Method_2_LN_LN_Model.ipynb

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      "name": "Method_2_LN_LN_Model.ipynb",
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        "<a href=\"https://colab.research.google.com/github/brentianpalmer/COVID-19/blob/master/Method_2_LN_LN_Model.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
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    {
      "cell_type": "code",
      "metadata": {
        "id": "QBfvGwQxcOlP"
      },
      "source": [
        "import math\n",
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "import matplotlib.pyplot as plt"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
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      "source": [
        "#@title\n",
        "# The primary class for calculating Generalized Black Scholes option prices and deltas\n",
        "# It is not intended to be part of this module's public interface\n",
        "\n",
        "# Inputs: option_type = \"p\" or \"c\", fs = price of underlying, x = strike, t = time to expiration, r = risk free rate\n",
        "#         b = cost of carry, v = implied volatility\n",
        "# Outputs: value, delta, gamma, theta, vega, rho\n",
        "def _gbs(option_type, fs, x, t, r, b, v):\n",
        "    # logging.debug(\"Debugging Information: _gbs()\")\n",
        "    # -----------\n",
        "    # Test Inputs (throwing an exception on failure)\n",
        "    # _gbs_test_inputs(option_type, fs, x, t, r, b, v)\n",
        "\n",
        "    # -----------\n",
        "    # Create preliminary calculations\n",
        "    t__sqrt = math.sqrt(t)\n",
        "    d1 = (math.log(fs / x) + (b + (v * v) / 2) * t) / (v * t__sqrt)\n",
        "    d2 = d1 - v * t__sqrt\n",
        "\n",
        "    if option_type == \"c\":\n",
        "        # it's a call\n",
        "        # logging.debug(\"     Call Option\")\n",
        "        value = fs * math.exp((b - r) * t) * norm.cdf(d1) - x * math.exp(-r * t) * norm.cdf(d2)\n",
        "        delta = math.exp((b - r) * t) * norm.cdf(d1)\n",
        "        gamma = math.exp((b - r) * t) * norm.pdf(d1) / (fs * v * t__sqrt)\n",
        "        theta = -(fs * v * math.exp((b - r) * t) * norm.pdf(d1)) / (2 * t__sqrt) - (b - r) * fs * math.exp(\n",
        "            (b - r) * t) * norm.cdf(d1) - r * x * math.exp(-r * t) * norm.cdf(d2)\n",
        "        vega = math.exp((b - r) * t) * fs * t__sqrt * norm.pdf(d1)\n",
        "        rho = x * t * math.exp(-r * t) * norm.cdf(d2)\n",
        "    else:\n",
        "        # # it's a put\n",
        "        # logging.debug(\"     Put Option\")\n",
        "        value = x * math.exp(-r * t) * norm.cdf(-d2) - (fs * math.exp((b - r) * t) * norm.cdf(-d1))\n",
        "        delta = -math.exp((b - r) * t) * norm.cdf(-d1)\n",
        "        gamma = math.exp((b - r) * t) * norm.pdf(d1) / (fs * v * t__sqrt)\n",
        "        theta = -(fs * v * math.exp((b - r) * t) * norm.pdf(d1)) / (2 * t__sqrt) + (b - r) * fs * math.exp(\n",
        "            (b - r) * t) * norm.cdf(-d1) + r * x * math.exp(-r * t) * norm.cdf(-d2)\n",
        "        vega = math.exp((b - r) * t) * fs * t__sqrt * norm.pdf(d1)\n",
        "        rho = -x * t * math.exp(-r * t) * norm.cdf(-d2)\n",
        "\n",
        "    # logging.debug(\"     d1= {0}\\n     d2 = {1}\".format(d1, d2))\n",
        "    # logging.debug(\"     delta = {0}\\n     gamma = {1}\\n     theta = {2}\\n     vega = {3}\\n     rho={4}\".format(delta, gamma,\n",
        "    #                                                                                                     theta, vega,\n",
        "    #                                                                                                     rho))\n",
        "\n",
        "    return value, delta, gamma, theta, vega, rho\n",
        "\n",
        "\n",
        "\n",
        "def black_76(option_type, fs, x, t, r, v):\n",
        "    \"\"\"Commodity option pricing.\n",
        "    The Black 76 model is for an option where the underlying commodity is traded\n",
        "    based on a future price rather than a spot price. Instead of dealing with a\n",
