FSP_PS1.ipynb

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  "metadata": {
    "colab": {
      "name": "FSP_PS1.ipynb",
      "provenance": [],
      "toc_visible": true,
      "authorship_tag": "ABX9TyMEbjbpH7YgQFxLse3UeJF2",
      "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/yuvalofek/FinancialSignalProcessing/blob/main/FSP_PS1.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TFvJaHBLuIrm"
      },
      "source": [
        "Imports"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "rOuTLKK_421k"
      },
      "source": [
        "import numpy as np\n",
        "import numpy.random as npr\n",
        "import matplotlib.pyplot as plt "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "M0II-ldquPOQ"
      },
      "source": [
        "# Be a Financial Engineer!"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "5p2bWSGS5KN6"
      },
      "source": [
        "RATE = 0.1\n",
        "def c(s_T,K):\n",
        "  '''\n",
        "  Call option at time T with security price s_T and strike price K\n",
        "  '''\n",
        "  return np.maximum(s_T-K, 0)\n",
        "def p(s_T, K):\n",
        "  '''\n",
        "  Put option at time T with security price s_T and strike price K\n",
        "  '''\n",
        "  return np.maximum(K-s_T, 0)\n",
        "def d_c(s_T, K):\n",
        "  '''\n",
        "  Digital call option at time T with security price s_T and strike price K\n",
        "  '''\n",
        "  return (s_T>K)*1\n",
        "def d_p(s_T,K):\n",
        "  '''\n",
        "  Digital put option at time T with security price s_T and strike price K\n",
        "  '''\n",
        "  return (s_T<K)*1"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pa0b6M--lTeA"
      },
      "source": [
        "###1a \n",
        "$V(S_T)$ for: long call, long put, short call, short put."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Lok0FTvR76ur",
        "outputId": "36c0f816-e144-4911-ed1d-5ce63365f584",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 992
        }
      },
      "source": [
        "#Parameters\n",
        "N = 1000\n",
        "s_Tmx = 100\n",
        "K = 50\n",
        "\n",
        "s_T = np.linspace(0,s_Tmx,N)\n",
        "\n",
        "\n",
        "fig, axes = plt.subplots(2,2, figsize = (15,15))\n",
        "fig.suptitle(r'$V(S_T)$ vs $S_T$', fontsize = 20)\n",
        "axes[0,0].plot(s_T,c(s_T,K))\n",
        "axes[0,0].set_title('Long Call', fontsize = 18)\n",
        "\n",
        "axes[0,1].plot(s_T,p(s_T,K))\n",
        "axes[0,1].set_title('Long Put', fontsize = 18)\n",
        "\n",
        "axes[1,0].plot(s_T,-c(s_T,K))\n",
        "axes[1,0].set_title('Short Call', fontsize = 18)\n",
        "\n",
        "axes[1,1].plot(s_T,-p(s_T,K))\n",
        "axes[1,1].set_title('Short Put', fontsize = 18)\n",
        "\n",
        "for ax in axes.flat:\n",
        "    ax.set(xlabel=r'$S_T$',\n",
        "           ylabel=r'$V(S_T)$',\n",
        "           xlim = (0,s_Tmx))\n",
        "    ax.xaxis.label.set_fontsize(14)\n",
        "    ax.yaxis.label.set_fontsize(14)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
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\n",
            "text/plain": [
              "<Figure size 1080x1080 with 4 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5ftxe4xUlcB6"
      },
      "source": [
        "##1b.  Straddle \n",
        "One unit of a call and one unit of a put for the\n",
        "same security at the same strike price K."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "GlO_kcuEmXpl",
        "outputId": "45ffbb51-2a23-486b-b002-28e9b80ac213",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        }
      },
      "source": [
        "#straddle \n",
        "plt.figure(figsize = (7,7))\n",
        "plt.plot(s_T, c(s_T,K)+p(s_T,K))\n",
        "plt.title('Straddle', fontsize = 18)\n",
        "plt.xlabel(r'$S_T$', fontsize = 14)\n",
        "plt.ylabel(r'$V(S_T)$', fontsize = 14)\n",
        "plt.vlines(K, 0, 50, 'r', '--')\n",
        "plt.ylim(0, 50);\n",
        "plt.xlim(0,s_Tmx)\n",
        "plt.legend([r'$V(S_T)$', 'K'])\n",
        "plt.show()\n",
        "\n",
        "#We indeed see that this is exactly |S_T - K|"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pyue0YHIl_vA"
      },
      "source": [
        "## 1c. Call-Put Spread\n",
        "long a call at $K_1$ and short a call at $K_2$ with $K_1 < K_2$.\n",
