FinMktsFinal_Method_2_Sensitivity_Analysis_FINAL.ipynb

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      "name": "FinMktsFinal_Method_2_Sensitivity_Analysis_FINAL",
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      "cell_type": "markdown",
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        "<a href=\"https://colab.research.google.com/github/brentianpalmer/FinMarketsFinal/blob/main/FinMktsFinal_Method_2_Sensitivity_Analysis_FINAL.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "5G4gZfjRt77M"
      },
      "source": [
        "# Pricing Function"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "bNua0W8rgUqm",
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "outputId": "2faba503-4f2a-4646-87cf-f96d429a3fe6"
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      "source": [
        "#@title\n",
        "import math\n",
        "import numpy as np\n",
        "from scipy.stats import norm\n",
        "import matplotlib.pyplot as plt\n",
        "import pprint\n",
        "from statsmodels.iolib.table import SimpleTable\n",
        "import pandas as pd\n",
        "import collections\n",
        "\n",
        "inputs = {\n",
        "          'delta': 0.25, \n",
        "          'T': 3, \n",
        "          'q': 0, \n",
        "          'k_stock_lognormal': 1, \n",
        "          'k_libor_lognormal': 1,\n",
        "          'Nsim': 100000, \n",
        "          'L0': 0.0034, \n",
        "          'sigma_l': 0.08, \n",
        "          'sigma_p': 0.05, \n",
        "          'rho_sl': 0.65, \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,\n",
        "                 0.32,\t0.80,\t1.27,\t1.63,\t2.20,\t2.32], \n",
        "          }\n",
        "\n",
        "def lognormalPricer(inputs):\n",
        "    outputs = {}\n",
        "    T = inputs.get('T')\n",
        "    delta = inputs.get('delta')\n",
        "    k_stock_lognormal = inputs.get('k_stock_lognormal')\n",
        "    S0 = 271.27211906501435\n",
        "    # Japan 3 year government bond yield (from market data (3yr yield)\n",
        "    r_f = -0.00138\n",
        "    # -------- Correlations --------- #\n",
        "    # Correlation stock and exchange rate #\n",
        "    # Live data # rho_sx = -0.3049678  # correl (NI225 in USD, USD/JPY (DOM exchange rate))\n",
        "    rho_sx = -0.3049678  # correl (NI225 in USD, USD/JPY (DOM exchange rate))\n",
        "    # Correl (NI225 in USD, bond maturing in 3 years) *** THIS IS MADE UP ***\n",
        "    rho_sl = inputs.get('rho_sl')\n",
        "    rho_sp = -rho_sl\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",
        "\n",
        "    quanto_adj = r_f - inputs.get('q') - rho_sx * sigma_s * sigma_x\n",
        "    girsanov_chg_measure_QT = sigma_s * inputs.get('sigma_p') * rho_sp\n",
        "\n",
        "    Nsim = inputs.get('Nsim')\n",
        "    # Process for Generating Correlated Random Samples from Normal distribution from Hull Chapter 21\n",
        "    np.random.seed(456)\n",
        "    # random sample from standard normal dist\n",
        "    rand1 = np.random.normal(0, 1, Nsim)\n",
        "    # another random sample from different standard normal dist\n",
        "    rand2 = np.random.normal(0, 1, Nsim)\n",
        "    eps = rand1  # eps for stock lognormal simulation\n",
        "    # eps for libor lognormal simulation\n",
        "    eps_tilda = (rho_sl*rand1)+rand2*np.sqrt(1-rho_sl**2)\n",
        "    outputs['eps'] = eps\n",
        "    outputs['eps_tilda'] = eps_tilda\n",
        "\n",
        "    # As a result, we now can simulate ST with a one-step monte carlo as follows:\n",
        "    # The MC scheme with vectorized NumPy code handling all paths at once.\n",
        "    ST = S0 * np.exp((quanto_adj + girsanov_chg_measure_QT-0.5*sigma_s*sigma_s)*\n",
        "                     T + sigma_s*np.sqrt(T)*eps) \n",
