MMA823_A3_Q3.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "MMA823_A3_Q3.ipynb",
      "provenance": [],
      "collapsed_sections": [
        "1VnEhMSYvlKt",
        "g6OKwawVvqbX",
        "G64G1qv_BDn_",
        "Ik8VP-SjBH6u",
        "bGWD0y9CBMxO"
      ],
      "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.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(random_seed)\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=0.0000033263,\n",
        "    beta=0.831932,\n",
        "    alpha=0.1,\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(random_seed)\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=0.00000000,\n",
        "    beta=0.8040613,\n",
        "    alpha=0.1,\n",
        "    kappa = 0.0070950,\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(random_seed)\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": "markdown",
      "metadata": {
        "id": "G64G1qv_BDn_",
        "colab_type": "text"
      },
      "source": [
        "### EWMA"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "XQ33h5Ruq63u",
        "colab_type": "code",
        "outputId": "3f95ac19-cd87-499f-d492-13ce85bb5c37",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 365
        }
      },
      "source": [
        "EWMA_sim()"
      ],
      "execution_count": 0,
      "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 0x7f2b0a4c1128>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 7
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "Ik8VP-SjBH6u",
        "colab_type": "text"
      },
      "source": [
        "### Garch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Renn3-3Xrgle",
        "colab_type": "code",
        "outputId": "3bb33865-f915-4698-ffab-2c1c4a460e69",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 365
        }
      },
      "source": [
        "Garch_sim()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "kurtosis : 0.12794428768303145\n",
            "skewness : 0.022088839115509455\n",
            "variance : 0.012181106365937912\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f2aff4522e8>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 8
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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YmVnG4WBmZhmHg5mZZcYcDpI+IGlr4XZQ0u9K+qKk3YX6RYXnXC+pV9JTki4o1BekWq+k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\nHA5mZpb5/42Io78VeEzCAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "bGWD0y9CBMxO",
        "colab_type": "text"
      },
      "source": [
        "### Asymmetric Garch"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HlTWekPFrghq",
        "colab_type": "code",
        "outputId": "e8becfc8-30fe-4b80-afa6-cb34639728a2",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 365
        }
      },
      "source": [
        "Asymmetric_Garch_sim()"
      ],
      "execution_count": 0,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "kurtosis : 0.37463918881769587\n",
            "skewness : -0.3808158840978681\n",
            "variance : 0.012105908703653153\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "array([[<matplotlib.axes._subplots.AxesSubplot object at 0x7f2aff388ba8>]],\n",
              "      dtype=object)"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 10
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": []
          }
        }
      ]
    }
  ]
}