Everlasting_Options_Price.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "name": "Everlasting Options Price.ipynb",
      "provenance": [],
      "collapsed_sections": [],
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/tazeemc/options/blob/main/Everlasting_Options_Price.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "zW_FdAgMEHI8"
      },
      "source": [
        "import numpy as np\n",
        "import matplotlib.pyplot as plt\n",
        "%matplotlib inline\n",
        "import seaborn as sbn\n",
        "import pandas as pd\n",
        "from matplotlib.pyplot import figure\n",
        "from itertools import cycle, islice"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "7lNCLlh5Egs1"
      },
      "source": [
        "# Put Payoff"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CJjRYKlCEEsl"
      },
      "source": [
        "strike = 3000\n",
        "vol = 1\n",
        "spot = np.arange(2750., 3250., 10.)\n",
        "payoff = np.maximum(strike - spot, 0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 642
        },
        "id": "4gG_mj4eEai2",
        "outputId": "b643f8c4-b761-4eaf-8384-0d22cab9f670"
      },
      "source": [
        "data = pd.DataFrame({'spot': spot, 'payoff': payoff}).set_index('spot')\n",
        "\n",
        "figure(figsize=(12, 9), dpi=80)\n",
        "ax = sbn.lineplot(data=data, legend=False)\n",
        "ax.set_ylabel(\"value\")\n",
        "ax.lines[0].set_linestyle(\"--\")\n",
        "ax.lines[0].set_color(\"orange\")\n",
        "ax.set_title(\"Put Payoff vs. Spot Price (3000 strike)\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Put Payoff vs. Spot Price (3000 strike)')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 3
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 960x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "0TqfZn0QEBK0"
      },
      "source": [
        "# Black Scholes Option Price"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "3gdm0-PWChhZ"
      },
      "source": [
        "# from https://numba.pydata.org/numba-examples/examples/finance/blackscholes/results.html\n",
        "def cnd(d):\n",
        "    A1 = 0.31938153\n",
        "    A2 = -0.356563782\n",
        "    A3 = 1.781477937\n",
        "    A4 = -1.821255978\n",
        "    A5 = 1.330274429\n",
        "    RSQRT2PI = 0.39894228040143267793994605993438\n",
        "    K = 1.0 / (1.0 + 0.2316419 * np.abs(d))\n",
        "    ret_val = (RSQRT2PI * np.exp(-0.5 * d * d) *\n",
        "               (K * (A1 + K * (A2 + K * (A3 + K * (A4 + K * A5))))))\n",
        "    return np.where(d > 0, 1.0 - ret_val, ret_val)\n",
        "\n",
        "    # SPEEDTIP: Despite the memory overhead and redundant computation, the above\n",
        "    # is much faster than:\n",
        "    #\n",
        "    # for i in range(len(d)):\n",
        "    #     if d[i] > 0:\n",
        "    #         ret_val[i] = 1.0 - ret_val[i]\n",
        "    # return ret_val\n",
        "\n",
        "\n",
        "def black_scholes(stockPrice, optionStrike, optionYears, Riskfree, Volatility):\n",
        "    S = stockPrice\n",
        "    X = optionStrike\n",
        "    T = optionYears\n",
        "    R = Riskfree\n",
        "    V = Volatility\n",
        "    sqrtT = np.sqrt(T)\n",
        "    d1 = (np.log(S / X) + (R + 0.5 * V * V) * T) / (V * sqrtT)\n",
        "    d2 = d1 - V * sqrtT\n",
        "    cndd1 = cnd(d1)\n",
        "    cndd2 = cnd(d2)\n",
        "\n",
        "    expRT = np.exp(- R * T)\n",
        "\n",
        "    callResult = S * cndd1 - X * expRT * cndd2\n",
        "    putResult = X * expRT * (1.0 - cndd2) - S * (1.0 - cndd1)\n",
        "\n",
        "    return callResult, putResult"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 642
        },
        "id": "7uYP_uqGGNnV",
        "outputId": "7e54980f-47e7-43f2-8e72-4ab80090eb05"
      },
      "source": [
        "_, one_day_put_price = black_scholes(spot, strike, 1.0/365, 0,vol)\n",
        "data = pd.DataFrame({'spot': spot, 'one day expiring put price': one_day_put_price, 'payoff': payoff}).set_index('spot')\n",
        "figure(figsize=(12, 9), dpi=80)\n",
        "ax = sbn.lineplot(data=data)\n",
        "ax.set_ylabel(\"value\")\n",
        "ax.set_title(\"Put Price vs. Spot Price (3000 strike, 100 vol)\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Put Price vs. Spot Price (3000 strike, 100 vol)')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 5