        "Graph $V (S_T)$ for one choice of the pair $K_1$, $K_2$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "r2lUGes-suKA",
        "outputId": "7555dc52-63a6-4d71-ffb3-e9754014e191",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        }
      },
      "source": [
        "#call-put spread\n",
        "K1 = 30\n",
        "K2 = 60\n",
        "ymin = -1\n",
        "ymax = 31\n",
        "\n",
        "plt.figure(figsize = (7,7))\n",
        "plt.plot(s_T, c(s_T,K1)-c(s_T,K2))\n",
        "plt.title('Call-Put Spread', fontsize = 18)\n",
        "plt.xlabel(r'$S_T$', fontsize = 14)\n",
        "plt.ylabel(r'$V(S_T)$', fontsize = 14)\n",
        "plt.ylim(ymin, ymax)\n",
        "plt.xlim(0,s_Tmx)\n",
        "plt.vlines(K1, ymin, ymax, 'b',  'dashed')\n",
        "plt.vlines(K2, ymin, ymax, 'r',  'dashed')\n",
        "plt.legend([r'$V(S_T)$', 'K1', 'K2'])\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "tT6wZujMmkd1"
      },
      "source": [
        "## 1d. Butterfly \n",
        "a combination of the following. Let $K_1 < K_2$, and $0 < \\lambda < 1$. Let\n",
        "$K^* = K_1 + (1-\\lambda) K_2$. Then:\n",
        "\n",
        "*   long $\\lambda$ calls at strike price $K_1$\n",
        "*   long (1 - $\\lambda$) calls at strike price $K_2$.\n",
        "*   short 1 call at strike price $K^*$\n",
        "\n",
        "Fix one choice for $K_1 < K_2$. Graph a butterfly $V (S_T)$ for each of the following cases: $\\lambda = 1/3, 1/2, 2/3$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "OKJtWG4NsxuB",
        "outputId": "4af54f40-78c3-4930-a5e1-db1be08c783d",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 904
        }
      },
      "source": [
        "##butterfly\n",
        "K1 = 20\n",
        "K2 = 80\n",
        "ymin = -1\n",
        "ymax = 16\n",
        "fig, axes = plt.subplots(3,1, figsize = (10,15), )\n",
        "fig.subplots_adjust(hspace =0.4)\n",
        "\n",
        "lambd = np.array([1/3, 0.5, 2/3])\n",
        "K_star = lambd*K1 + (1-lambd)*K2\n",
        "\n",
        "for i in range(len(lambd)):\n",
        "  axes[i].plot(s_T, lambd[i]*c(s_T,K1)+(1-lambd[i])*c(s_T,K2)-c(s_T,K_star[i]))\n",
        "  axes[i].set_title(r'Butterfly, $\\lambda$='+str(np.around(lambd[i],2)),\n",
        "                    fontsize = 16)\n",
        "  axes[i].vlines(K1, ymin, ymax, 'b',  'dashed')\n",
        "  axes[i].vlines(K2, ymin, ymax, 'r',  'dashed')\n",
        "  axes[i].vlines(K_star[i], ymin, ymax, 'y',  'dashed')\n",
        "  axes[i].legend([r'$V(S_T)$', 'K1', 'K2', r'$K^*$'])\n",
        "\n",
        "for ax in axes.flat:\n",
        "    ax.set(xlabel=r'$S_T$',\n",
        "           ylabel=r'$V(S_T)$',\n",
        "           xlim = (0,s_Tmx),\n",
        "           ylim = (ymin, ymax)\n",
        "           )\n",
        "    ax.xaxis.label.set_fontsize(14)\n",
        "    ax.yaxis.label.set_fontsize(14)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x1080 with 3 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "2iMkJC06nZJ-"
      },
      "source": [
        "## 1e. Call Ladder\n",
        "with $K_1 < K_2 < K_3$, long one $K_1$ call, short one $K_2$ call, short one\n",
        "$K_3$ call."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "nbn-MWNRszku",
        "outputId": "d32cf5d7-de48-40be-d8da-a8d0f42be117",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        }
      },
      "source": [
        "#Call Ladder \n",
        "K1 = 20\n",
        "K2 = 40\n",
        "K3 = 60\n",
        "ymin = -20\n",
        "ymax = 25\n",
        "\n",
        "plt.figure(figsize = (7,7))\n",
        "plt.plot(s_T, c(s_T,K1)-c(s_T,K2)-c(s_T, K3))\n",
        "plt.title('Call Ladder', fontsize = 18)\n",
        "plt.xlabel(r'$S_T$', fontsize = 14)\n",
        "plt.ylabel(r'$V(S_T)$', fontsize = 14)\n",
        "plt.ylim(ymin, ymax)\n",
        "plt.xlim(0,s_Tmx)\n",
        "plt.vlines(K1, ymin, ymax, 'b',  'dashed')\n",
        "plt.vlines(K2, ymin, ymax, 'r',  'dashed')\n",
        "plt.vlines(K3, ymin, ymax, 'k',  'dashed')\n",
        "plt.legend([r'$V(S_T)$', 'K1', 'K2', 'K3'])\n",
        "plt.show()\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "u8wMiV0MnrZk"
      },
      "source": [
        "## 1f. Digital Call Spread\n",
        "with $K_1 < K_2$, a long a digital call with strike $K_1$ and short\n",
        "a digital call with strike $K_2$."
