MMA823_A3_Q3_Michael.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MMA823_A3_Q3.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "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/Wangmiaobeng/MMA_Share/blob/master/MMA823_A3_Q3_Michael.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "chBP75zzvew6",
        "colab_type": "text"
      },
      "source": [
        "#MMA 823 Assignment 3"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1VnEhMSYvlKt",
        "colab_type": "text"
      },
      "source": [
        "## Import packages"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dDNNFh9KF6NQ",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "import pandas as pd\n",
        "import numpy as np\n",
        "from scipy.stats import kurtosis, skew,variation\n",
        "import statistics \n",
        "\n",
        "from IPython.core.interactiveshell import InteractiveShell\n",
        "InteractiveShell.ast_node_interactivity = \"all\"\n",
        "\n",
        "pd.set_option(\"display.max_colwidth\", 200)\n",
        "pd.options.display.max_columns = None\n"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "g6OKwawVvqbX",
        "colab_type": "text"
      },
      "source": [
        "## Define 3 functions to simulate"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "B6wM6jk4nQg0",
        "colab_type": "code",
        "colab": {}
      },
      "source": [
        "def EWMA_sim(\n",
        "    simulations=50000,\n",
        "    lambda_Q2=0.942285798061926,\n",
        "    days=252,\n",
        "    return_ini=0.003323116,\n",
        "    variance_ini=0.000030328,\n",
        "    mu=0.07,\n",
        "    random_seed=1121,\n",
        "):\n",
        "    \"\"\"simulate using EWMA\"\"\"\n",
        "    np.random.seed(1121)\n",
        "    SP_return = np.full(days, np.nan)\n",
        "    SP_variance = np.full(days, np.nan)\n",
        "    SP_simulations = pd.DataFrame({\"SP_return\": np.full(simulations, np.nan)})\n",
        "    for i in range(simulations):\n",
        "        for k in range(days):\n",
        "            if k == 0:\n",
        "                return_day = return_ini\n",
        "                variance_day = variance_ini\n",
        "            else:\n",
        "                return_day = SP_return[k - 1]\n",
        "                variance_day = SP_variance[k - 1]\n",
        "            SP_variance[k] = (1 - lambda_Q2) * (\n",
        "                return_day ** 2\n",
        "            ) + lambda_Q2 * variance_day\n",
        "            SP_return[k] = np.random.normal(\n",
        "                loc=mu / days, scale=np.sqrt(SP_variance[k]), size=1\n",
        "            )\n",
        "        SP_simulations.SP_return[i] = sum(SP_return)\n",
        "    print(\"kurtosis : {}\".format(kurtosis(SP_simulations.SP_return)))\n",
        "    print(\"skewness : {}\".format(skew(SP_simulations.SP_return)))\n",
        "    print(\"variance : {}\".format(statistics.variance(SP_simulations.SP_return)))\n",
        "    return SP_simulations.hist()\n",
        "\n",
        "\n",
        "def Garch_sim(\n",
        "    simulations=50000,\n",
        "    omega=0.0000049038,\n",
        "    beta=0.738356,\n",
        "    alpha=0.179255,\n",
        "    days=252,\n",
        "    return_ini=0.003323116,\n",
        "    variance_ini=0.000030328,\n",
        "    mu=0.07,\n",
        "    random_seed=1121,\n",
        "):\n",
        "    \"\"\"simulate using Garch\"\"\"\n",
        "    np.random.seed(1121)\n",
        "    SP_return = np.full(days, np.nan)\n",
        "    SP_variance = np.full(days, np.nan)\n",
        "    SP_simulations = pd.DataFrame({\"SP_return\": np.full(simulations, np.nan)})\n",
        "    for i in range(simulations):\n",
        "        for k in range(days):\n",
        "            if k == 0:\n",
        "                return_day = return_ini\n",
        "                variance_day = variance_ini\n",
        "            else:\n",
        "                return_day = SP_return[k - 1]\n",
        "                variance_day = SP_variance[k - 1]\n",
        "            SP_variance[k] = omega + alpha * (return_day ** 2) + beta * variance_day\n",
        "            SP_return[k] = np.random.normal(\n",
        "                loc=mu / days, scale=np.sqrt(SP_variance[k]), size=1\n",
        "            )\n",
        "        SP_simulations.SP_return[i] = sum(SP_return)\n",
        "    print(\"kurtosis : {}\".format(kurtosis(SP_simulations.SP_return)))\n",