        "    ST_avg = np.average(ST)\n",
        "\n",
        "    # Equity Ratio at time T:\n",
        "    ST_over_S0 = ST/S0\n",
        "    ST_over_S0_avg = np.average(ST_over_S0)\n",
        "\n",
        "    # Equity Ratio vs. strike price k\n",
        "    ST_over_S0_k = ST_over_S0-k_stock_lognormal\n",
        "    ST_over_S0_avg_k = ST_over_S0_avg-k_stock_lognormal\n",
        "\n",
        "    outputs['ST'] = ST\n",
        "    outputs['ST_avg'] = ST_avg\n",
        "    outputs['ST_over_S0'] = ST_over_S0\n",
        "    outputs['ST_over_S0_avg'] = ST_over_S0_avg\n",
        "    outputs['ST_over_S0_k'] = ST_over_S0_k\n",
        "    outputs['ST_over_S0_avg_k'] = ST_over_S0_avg_k\n",
        "\n",
        "    xp = inputs.get('xp')\n",
        "    yp = inputs.get('yp')\n",
        "    L0 = inputs.get('L0')\n",
        "\n",
        "    x_hat = np.arange(0, 30.25, 0.25)\n",
        "    y_interp = np.interp(x_hat, xp, yp)\n",
        "    \n",
        "    # Y(0,T) is the yield-to-maturity on a zero coupon bond maturing at time T, \n",
        "    # which we use to calculate p(0,T).\n",
        "    y_0T = np.interp(T, xp, yp)\n",
        "\n",
        "    # Y(0,T-delta) is the yield-to-maturity on a zero coupon bond maturing \n",
        "    # at time T-delta. This is used to calculated p(0,T-delta).\n",
        "    y_0Td = np.interp(T-delta, xp, yp)\n",
        "    \n",
        "    # p(0,T) is the value at time 0 of receiving a dollar at time T\n",
        "    # This is also called the discount factor\n",
        "    p_0T = np.exp(-y_0T/100*T)\n",
        "\n",
        "    # p(0,T-delta)is the value at time 0 of receiving a dollar at time T-delta\n",
        "    p_0Td = np.exp(-y_0Td/100*(T-delta)) \n",
        "\n",
        "    # sigma_l is the vol of libor\n",
        "    sigma_l = inputs.get('sigma_l')\n",
        "\n",
        "    # We then simulate L(T-delta,T-delta,T) via a Monte Carlo simulation \n",
        "    # starting at L0\n",
        "    L_TdTdT = L0 * np.exp(sigma_l * np.sqrt(T - delta) * eps_tilda \n",
        "                          - 0.5*sigma_l*sigma_l*(T-delta))\n",
        "    \n",
        "    # Average L(T-delta,T-delta,T) # Numerator of payoff\n",
        "    L_TdTdT_avg = np.average(L_TdTdT) \n",
        "\n",
        "\n",
        "    # We then derive from market data for L(0,T-delta,T) \n",
        "    # L(0,T-delta,T) is L_0TdT #Denominator of payoff\n",
        "    L_0TdT = -(p_0T - p_0Td)/(delta*p_0T)\n",
        "\n",
        "    # Average of L(0,T-delta,T) is L_0TdT #Denominator of payoff L(0,T-delta,T)\n",
        "    L_0TdT_avg = np.average(L_0TdT)\n",
        "\n",
        "    # Libor ratio of payoff L(T-delta,T-delta,T) over L(0,T-delta,T)\n",
        "    L_TdTdT_over_L_0TdT = L_TdTdT/L_0TdT\n",
        "    L_TdTdT_over_L_0TdT_avg = np.average(L_TdTdT_over_L_0TdT)\n",
        "\n",
        "    # Get libor strike K from inputs\n",
        "    k_libor_lognormal = inputs.get('k_libor_lognormal')\n",
        "\n",
        "    k_L_TdTdT_over_L_0TdT_avg = k_libor_lognormal-L_TdTdT_over_L_0TdT_avg\n",
        "    \n",
        "    # Calculate payoff for equity and libor ratios relative to strikes, k, and multiply\n",
        "    pi = np.maximum(0, np.multiply(\n",
        "        (ST_over_S0 - k_stock_lognormal), (k_libor_lognormal-L_TdTdT_over_L_0TdT)))\n",
        "    pi_avg = np.average(pi)\n",
        "\n",
        "    # Discount pi back to today using p(0,T)\n",
        "    price = p_0T * pi_avg\n",
        "\n",
        "    outputs['rho_sp'] = rho_sp\n",
        "    outputs['x_hat'] = x_hat\n",
        "    outputs['y_interp'] = y_interp\n",
        "    outputs['y_0T'] = y_0T\n",
        "    outputs['y_0Td'] = y_0Td\n",
        "    outputs['p_0T'] = p_0T\n",
        "    outputs['p_0Td'] = p_0Td\n",
        "    outputs['L_0TdT'] = L_0TdT\n",
        "    outputs['L_0TdT_avg'] = L_0TdT_avg\n",