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "dKJiuSoTtqlJ",
        "outputId": "559dcc62-ce0b-4acf-e8d2-c4b0bedd7c27",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 469
        }
      },
      "source": [
        "#digital call spread\n",
        "K1 = 20\n",
        "K2 = 80\n",
        "ymin = -1\n",
        "ymax = 2\n",
        "plt.figure(figsize = (7,7))\n",
        "plt.plot(s_T, d_c(s_T,K1)-d_c(s_T,K2))\n",
        "plt.title('Digital Call Spread', fontsize = 18)\n",
        "plt.xlabel(r'$S_T$', fontsize = 14)\n",
        "plt.ylabel(r'$V(S_T)$', fontsize = 14)\n",
        "plt.ylim(ymin, ymax)\n",
        "plt.xlim(0,s_Tmx)\n",
        "plt.vlines(K1, ymin, ymax, 'b',  'dashed')\n",
        "plt.vlines(K2, ymin, ymax, 'r',  'dashed')\n",
        "plt.legend([r'$V(S_T)$', 'K1', 'K2'])\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 504x504 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HSTuZS3-uowN"
      },
      "source": [
        "#Binomial Asset Pricing Model\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "gRBgm-rDi7l1"
      },
      "source": [
        "##2.a\n",
        "Q: What is the distribution of $S_n$?\n",
        "\n",
        "A: We first ignore the assumption that $S_0 = 1$, just to get a more general answer: \n",
        "\n",
        "\n",
        "\n",
        "\\begin{equation}\n",
        "S_1 =\n",
        "  \\begin{cases} \n",
        "    u*S_0, & with\\,probability: \\; (p) \\\\\n",
        "    d*S_0, & with\\,probability: \\; (1-p) \n",
        "  \\end{cases}\n",
        "\\end{equation}\n",
        "\n",
        "\\begin{equation}\n",
        "S_2 =\n",
        "  \\begin{cases} \n",
        "    u^2*S_0, & with\\,probability: \\; (p), \\\\\n",
        "    u*d*S_0, & with\\, probability:\\; (2*p*q), \\\\\n",
        "    d^2*S_0, & with\\,probability: \\; (1-p) \n",
        "  \\end{cases}\n",
        "\\end{equation}\n",
        "\n",
        "$\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad\\qquad \\vdots $\n",
        "\n",
        "\\begin{equation}\n",
        "  S_n =  u^k * d^{n-k} * S_0, \\;with\\,probability:\\; (\\binom{n}{k} * p^k * q^{n-k}), \\;0\\leq k\\leq n.\n",
        "\\end{equation}\n",
        "\n",
        "\n",
        "\n",
        "---\n",
        "\n",
        "\n",
        "Q: $R_n = log(S_n/S_0)$, show that $R_n = c_n*Y_n + d_n$ for some constant $c_n$ & $d_n$:\n",
        "\n",
        "A:  We first notice that $k \\sim Binomial(n,p)$. Thus we have:\n",
        "\n",
        "\\begin{equation}\n",
        "  R_n = log (S_n/S_0) \\\\\n",
        "    \\rightarrow R_n = log(u^k * d^{n-k})\\\\\n",
        "    \\rightarrow R_n = k*log(u) + (n-k)*log(d) \\\\\n",
        "    \\rightarrow R_n = k*log(u/d) + n*log(d) \\\\\\\\\n",
        "    \\implies c_n = log(u/d),\\; d_n = n*log(d)\n",
        "\\end{equation}"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "TIVA3WBZK4Re"
      },
      "source": [
        "##2.b\n",
        "\n",
        "Parameters\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RDIwbqIYK6Ul"
      },
      "source": [
        "N = 5\n",
        "SEED = 25\n",
        "\n",
        "r1 = 0.05\n",
        "u1 = 1.1\n",
        "d1 = 1.01\n",
        "S0 = 1\n",
        "\n",
        "p_tilda1 = ((1+r1)-d1)/(u1-d1)\n",
        "\n",
        "\n",
        "npr.seed(25)\n",
        "#We can get K by K = (1+R)^N * S0, like putting S0 into the money market\n",
        "K1 = S0*(1+r1)**N\n",
        "\n",
        "def ER_call(Sn, K = K1):\n",
        "  return np.maximum(0, Sn-K)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "pztn2rLrLXLk"
      },
      "source": [
        "Getting $V_0$ by going through all paths"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Mi4-4A1hxvTG"