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 960x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8xcP3KWQECvP"
      },
      "source": [
        "def everlasting_put_price(spot, strike, vol, funding_period_days):\n",
        "  one_day = 1.0/365\n",
        "  num_fundings = np.arange(1.0, 21.0, 1.0)\n",
        "\n",
        "  expo = one_day * num_fundings * funding_period_days\n",
        "  \n",
        "  _, put_px  = black_scholes(spot, strike, expo, 0, vol)\n",
        "\n",
        "  weight = 1/2 ** num_fundings\n",
        "  \n",
        "  return np.sum(weight * put_px)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "En71exmDEMrs",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 642
        },
        "outputId": "c3658fc3-b03b-47bd-a4c3-4c65f9ba8ae9"
      },
      "source": [
        "funding_period_days = 0.5\n",
        "ever_price = [everlasting_put_price(x, strike, vol, funding_period_days) for x in spot]\n",
        "_, one_day_put_price = black_scholes(spot, strike, 1.0/365, 0,vol)\n",
        "data = pd.DataFrame({'spot': spot, 'one day expiring put price': one_day_put_price, 'payoff': payoff, 'everlasting put price (funding 2x daily)' : ever_price,}).set_index('spot')\n",
        "figure(figsize=(12, 9), dpi=80)\n",
        "ax = sbn.lineplot(data=data)\n",
        "ax.set_ylabel(\"value\")\n",
        "ax.set_title(\"Put Price vs. Spot Price (3000 strike, 100 vol)\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "Text(0.5, 1.0, 'Put Price vs. Spot Price (3000 strike, 100 vol)')"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 66
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 960x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "jYtjKdTb7k4D"
      },
      "source": [
        "# Portfolio Composition"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ndJ90eLd7miS"
      },
      "source": [
        "expos = np.arange(10)\n",
        "\n",
        "comp_pre = 1.0 / 2 ** (expos+1)\n",
        "\n",
        "\n",
        "remaining = np.copy(comp_pre)\n",
        "remaining[0] = 0\n",
        "\n",
        "will_expire = np.zeros(10)\n",
        "will_expire[0] = 0.5\n",
        "\n",
        "init_df = pd.DataFrame({'will remain after funding (.5 contracts total)' : remaining,\n",
        "                        'will expire at funding (.5 contracts total)' : will_expire},\n",
        "                  index = expos)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 639
        },
        "id": "kSltO7yY8MEW",
        "outputId": "84206f93-3171-4708-a97e-68898bbd9242"
      },
      "source": [
        "my_colors = list(islice(cycle(['teal', 'r']), None, len(df)))\n",
        "init_df.plot(kind=\"bar\",\n",
        "             title=\"Equivalent Portfolio Before Today's Funding Payment\",\n",
        "             ylabel = \"contracts\",\n",
        "             xlabel = \"days until expiry\",\n",
        "             color = my_colors,\n",
        "             stacked=True,\n",
        "            figsize = (12, 9))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f4be7b1da90>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 64
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 960x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 639
        },
        "id": "QWqDaF739nHd",
        "outputId": "295ba235-e9ec-4a97-8db8-ef1e93d1120d"
      },
      "source": [
        "added = np.copy(remaining)\n",
        "\n",
        "after_df = pd.DataFrame({\n",
        "                   'left over position (.5 contracts total)' : remaining,\n",
        "                   'added at funding (.5 contracts total)' : added}, \n",
        "                  index = expos)\n",
        "my_colors = list(islice(cycle(['teal', 'orange']), None, len(df)))\n",
        "after_df.plot(kind=\"bar\",\n",
        "             title=\"Equivalent Portfolio After Today's Funding Payment\",\n",
        "             ylabel = \"contracts\",\n",
        "             xlabel = \"days until expiry\",\n",
        "             stacked=True,\n",
        "              color = my_colors,\n",
        "            figsize = (12, 9))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.axes._subplots.AxesSubplot at 0x7f4be7c578d0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 62
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 960x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "UXENe4qa_ofe"
      },
      "source": [
        ""
      ],
      "execution_count": null,
      "outputs": []
    }
  ]
}