        "    spot price that drifts upwards at the risk free rate, this model deals with\n",
        "    a forward price that needs to be present valued.\n",
        "    Args:\n",
        "        option_type (str): Type of the option. \"p\" for put and \"c\" for call options.\n",
        "        fs (float): Price of underlying asset.\n",
        "        x (float): Strike price.\n",
        "        t (float): Time to expiration in years. 1 for one year, 0.5 for 6 months.\n",
        "        r (float): Risk free rate.\n",
        "        v (float): Implied volatility of underlying asset.\n",
        "    Returns:\n",
        "        value (float): Price of the option.\n",
        "        delta (float): First derivative of value with respect to price of underlying.\n",
        "        gamma (float): Second derivative of value w.r.t price of underlying.\n",
        "        theta (float): First derivative of value w.r.t. time to expiration.\n",
        "        vega (float): First derivative of value w.r.t. implied volatility.\n",
        "        rho (float): First derivative of value w.r.t. risk free rates.\n",
        "    \"\"\"\n",
        "    b = 0\n",
        "    return _gbs(option_type, fs, x, t, r, b, v)\n",
        "\n",
        "# Black Scholes: stock Options (no dividend yield)\n",
        "def black_scholes(option_type, fs, x, t, r, v):\n",
        "    b = r\n",
        "    return _gbs(option_type, fs, x, t, r, b, v)"
      ],
      "execution_count": null,
      "outputs": []
    },
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        "outputId": "29481555-e991-40f7-a2b1-6481fd604ab6"
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      "source": [
        "#@title\n",
        "# Generating Correlated Random Samples from Normal distribution from Hull Chapter 21\n",
        "Nsim = 100000\n",
        "rho_sl = 0.9\n",
        "rand1 = np.random.normal(0,1,Nsim) # random sample from standard normal dist\n",
        "rand2 = np.random.normal(0,1,Nsim) # another random sample from different standard normal dist\n",
        "eps = rand1 # eps for stock lognormal simulation\n",
        "eps_tilda = (rho_sl*rand1)+rand2*np.sqrt(1-rho_sl**2) # eps for libor lognormal simulation\n",
        "plt.scatter(eps,eps_tilda)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.collections.PathCollection at 0x7f732f3a9ad0>"
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          "metadata": {
            "tags": []
          },
          "execution_count": 79
        },
        {
          "output_type": "display_data",
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            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "-6TYGM1Idbw1"
      },
      "source": [
        "# Method II: Equity Log-normal, Libor Log-Normal"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "HV-9R0Qsdnbu"
      },
      "source": [
        "### Model Parameters"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "72_neNJ9dmmZ"
      },
      "source": [
        "# -------- Initial Values --------- # \n",
        "S0 = 271.27211906501435 # equity_initial_value NI225 quote today: 29518.3400, converted to USD: 29518.3400  / 108.8145\n",
        "q = 0.0 # Ni225 pays no div\n",
        "r_f = -0.00138 # Japan 3 year government bond yield (from market data (3yr yield)\n",
        "delta = 0.25\n",
        "T = 3.0\n",
        "\n",
        "# -------- Correlations --------- #  \n",
        "# Correlation stock and exchange rate #\n",
        "rho_sx = -0.3049678 # correl (NI225 in USD, USD/JPY (DOM exchange rate))\n",
        "\n",
        "# Correlation stock and bond #\n",
        "rho_sp = -0.65 # Correl (NI225 in USD, bond maturing in 3 years) *** THIS IS MADE UP *** \n",
        "# (maybe pull from nikkei in USD and r_f???)\n",
        "\n",
        "## Correlation stock and libor #\n",
        "rho_sl = 0.65 # Correl (NI225 in USD, Libor) *** THIS IS MADE UP ***\n",
        "\n",
        "# ** IMPORTANT ** \n",
        "# rho_sl and rho_sp are linked, but they are not the same\n",
        "# need to comment / research relationship\n",
        "# perhaps can assume rho_sl = -rho_sp  \n",
        "# ** IMPORTANT **\n",
        "\n",
        "# -------- Volatilities --------- #  \n",