      },
      "source": [
        "def get_all_paths(N):\n",
        "  #Thanks to https://stackoverflow.com/questions/22227595/\n",
        "  #    convert-integer-to-binary-array-with-suitable-padding\n",
        "  d = np.arange(0,2**N)\n",
        "  m = N\n",
        "  return (((d[:,None] & (1 << np.arange(m)))) > 0).astype(int)\n",
        "\n",
        "def V0_all_paths(N, V, K, p_tilda, u, d, r, S0= S0):\n",
        "  \n",
        "  #Get all the paths and find the number of heads in each\n",
        "  W_ns = get_all_paths(N)\n",
        "  numH= np.sum(W_ns, axis = 1)\n",
        "  #calculate the probabilities and the S_N for each path\n",
        "  probs = (p_tilda**numH) * (1-p_tilda)**(N-numH)\n",
        "  SN = (u**numH)*(d)**(N-numH)*S0\n",
        "\n",
        "  #finish up with an expectation over V_N going over all paths\n",
        "  V_N = V(SN,K)\n",
        "  V0 = np.sum((V_N*probs)/(1+r)**N)\n",
        "  return V0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "CuyVEQGZYghj",
        "outputId": "1ff43e42-5421-491d-95ae-87a351ac3da5",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "V0_all_paths(N, ER_call, K1, p_tilda1, u1, d1, r1)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.039031475205349914"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 46
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "4VXtgvsqLcLQ"
      },
      "source": [
        "Getting $V_0$ by getting all paths recursively"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "4wROq7AQrzHy"
      },
      "source": [
        "def repl_portf(Vn_H, Vn_T, u, d, r, p_tilda, Wn = np.empty(0), S0= S0):\n",
        "  Sn = S0\n",
        "  if len(Wn) != 0:\n",
        "    numH = np.sum(Wn)\n",
        "    Sn = (u**numH)*(d)**(len(Wn)-numH)*S0\n",
        "  Snp1H = Sn*u\n",
        "  Snp1T = Sn*d\n",
        "\n",
        "  delta_n = (Vn_H - Vn_T)/(Snp1H - Snp1T)\n",
        "  V_n = 1/(1+r)*np.sum(Vn_H*p_tilda +Vn_T*(1-p_tilda))\n",
        "\n",
        "  return delta_n, V_n\n",
        "\n",
        "def V0_recurse (N, V, u, d, r, p_tilda, deltas = None, Wn = np.empty(0),  S0 = S0):\n",
        "  #base case: if path is N long, compute S_N and then V(S_N) and return \n",
        "  if deltas is None: \n",
        "    deltas = np.full(shape = (2**(N-1), N), fill_value = np.inf)\n",
        "  if len(Wn) == N:\n",
        "    numH = np.sum(Wn)\n",
        "    SN = (u**numH)*(d)**(N-numH)*S0\n",
        "    return V(SN), deltas\n",
        "  \n",
        "  numH = np.sum(Wn)\n",
        "  Snp1H = S0*u**(numH+1)*d**(len(Wn)-numH)\n",
        "  Snp1T = S0*u**(numH)*d**(len(Wn)+1-numH)\n",
        "\n",
        "  #from these values, get the V_{n+1}s recursively, keep the delta matrix\n",
        "  V_np1H, deltas = V0_recurse (N, V, u, d, r, p_tilda,\n",
        "                               deltas, np.append(Wn, np.array(1)))\n",
        "  V_np1T, deltas = V0_recurse (N, V,u, d, r, p_tilda,\n",
        "                               deltas, np.append(Wn, np.array(0)))\n",
        "  \n",
        "  #return V_0\n",
        "  delta_n, V_0 = repl_portf(V_np1H, V_np1T, u, d, r, p_tilda, Wn)\n",
        "  \n",
        "  #A bit of a hack to get the deltas in a nice format\n",
        "  #Loop through the possible value that the delta should go to until\n",
        "  #one isn't infinity. Once found, insert the delta_n there. \n",
        "  #This generates a matrix where all rows are different paths\n",
        "  for i in range(0, deltas.shape[0], 2**(N-len(Wn)-1)):\n",
        "    if not(np.isfinite(deltas[i, len(Wn)])):\n",
        "      deltas[i:i+2**(N-len(Wn)-1), len(Wn)] = delta_n\n",
        "      break\n",
        "\n",
