
        "plt.legend();"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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6bBbH07LoEdnQ26E4RdcWDQjy97voCVmDwZWYRG+oURR6vPf08Qux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\nRU5ErkJggg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1o8kFQ4yMSXz",
        "colab_type": "text"
      },
      "source": [
        "##4: Financial Applications:\n",
        "\n",
        "Fit the returns of SPY from 2016-01-01 to 2016-05-01 to a normal distribution.\n",
        "\n",
        "Fit the returns to a normal distribution by clacluating the values of `μ`\n",
        "\n",
        "and `σ`\n",
        "Plot the returns and the distribution, along with 3 confidence intervals.\n",
        "Use the `Jarque-Bera` test to check for normality. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "I834uXIzMNY8",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Collect prices and returns. \n",
        "prices = get_pricing('SPY', start_date = '2016-01-01', end_date='2016-05-01', \n",
        "                     fields = 'price')\n",
        "returns = prices.pct_change()[1:]"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "TZbTuy27Mn5A",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Calculating the mean and standard deviation. \n",
        "sample_mean = np.mean(returns)\n",
        "sample_std_dev = np.std(returns)\n",
        "\n",
        "x = np.linspace(-(sample_mean + 4 * sample_std_dev), (sample_mean + 4 * sample_std_dev), len(returns))\n",
        "sample_distribution = ((1/(sample_std_dev * 2 * np.pi)) * \n",
        "                       np.exp(-(x - sample_mean)*(x - sample_mean) / (2 * sample_std_dev * sample_std_dev)))"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "96Jp0L2xMtU3",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Plotting histograms and confidence intervals. \n",
        "plt.hist(returns, range=(returns.min(), returns.max()), normed = True);\n",
        "plt.plot(x, sample_distribution)\n",
        "\n",
        "plt.axvline(sample_std_dev, linestyle='dashed', color='red', label='1st Confidence Interval')\n",
        "plt.axvline(-sample_std_dev, linestyle='dashed', color='red')\n",
        "plt.axvline(2*sample_std_dev, linestyle='dashed', color='k', label='2st Confidence Interval')\n",
        "plt.axvline(-2*sample_std_dev, linestyle='dashed', color='k')\n",
        "plt.axvline(3*sample_std_dev, linestyle='dashed', color='green', label='3st Confidence Interval')\n",
        "plt.axvline(-3*sample_std_dev, linestyle='dashed', color='green')\n",
        "\n",
        "plt.legend();"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "de0Wtvv1M0sf",
        "colab_type": "text"
      },
      "source": [
        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)"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xmz2eblTMyCH",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "# Run the JB test for normality. \n",
        "cutoff = 0.01\n",
        "_, p_value, skewness, kurtosis = stattools.jarque_bera(returns)\n",
        "print (\"The JB test p-value is: \", p_value)\n",
        "print (\"We reject the hypothesis that the data are normally distributed \", p_value < cutoff)\n",
        "print (\"The skewness of the returns is: \", skewness)\n",
        "print (\"The kurtosis of the returns is: \", kurtosis)"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Nj2XC5jqNFPn",
        "colab_type": "text"
      },
      "source": [
        "\n",
        "\n",
        "```\n",
        "The JB test p-value is:  0.923015693884\n",
        "We reject the hypothesis that the data are normally distributed  False\n",
        "The skewness of the returns is:  -0.102081900914\n",
        "The kurtosis of the returns is:  3.07608657316\n",
        "```\n",
        "\n"
      ]
    }
  ]
}