        "sigma_s = 0.199468950979314 # Volatility of NI225 in USD\n",
        "sigma_x = 0.0519824811701589  # Volatility of USD/JPY (DOM exchange rate).\n",
        "sigma_l = 0.08 # Libor Vol *** THIS IS MADE UP ***\n",
        "sigma_p = 0.05 # vol of the bond that is 3 years *** THIS IS MADE UP *** "
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "1kk_d2uPSNER"
      },
      "source": [
        "### Equity Log-normal Model"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "53t6yCuadZwK"
      },
      "source": [
        "# quanto adjustment = r_f - q - rho_sx sigma_s sigma_x \n",
        "quanto_adj = r_f - q - rho_sx * sigma_s * sigma_x\n",
        "\n",
        "girsanov_chg_measure_QT = sigma_s * sigma_p * rho_sp\n",
        "\n",
        "# Process for Generating Correlated Random Samples from Normal distribution from Hull Chapter 21\n",
        "np.random.seed(456)\n",
        "Nsim = 10000\n",
        "rand1 = np.random.normal(0,1,Nsim) # random sample from standard normal dist\n",
        "rand2 = np.random.normal(0,1,Nsim) # another random sample from different standard normal dist\n",
        "\n",
        "eps = rand1 # eps for stock lognormal simulation\n",
        "eps_tilda = (rho_sl*rand1)+rand2*np.sqrt(1-rho_sl**2) # eps for libor lognormal simulation\n",
        "\n",
        "# As a result, we now can simulate ST with a one-step monte carlo as follows:\n",
        "ST = S0 * np.exp((quanto_adj + girsanov_chg_measure_QT-0.5*sigma_s*sigma_s)*T + sigma_s*np.sqrt(T)*eps) # The MC scheme with vectorized NumPy code handling all paths at once.\n",
        "ST_avg = np.average(ST)\n",
        "\n",
        "ST_over_S0 = ST/S0\n",
        "ST_over_S0_avg = np.average(ST_over_S0)\n"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "cellView": "form",
        "id": "85jzp4SAc5HQ",
        "outputId": "d129b182-1396-4ace-bf6e-f4a64948e6cc"
      },
      "source": [
        "#@title\n",
        "# Chart for 1 step MC simulation of equity price ST\n",
        "x=[]\n",
        "y=[]\n",
        "for i in ST:\n",
        "    y.append(i)\n",
        "    y.append(S0)\n",
        "    x.append(1)            \n",
        "    x.append(0)            \n",
        "    \n",
        "plt.title(\"One-Step Monte Carlo Simulation for Stock\")\n",
        "plt.plot(x, y, label='paths')\n",
        "plt.axhline(ST.mean(), color='r', label='mean value of ST')\n",
        "plt.legend(loc='upper left')\n",
        "plt.xticks()\n",
        "plt.xticks(np.arange(0, 1.1, step=1))\n",
        "plt.xticks([0, 1],['0','T'])\n",
        "print(\"ST mean: \", ST.mean())"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ST mean:  267.35730895270837\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 813
        },
        "id": "-vodZuVnkKkG",
        "outputId": "c69520e0-e00a-41fa-ed9a-db423035a1ae"
      },
      "source": [
        "#@title\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.hist(ST, bins=35, label='ST')\n",
        "plt.axvline(ST_avg, color='r', label='ST_avg')\n",
        "plt.title(\"ST Outcomes\")\n",
        "plt.legend(loc=0)\n",
        "print(\"ST_avg: \" , ST_avg)\n",
        "plt.legend(loc=0)\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.hist(ST_over_S0, bins=35, label='Stock Payoff (ST/SO)')\n",
        "plt.title(\"Stock Payoff (ST/S0)\")\n",
        "plt.axvline(ST_over_S0_avg, color='r', label='Stock_payoff_avg')\n",
        "plt.legend(loc=0)\n",
        "print(\"ST_over_S0_avg (ST/S0): \", ST_over_S0_avg)\n",
        "plt.legend(loc=0)\n",
        "print(\"Stock Portion of Payoff ((ST/S0)- k, where k=1): \", ST_over_S0_avg-1)\n",
        "print:(\"\\n\")"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ST_avg:  267.35730895270837\n",
            "ST_over_S0_avg (ST/S0):  0.9855686971230251\n",
            "Stock Portion of Payoff ((ST/S0)- k, where k=1):  -0.014431302876974916\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "Y_BaiIXBmlbo"
      },
      "source": [
        "#@title\n",
        "class ForwardRates(object):\n",
        "\n",
        "    def __init__(self):\n",
        "        self.forward_rates = []\n",
        "        self.spot_rates = dict()\n",
        "\n",