        "    outputs['L_TdTdT'] = L_TdTdT\n",
        "    outputs['L_TdTdT_avg'] = L_TdTdT_avg\n",
        "    outputs['L_TdTdT_over_L_0TdT'] = L_TdTdT_over_L_0TdT\n",
        "    outputs['L_TdTdT_over_L_0TdT_avg'] = L_TdTdT_over_L_0TdT_avg\n",
        "    outputs['k_L_TdTdT_over_L_0TdT_avg'] = k_L_TdTdT_over_L_0TdT_avg\n",
        "    outputs['pi'] = pi\n",
        "    outputs['pi_avg'] = pi_avg\n",
        "    outputs['price'] = price\n",
        "\n",
        "    return outputs\n",
        "\n",
        "\n",
        "# print(\"Complete\")\n",
        "\n"
      ],
      "execution_count": 1,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/statsmodels/tools/_testing.py:19: FutureWarning: pandas.util.testing is deprecated. Use the functions in the public API at pandas.testing instead.\n",
            "  import pandas.util.testing as tm\n"
          ],
          "name": "stderr"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "GG3kAICSj_kY"
      },
      "source": [
        "#Graph Functions"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "IiWiX2m26IiY"
      },
      "source": [
        "#@title\n",
        "def stock_graph():\n",
        "    S0 = inputs.get('S0')\n",
        "    ST = outputs.get('ST')\n",
        "    ST_avg = outputs.get('ST_avg')\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",
        "    plt.figure(figsize=(10, 6))\n",
        "    plt.title(\"One-Step Monte Carlo Simulation for Stock\")\n",
        "    plt.plot(x, y, label='paths')\n",
        "    plt.axhline(ST_avg, 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())\n",
        "    plt.show()\n",
        "\n",
        "def ST_outcomes():\n",
        "    ST = outputs.get('ST')\n",
        "    ST_avg = outputs.get('ST_avg')\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(\"Stock at Time T Outcomes\")\n",
        "    plt.xlabel('Stock Price') # Add an x-label to the axes.\n",
        "    plt.ylabel('Frequency') # Add a y-label to the axes.\n",
        "    plt.legend(loc=0)\n",
        "    print(\"ST Average: \", ST_avg)\n",
        "    plt.legend(loc=0)\n",
        "    plt.show()\n",
        "\n",
        "def ST_over_SO_outcomes():\n",
        "    ST_over_S0_avg = outputs.get('ST_over_S0_avg')\n",
        "    ST_over_S0 = outputs.get('ST_over_S0')\n",
        "    plt.figure(figsize=(10, 6))\n",
        "    plt.hist(ST_over_S0, bins=35, label='(ST/SO)')\n",
        "    plt.title(\"Stock Payoff (ST/S0)\")\n",
        "    plt.xlabel('(ST/S0)') # Add an x-label to the axes.\n",
        "    plt.ylabel('Frequency') # Add a y-label to the axes.\n",
        "    plt.axvline(ST_over_S0_avg, color='r', label='(ST/SO) Avg')\n",
        "    plt.legend(loc=0)\n",
        "    print(\"(ST/S0) Average: \", 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",
        "    plt.show()\n",
        "\n",
        "def yield_curve_display():\n",
        "    xp = inputs.get('xp')\n",
        "    yp = inputs.get('yp')\n",
        "    x_hat = outputs.get('x_hat')\n",
        "    y_interp = outputs.get('y_interp')\n",
        "    plt.figure(figsize=(10, 6))\n",
        "    plt.plot(xp, yp, 'o', label='US Treasury Yield Curve Constant Maturity Rates')\n",
        "    plt.title(\"Interpolated US Treasury Yield Curve Rates on May 10, 2021\")\n",
        "    plt.plot(x_hat, y_interp, 'o', alpha=0.5, label='Interpolated Treasury Yield Curve')\n",
        "    plt.legend(loc=0)\n",
        "    plt.xlabel(\"Maturity\")\n",
        "    plt.ylabel(\"Yield\")\n",
        "    plt.show()\n",
        "\n",
        "def TS_info():\n",
        "    y_0T = outputs.get('y_0T')\n",
        "    print (\"y_0T:\", y_0T)\n",
        "    y_0Td = outputs.get('y_0Td') \n",
        "    print (\"y_0Td:\", y_0Td)\n",
        "    p_0T = outputs.get('p_0T') \n",
        "    print(\"p_0T: \",p_0T)    \n",
        "    L0 = inputs.get('L0')\n",