        "  return (V_0, deltas)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KTQB6FgsYgaI",
        "outputId": "81ccb331-ca64-4303-a06a-422a120e1ea4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "(V_0, deltas) = V0_recurse(5, ER_call,u1, d1, r1, p_tilda1)\n",
        "V_0"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.039031475205349914"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 13
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "c2VbikmyT2Hy",
        "outputId": "8c1441cc-7def-4b89-faa9-bd2d0c321f26",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 628
        }
      },
      "source": [
        "#plotting\n",
        "plt.figure(figsize = (10,10))\n",
        "for i in range(deltas.shape[0]):\n",
        "  plt.plot(np.arange(0,5), deltas[i,:])\n",
        "  plt.xlabel('n')\n",
        "plt.ylabel(r'$\\Delta_n$', fontsize = 14)\n",
        "plt.title(r'$\\Delta_n$ vs. n', fontsize = 20)\n",
        "plt.xlim(0, N-1)\n",
        "plt.xticks(np.arange(0,N))\n",
        "#plt.ylim(-0.1,1.1)\n",
        "plt.show()"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x720 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "e2LpBMweLlxg"
      },
      "source": [
        "##2.c\n",
        "\n",
        "Monte Carlo"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "ONQdBghfS6ib"
      },
      "source": [
        "def MC(N, m, u, d, r, p, V = None, K = K1, S0 = S0, seed = SEED):\n",
        "  npr.seed(SEED)\n",
        "  numHs = npr.binomial(N, p, size= m)\n",
        "  S_N = (u**numHs)*(d)**(N-numHs)*S0\n",
        "  if V is None:\n",
        "    value =  np.sum(S_N)/(m*(1+r)**N)\n",
        "  else:\n",
        "    value =  np.sum(V(S_N, K))/(m*(1+r)**N)\n",
        "  return value"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MBHYxHBa0iQC"
      },
      "source": [
        "###2c1"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "PGlUwfS0xbQh"
      },
      "source": [
        "Estimating $V_0$ and $S_0$ for N = 5 and M = 1,5,10,32 (in that order)\n"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "7Kr9XTUZuY7E",
        "outputId": "c6a1abfb-61cc-4154-da70-68f64ec52869",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        }
      },
      "source": [
        "M_vals = [1,5,10,32, 1000]\n",
        "\n",
        "S_0 = np.ndarray(shape = (len(M_vals)))\n",
        "V_0 = np.ndarray(shape = (len(M_vals)))\n",
        "for i,m in enumerate(M_vals):\n",
        "  S_0[i] = MC(N,m, u1, d1, r1, p_tilda1)\n",
        "  V_0[i] = MC(N,m, u1, d1, r1, p_tilda1, ER_call)\n",
        "  \n",
        "print('M:\\t\\t\\t1\\t  5\\t    10\\t       32\\t 1000')\n",
        "print('S_0 Estimations:', S_0)\n",
        "print('V_0 Estimations:', V_0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "M:\t\t\t1\t  5\t    10\t       32\t 1000\n",
            "S_0 Estimations: [1.06383508 0.97821834 0.97821834 0.9902049  1.00014637]\n",
            "V_0 Estimations: [0.06383508 0.01276702 0.01276702 0.02311514 0.03809687]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "KKIT7H7LB9y7"
      },
      "source": [
        "We can see how the $V_0$ is going towards the values we got earlier. This became even clearer when I added M = 1000 to the list. "
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "uiNYx6doLwyk"
      },
      "source": [
        "###2c2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8e6J-OqZx0kU"
      },
      "source": [
        "N = 100\n",
        "r2 = 1e-3\n",
        "u2 = 1+5e-3\n",
        "d2 = 1+1e-4\n",
        "\n",
        "p_tilda2 = ((1+r2)-d2)/(u2-d2)\n",
        "K2 = S0*(1+r2)**N"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "VoI-vFpb0dx9",