        "    def add_spot_rate(self, T, spot_rate):\n",
        "        self.spot_rates[T] = spot_rate\n",
        "\n",
        "    def get_forward_rates(self):\n",
        "        \"\"\"\n",
        "        Returns a list of forward rates\n",
        "        starting from the second time period.\n",
        "        \"\"\"\n",
        "        periods = sorted(self.spot_rates.keys())\n",
        "        for T2, T1 in zip(periods, periods[1:]):\n",
        "            forward_rate = self.calculate_forward_rate(T1, T2)\n",
        "            self.forward_rates.append(forward_rate)\n",
        "\n",
        "        return self.forward_rates\n",
        "\n",
        "    def calculate_forward_rate(self, T1, T2):\n",
        "        R1 = self.spot_rates[T1]\n",
        "        R2 = self.spot_rates[T2]\n",
        "        forward_rate = (R2*T2-R1*T1)/(T2-T1)\n",
        "        return forward_rate"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "cellView": "form",
        "id": "AHNWKUbUmvhF"
      },
      "source": [
        "#@title\n",
        "fr = ForwardRates()\n",
        "merged_list = tuple(zip(xp, yp))\n",
        "merged_list\n",
        "\n",
        "for i in merged_list:\n",
        "  fr.add_spot_rate(i[0],i[1])\n",
        "\n",
        "my_fr = fr.get_forward_rates()\n",
        "my_fr_copy = my_fr.copy()\n",
        "my_fr_copy.insert(0,0)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 421
        },
        "cellView": "form",
        "collapsed": true,
        "id": "doN7t9o-m_Bt",
        "outputId": "6992ffaa-d4de-43c0-e200-3efd2e9e014e"
      },
      "source": [
        "#@title\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(xp,yp, '-*', label='Spot Rate')\n",
        "plt.plot(xp,my_fr_copy, '-*', color='r', label='Forward Rate')\n",
        "plt.title(\"Daily US Treasury Yield Curve Rate on May 10, 2021\")\n",
        "plt.xlabel('Maturity')\n",
        "plt.ylabel('Yield (y)')\n",
        "plt.legend(loc=0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f732f0fbc10>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 86
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 388
        },
        "cellView": "form",
        "collapsed": true,
        "id": "D5jb-LGDnCX3",
        "outputId": "48d6c852-5d74-482c-e98e-5555dc6b4c68"
      },
      "source": [
        "#@title\n",
        "x_hat = np.arange(0, 30.25, 0.25)\n",
        "y_interp = np.interp(x_hat, xp, yp)\n",
        "y_fr_interp = np.interp(x_hat,xp,my_fr_copy)\n",
        "# print(x_hat)\n",
        "\n",
        "# points = xp\n",
        "# values = yp\n",
        "# x= x_hat\n",
        "# y = y_interp\n",
        "\n",
        "plt.figure(figsize=(10, 6))\n",
        "plt.plot(xp, yp, 'o')\n",
        "plt.plot(x_hat, y_interp, 'o', alpha=0.5, label='Treasury Yield Curve')\n",
        "plt.plot(xp, my_fr_copy, '*')\n",
        "plt.plot(x_hat, y_fr_interp, '*', alpha=0.5, label=\"Forward Rate Curve\")\n",
        "plt.legend(loc=0)\n",
        "plt.xlabel(\"Maturity\")\n",
        "plt.ylabel(\"Yield\");"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "JUw2r6IgmUCm"
      },
      "source": [
        "#@title\n",
        "# Calculate L0, which is f(0,T)\n",
        "\n",
        "# Start with Daily US Treasury Yield Curve Rate on May 10, 2021\n",
        "# Date\t1 Mo\t2 Mo\t3 Mo\t6 Mo\t1 Yr\t2 Yr\t3 Yr\t5 Yr\t7 Yr\t10 Yr\t20 Yr\t30 Yr\n",
        "# 05/10/21\t0.02\t0.01\t0.02\t0.04\t0.05\t0.16\t0.32\t0.80\t1.27\t1.63\t2.20\t2.32\n",
        "# Source: https://www.treasury.gov/resource-center/data-chart-center/interest-rates/Pages/TextView.aspx?data=yield\n",
        "\n",
        "xp = [1.0/12, 2.0/12, 3.0/12, 0.5, 1, 2, 3, 5, 7, 10, 20, 30]\n",
        "yp = [0.02,\t0.01,\t0.02,\t0.04,\t0.05,\t0.16,\t0.32,\t0.80,\t1.27,\t1.63,\t2.20,\t2.32]"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "bW5aZzRRquSr",
        "outputId": "20822438-b23f-44c0-904f-1e71410541bd"
      },
      "source": [
        "ytm1 = 0.32 # yield on 3Y treasury; used to calculate p(0,T), where T=3 yrs. \n",
        "# ytm1 = 0.32, yield on 3Y treasury\n",
        "print (\"ytm1:\", ytm1)\n",
        "\n",