        "    print(\"skewness : {}\".format(skew(SP_simulations.SP_return)))\n",
        "    print(\"variance : {}\".format(statistics.variance(SP_simulations.SP_return)))\n",
        "    return SP_simulations.hist()\n",
        "\n",
        "def Asymmetric_Garch_sim(\n",
        "    simulations=50000,\n",
        "    omega=0.0000049038,\n",
        "    beta=0.738356,\n",
        "    alpha=0.179255,\n",
        "    kappa = 0.005967,\n",
        "    days=252,\n",
        "    return_ini=0.003323116,\n",
        "    variance_ini=0.000030328,\n",
        "    mu=0.07,\n",
        "    random_seed=1121,\n",
        "):\n",
        "    \"\"\"simulate using Asymmetric Garch\"\"\"\n",
        "    np.random.seed(1121)\n",
        "    SP_return = np.full(days, np.nan)\n",
        "    SP_variance = np.full(days, np.nan)\n",
        "    SP_simulations = pd.DataFrame({\"SP_return\": np.full(simulations, np.nan)})\n",
        "    for i in range(simulations):\n",
        "        for k in range(days):\n",
        "            if k == 0:\n",
        "                return_day = return_ini\n",
        "                variance_day = variance_ini\n",
        "            else:\n",
        "                return_day = SP_return[k - 1]\n",
        "                variance_day = SP_variance[k - 1]\n",
        "            SP_variance[k] = omega + alpha * ((return_day - kappa) ** 2) + beta * variance_day\n",
        "            SP_return[k] = np.random.normal(\n",
        "                loc=mu / days, scale=np.sqrt(SP_variance[k]), size=1\n",
        "            )\n",
        "        SP_simulations.SP_return[i] = sum(SP_return)\n",
        "    print(\"kurtosis : {}\".format(kurtosis(SP_simulations.SP_return)))\n",
        "    print(\"skewness : {}\".format(skew(SP_simulations.SP_return)))\n",
        "    print(\"variance : {}\".format(statistics.variance(SP_simulations.SP_return)))\n",
        "    return SP_simulations.hist()"
      ],
      "execution_count": 0,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "azvpns-ew1lG",
        "colab_type": "text"
      },
      "source": [
        "## Check the results"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XQ33h5Ruq63u",
        "colab_type": "code",
        "outputId": "4601def4-958b-415a-8052-1a99414ce729",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 371
        }
      },
      "source": [
        "EWMA_sim()"
      ],
      "execution_count": 85,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "kurtosis : 2.82721779709183\n",
            "skewness : 0.17091592671773623\n",
            "variance : 0.007508955468771462\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fc50aa66358>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 85
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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MLm0+K8WOF59VIW5mZm1Sz91KAm4FnoyIvy41bQGG7zhaBdxVil+a7lpaDByNiAPANmCp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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Renn3-3Xrgle",
        "colab_type": "code",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 371
        },
        "outputId": "e096922d-7d51-4163-af09-cc03691732f1"
      },
      "source": [
        "Garch_sim()"
      ],
      "execution_count": 86,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "kurtosis : 0.3158850078941513\n",
            "skewness : 0.0317751376938357\n",
            "variance : 0.014815984633736146\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fc50aa66c50>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 86
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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j3WsWlvEbJS2sq8+VtL685mqVP0wdERGd0eyRw9eA+fvUlgJrbc8G1pbnAGcCs8tjMXAN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\ngg==\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HlTWekPFrghq",
        "colab_type": "code",
        "outputId": "5fbf0c94-4d84-4eac-a535-ab41e018875e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 371
        }
      },
      "source": [
        "Asymmetric_Garch_sim()"
      ],
      "execution_count": 87,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "kurtosis : 0.710328162168754\n",
            "skewness : -0.41176595965227236\n",
            "variance : 0.03186381873374462\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7fc50a9c1518>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 87
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}