        "outputId": "df15a196-a4c8-423d-e999-b7017c35d26b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "##Checking for different M\n",
        "M_vals2 = [2,4,8,16,32]\n",
        "\n",
        "S_0 = np.ndarray(shape = (len(M_vals2)))\n",
        "for i,m in enumerate(M_vals2):\n",
        "  S_0[i] = MC(N,m, u2, d2, r2, p_tilda2)\n",
        "\n",
        "\n",
        "print('M:\\t\\t\\t2\\t  4\\t    8\\t       16\\t  32')\n",
        "print('S_0 Estimations:', S_0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "M:\t\t\t2\t  4\t    8\t       16\t  32\n",
            "S_0 Estimations: [1.01281716 0.9993634  0.99689727 0.99534967 0.99906657]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "SojtHSMT1Dy9"
      },
      "source": [
        "All seems good, we are gettng S_0 ~ 1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "HwyByob62MsN",
        "outputId": "6654a040-8f24-4654-9056-72d41ee99db4",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "V_0 = np.ndarray(shape = (len(M_vals)))\n",
        "for i,m in enumerate(M_vals):\n",
        "  V_0[i] = MC(N,m, u2, d2, r2, p_tilda2, ER_call, K2)\n",
        "\n",
        "\n",
        "print('M:\\t\\t\\t1\\t  5\\t    10\\t       32\\t 1000')\n",
        "print('V_0 Estimations:', V_0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "M:\t\t\t1\t  5\t    10\t       32\t 1000\n",
            "V_0 Estimations: [0.02271723 0.00512687 0.00363823 0.00504928 0.00761259]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1ziJtzWJdlNO"
      },
      "source": [
        "It appearrs that the resulting $V_0$ should be somewhere around 0.007 for the new values and $N = 100$"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1mkWbfOBRTJq"
      },
      "source": [
        "#### Calculations for $V_{10}$\n",
        "I saw that this calculation essentially was the same as before, just going $N-10$ deep as opposed to $N$ and also starting at $S_{10}$ for the given $\\omega_{10}$ as opposed to $S_0$. "
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "8qAP7HTbRJiJ",
        "outputId": "79185c8c-2cd5-4c0b-bc5b-82faa0cc57de",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 67
        }
      },
      "source": [
        "S10_H = S0*u2**10\n",
        "S10_T = S0*d2**10\n",
        "\n",
        "V_10H = np.ndarray(shape = (len(M_vals)))\n",
        "V_10T = np.ndarray(shape = (len(M_vals)))\n",
        "for i,m in enumerate(M_vals):\n",
        "  V_10H[i] = MC(N-10,m, u2, d2, r2, p_tilda2, ER_call, K2, S10_H)\n",
        "  V_10T[i] = MC(N-10,m, u2, d2, r2, p_tilda2, ER_call, K2, S10_T )\n",
        "\n",
        "\n",
        "print('M:\\t\\t\\t\\t\\t   1\\t      5\\t\\t10\\t    32\\t     1000')\n",
        "print('V_10 Estimations, previous 10 Heads:', V_10H)\n",
        "print('V_10 Estimations, previous 10 Tails:', V_10T)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "M:\t\t\t\t\t   1\t      5\t\t10\t    32\t     1000\n",
            "V_10 Estimations, previous 10 Heads: [0.06413577 0.03932609 0.03776749 0.04008627 0.04148629]\n",
            "V_10 Estimations, previous 10 Tails: [0.01289704 0.00257941 0.0012897  0.00249967 0.00376811]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "QCTXrtddCLsA"
      },
      "source": [
        "As expected, the value when we have 10 tails is less than that for when we start with 10 heads"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GQ0dlICjSXnZ"
      },
      "source": [
        "####$p_0$ changes"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "q45u7l_pScpV",
        "outputId": "30aff41a-e140-4721-b6f9-70bc149412a3",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 134
        }
      },
      "source": [
        "S_0_09 = np.ndarray(shape = (len(M_vals)))\n",
        "V_0_09 = np.ndarray(shape = (len(M_vals)))\n",