        "ytm2 = np.interp(T-delta, xp, yp) #yield to maturity for T-delta (2.75 months here)\n",
        "print (\"ytm2:\", ytm2)\n",
        "p_0T = 1.0/(1+ytm1/100)**T #price of p(0,T)\n",
        "p_0Td = 1.0/(1+ytm2/100)**(T-delta) #price of p(0,T-delta)\n",
        "\n",
        "print(\"p_0T: \",p_0T,)\n",
        "print(\"p_0Td: \", p_0Td)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ytm1: 0.32\n",
            "ytm2: 0.28\n",
            "p_0T:  0.9904611138858473\n",
            "p_0Td:  0.9923402465011337\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Hrv-OHEV81la"
      },
      "source": [
        "# L0 from Treasury YC via NS method:\n",
        "# L0 = f(0,T)\n",
        "L0 = 0.0034"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "LvTB0fHqoBK8"
      },
      "source": [
        "L_Td = L0 * np.exp(sigma_l * np.sqrt(T - delta) * eps_tilda - 0.5*sigma_l*sigma_l*(T-delta))\n",
        "L_Td_avg = np.average(L_Td)"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "Q-SzyX-6O011",
        "outputId": "f1895510-31eb-4a1c-e009-d6ea94dce26b"
      },
      "source": [
        "plt.figure(figsize=(10, 6))\n",
        "plt.hist(L_Td,  label='L_Td')\n",
        "plt.axvline(L_Td_avg, color='r', label='L_Td_avg')\n",
        "plt.title(\"L_Td Outcomes\")\n",
        "plt.legend(loc=0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f732f786dd0>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 92
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "qGpbtbU0FVK8"
      },
      "source": [
        "p_temp1 = p_0T + L_Td * delta * p_0T"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "RzElZ79iFkxA"
      },
      "source": [
        "p_temp2 = np.zeros_like(p_temp1)\n",
        "p_temp2 = p_0T/p_0Td"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "CfudXTkczfWh",
        "outputId": "65016a6d-8897-4549-c474-6235fcb84b98"
      },
      "source": [
        "#Libor portion of final payoff\n",
        "#p(T-Delta,T) and p(0,T-Delta) are both input from the simulated Libor portion\n",
        "def L_portion(pTdT, p_0Td):\n",
        "    return ((1-pTdT)*(p_0T))/(pTdT*(p_0Td-p_0T))\n",
        "\n",
        "L_portion = L_portion(p_temp2, p_temp1)\n",
        "L_portion_avg = np.average(L_portion)\n",
        "L_portion_avg"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "2.272674493955732"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 95
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 406
        },
        "id": "qNbZ2d9yG-N4",
        "outputId": "dc06856e-ad91-4976-93ec-445339724cec"
      },
      "source": [
        "plt.figure(figsize=(10, 6))\n",
        "plt.hist(L_portion, label='L_portion')\n",
        "plt.axvline(L_portion_avg, color='r', label='L_portion_avg')\n",
        "plt.title(\"LT Outcomes\")\n",
        "plt.legend(loc=0)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "<matplotlib.legend.Legend at 0x7f732f8c3490>"
            ]
          },
          "metadata": {
            "tags": []
          },
          "execution_count": 96
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 720x432 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "uy_aL4VJJRdX"
      },
      "source": [
        "S0_denom = np.ones_like(ST)*S0"
      ],
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 298
        },
        "id": "OZPq0qvtHmnZ",
        "outputId": "1e7ae0cb-a615-46b2-a4ea-a60bafd8f66a"
      },
      "source": [
        "k_stock_lognormal = 1\n",
        "k_libor_lognormal = 1\n",
        "pi = np.maximum(0, np.multiply((ST/S0_denom - k_stock_lognormal), (k_libor_lognormal-L_portion)))\n",
        "plt.hist(pi,bins=50)\n",
        "plt.title(\"Method 2: payoff at T\")\n",
        "print(\"Average payoff is:\", np.average(pi))"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Average payoff is: 0.2156762871315974\n"
          ],
          "name": "stdout"
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "9oGHjVdQLwAl",
        "outputId": "82d52f69-f336-41e7-a607-32a4e2ce848e"
      },
      "source": [
        "price = p_0T * np.average(pi)\n",
        "print(price)"
      ],
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "0.2136189755911258\n"
          ],
          "name": "stdout"
        }
      ]
    }
  ]
}