        "S_0_11 = np.ndarray(shape = (len(M_vals)))\n",
        "V_0_11 = np.ndarray(shape = (len(M_vals)))\n",
        "\n",
        "for i,m in enumerate(M_vals):\n",
        "  S_0_09[i] =  MC(N,m, u2, d2, r2, p_tilda2*0.9)\n",
        "  V_0_09[i] = MC(N,m, u2, d2, r2, p_tilda2*0.9, ER_call, K2)\n",
        "  S_0_11[i] =  MC(N,m, u2, d2, r2, p_tilda2*1.1)\n",
        "  V_0_11[i] =  MC(N,m, u2, d2, r2, p_tilda2*1.1, ER_call, K2)\n",
        "  \n",
        "print('M:\\t\\t\\t\\t  1\\t      5\\t\\t 10\\t   32\\t     1000')\n",
        "print('S_0 Estimations for 0.9*P^~:', S_0_09)\n",
        "print('V_0 Estimations for 0.9*P^~:', V_0_09)\n",
        "print('\\n')\n",
        "print('S_0 Estimations for 1.1*P^~:', S_0_11)\n",
        "print('V_0 Estimations for 1.1*P^~:', V_0_11)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "M:\t\t\t\t  1\t      5\t\t 10\t   32\t     1000\n",
            "S_0 Estimations for 0.9*P^~: [1.01276878 0.98937749 0.987908   0.99025389 0.99139292]\n",
            "V_0 Estimations for 0.9*P^~: [0.01276878 0.00255376 0.00127688 0.00263449 0.00381544]\n",
            "\n",
            "\n",
            "S_0 Estimations for 1.1*P^~: [1.03276341 1.00792756 1.00594719 1.00766307 1.00936718]\n",
            "V_0 Estimations for 1.1*P^~: [0.03276341 0.00968986 0.00847831 0.01027257 0.0132871 ]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ol9S52StCWlu"
      },
      "source": [
        "As $p$ goes up, we have a higher likelyhood of getting 'up', so it makes sense that $V_0$ is greater for the $1.1\\tilde{p}$ compared to $0.9\\tilde{p}$\n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5UZIjKWjT-cI"
      },
      "source": [
        "**If I told you that your expected return was better than putting it into a money market, you may still have decided not to purchase this option. Why not?**\n",
        "\n",
        "If the expected return was better, it has no implication of the risk. The risk might be really high, at which point you might not want to purchase the option. \n"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "Ncs-JDqDCmCw"
      },
      "source": [
        "##2.d"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MEL7TTBgClcD"
      },
      "source": [
        " def lookback_option(Wn, u, d, r, S0 =S0):\n",
        "  '''Assume we have a path, Wn that is non-empty'''\n",
        "  N = len(Wn)\n",
        "  n = np.arange(1,N+1)\n",
        "\n",
        "  #number of Hs at each timestamp\n",
        "  numH = np.cumsum(Wn)\n",
        "  #Sn at each time\n",
        "  Sns = (u**numH)*(d)**(n-numH)*S0\n",
        "\n",
        "  #Including the time value of money forward\n",
        "  Sn_w = Sns*(1+r)**(N-n)\n",
        "\n",
        "  #lookback option equation\n",
        "  return np.max(Sn_w[:-1] - Sn_w[-1])"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "U170JS1DIoHh"
      },
      "source": [
        "def V0_recurse_path_dep (N, V, u, d, r, p_tilda, Wn = np.empty(0), S0 = S0):\n",
        "  #base case: if path is N-1 long, compute S_N and then V(S_N) and return \n",
        "  if len(Wn) == N:\n",
        "    return V(Wn, u, d, r)\n",
        "\n",
        "  numH = np.sum(Wn)\n",
        "  Snp1H = S0*u**(numH+1)*d**(len(Wn)-numH)\n",
        "  Snp1T = S0*u**(numH)*d**(len(Wn)+1-numH)\n",
        "\n",
        "  #from these values, get the V_{n+1}s recursively\n",
        "  V_np1H = V0_recurse_path_dep (N, V, u, d, r, p_tilda, np.append(Wn, np.array(1)))\n",
        "  V_np1T = V0_recurse_path_dep (N, V,u, d, r, p_tilda, np.append(Wn, np.array(0)))\n",
        "  #return V_0\n",
        "  _, V_0 = repl_portf(V_np1H, V_np1T, u, d, r, p_tilda, Wn)\n",
        "\n",
        "  return V_0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "MhyU_WFFJLLw"
      },
      "source": [
        "def MC_path_dep(N, m, u, d, r, p, V = None, S0 = S0, seed = SEED):\n",
        "  npr.seed(SEED)\n",
        "  Wns = npr.binomial(1, p, size = (m, N))\n",
        "  VT = np.ndarray(shape = (m))\n",
        "  for i in range(m):\n",
        "    VT[i] = V(Wns[i], u, d, r, S0 =S0)\n",
        "  return np.sum(VT)/(m*(1+r)**N)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "KfOFxmt2I7fg",
        "outputId": "2af5f4fa-c051-4fc4-ac12-83b38d2a7faf",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 34
        }
      },
      "source": [
        "N = 5\n",
        "V_0 = V0_recurse_path_dep(N, lookback_option,u1, d1, r1, p_tilda1)\n",
        "V_0"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "0.0436623100042377"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 25
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xWth9k91JUfl",
        "outputId": "1967a0dd-1e14-44e5-917a-d8688210a69e",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 50
        }
      },
      "source": [
        "\n",
        "M_val = [1, 10, 100, 1_000, 10_000]\n",
        "\n",
        "V0_MC = np.ndarray(shape = (len(M_val)))\n",
        "M_str = ''\n",
        "for i, m in enumerate(M_val):\n",
        "  V0_MC[i] = MC_path_dep(N, m, u1, d1, r1, p_tilda1, lookback_option)\n",
        "  M_str += str(m) + '        '\n",
        "\n",
        "print('M:\\t  ', M_str)\n",
        "print('V_0:', V0_MC)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "M:\t   1        10        100        1000        10000        \n",
            "V_0: [0.12071164 0.04888633 0.05064523 0.04113098 0.04386696]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "NBhkc4hEHJEW"
      },
      "source": [
        "The Monte Carlo and the exact value we get from going over all paths match"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "MXcaHYh8Pe-4"
      },
      "source": [
        "###2d2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "xvqiDU81SILd",
        "outputId": "dd6a6450-fc32-493a-cf58-b75f8006709b",
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 84
        }
      },
      "source": [
        "N = 100\n",
        "\n",
        "M_val = [1, 10, 100, 1_000, 10_000]\n",
        "V0_MC = np.ndarray(shape = (len(M_val)))\n",
        "V0_MC_09 = np.ndarray(shape = (len(M_val)))\n",
        "V0_MC_11 = np.ndarray(shape = (len(M_val)))\n",
        "\n",
        "M_str = ''\n",
        "for i, m in enumerate(M_val):\n",
        "  V0_MC[i] = MC_path_dep(N, m, u2, d2, r2, p_tilda2, lookback_option)\n",
        "  V0_MC_09[i] = MC_path_dep(N, m, u2, d2, r2, (p_tilda2*0.9), lookback_option)\n",
        "  V0_MC_11[i] = MC_path_dep(N, m, u2, d2, r2, (p_tilda2*1.1), lookback_option)\n",
        "  \n",
        "  M_str += str(m) + '        '\n",
        "\n",
        "print('M:\\t\\t\\t\\t     ', M_str)\n",
        "print('E_{p0}(V_N^~), p0 = 0.9*p^~:\\t', V0_MC_09)\n",
        "print('V_0:\\t\\t\\t\\t', V0_MC)\n",
        "print('E_{p0}(V_N^~), p0 = 1.1*p^~:\\t', V0_MC_11)\n",
        "\n"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "M:\t\t\t\t      1        10        100        1000        10000        \n",
            "E_{p0}(V_N^~), p0 = 0.9*p^~:\t [0.03953658 0.0167473  0.01692952 0.01782732 0.01850569]\n",
            "V_0:\t\t\t\t [0.0204957  0.01161356 0.01325806 0.01354813 0.01405035]\n",
            "E_{p0}(V_N^~), p0 = 1.1*p^~:\t [0.0204957  0.00845909 0.00994886 0.01011811 0.01049628]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "OY6aQdZlYift"
      },
      "source": [
        "We see that $E_{0.9\\tilde{p}}(\\tilde{V}_N) > V_0 > E_{1.1\\tilde{p}}(\\tilde{V}_N)$\n"
      ]
    }
  ]
}