        "    print(\"L0: \",L0)\n",
        "\n",
        "# (L(T-D,T-D,T) / L(0,T-D,T)\n",
        "\n",
        "def L_TdTdT_Outcomes():\n",
        "    L_TdTdT = outputs.get('L_TdTdT')\n",
        "    L_TdTdT_avg = outputs.get('L_TdTdT_avg')\n",
        "    plt.figure(figsize=(10, 6))\n",
        "    plt.hist(L_TdTdT, bins=35, label='(L(T-D,T-D,T)')\n",
        "    plt.axvline(L_TdTdT_avg, color='r', label='(L(T-D,T-D,T) Average')\n",
        "    plt.title(\"(L(T-D,T-D,T) Outcomes\")\n",
        "    plt.xlabel('(L(T-D,T-D,T)') # Add an x-label to the axes.\n",
        "    plt.ylabel('Frequency') # Add a y-label to the axes.\n",
        "    print(\"(L(T-D,T-D,T) Average: \", L_TdTdT_avg)\n",
        "    plt.legend(loc=0)\n",
        "    plt.show()\n",
        "\n",
        "def L_TdTdT_over_L_0TdT_Outcomes():\n",
        "    L_TdTdT_over_L_0TdT = outputs.get('L_TdTdT_over_L_0TdT')\n",
        "    L_TdTdT_over_L_0TdT_avg = outputs.get('L_TdTdT_over_L_0TdT_avg')\n",
        "    print(\"(L(T-D,T-D,T) / L(0,T-D,T) Average: \", L_TdTdT_over_L_0TdT_avg)\n",
        "    plt.figure(figsize=(10, 6))\n",
        "    plt.hist(L_TdTdT_over_L_0TdT, bins=35, label='(L(T-D,T-D,T) / L(0,T-D,T)')\n",
        "    plt.axvline(L_TdTdT_over_L_0TdT_avg, color='r', label='(L(T-D,T-D,T) / L(0,T-D,T) Avg')\n",
        "    plt.title(\"(L(T-D,T-D,T) / L(0,T-D,T) Outcomes\")\n",
        "    plt.xlabel('(L(T-D,T-D,T) / L(0,T-D,T)') # Add an x-label to the axes.\n",
        "    plt.ylabel('Frequency') # Add a y-label to the axes.\n",
        "    plt.legend(loc=0)\n",
        "    plt.show()\n",
        "\n",
        "def pi_outcomes():\n",
        "    plt.figure(figsize=(10, 6))\n",
        "    pi = outputs.get('pi')\n",
        "    pi_avg = outputs.get('pi_avg')\n",
        "    plt.xlabel('pi') # Add an x-label to the axes.\n",
        "    plt.ylabel('Frequency') # Add a y-label to the axes.\n",
        "    plt.hist(pi, bins=50, label='pi')\n",
        "    plt.axvline(pi_avg, color='r', label='pi Average')\n",
        "    plt.title(\"Method 2: Payoff (pi) at T\")\n",
        "    print(\"Average payoff is: \", pi_avg)\n",
        "    plt.show()\n",
        "\n",
        "def display_price():\n",
        "    price = outputs.get('price')\n",
        "    print(\"Discounted Price: \", price)\n"
      ],
      "execution_count": 2,
      "outputs": []
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "AGo8ZdgLnVRB"
      },
      "source": [
        "# Single Simulation"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "ePnuu7km1eJx",
        "cellView": "form",
        "outputId": "d827e5cd-1966-4e53-f117-af644923f7e0"
      },
      "source": [
        "#@title\n",
        "print(\"Inputs:\")\n",
        "\n",
        "for k,v in inputs.items():\n",
        "  print(k,v)"
      ],
      "execution_count": 3,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Inputs:\n",
            "delta 0.25\n",
            "T 3\n",
            "q 0\n",
            "k_stock_lognormal 1\n",
            "k_libor_lognormal 1\n",
            "Nsim 100000\n",
            "L0 0.0034\n",
            "sigma_l 0.08\n",
            "sigma_p 0.05\n",
            "rho_sl 0.65\n",
            "xp [0.08333333333333333, 0.16666666666666666, 0.25, 0.5, 1, 2, 3, 5, 7, 10, 20, 30]\n",
            "yp [0.02, 0.01, 0.02, 0.04, 0.05, 0.16, 0.32, 0.8, 1.27, 1.63, 2.2, 2.32]\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "Bjba6VT6DxV4"
      },
      "source": [
        "outputs = lognormalPricer(inputs)"
      ],
      "execution_count": 4,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "QuCZbA2yvMNm",
        "cellView": "form",
        "outputId": "6e7ceca6-3379-47a9-8289-2774af8ea6c1"
      },
      "source": [
        "#@title\n",
        "display_outputs = {key: outputs[key] for key in outputs.keys()\n",
        "                               & { 'ST_avg', \n",
        "'ST_over_S0_avg', \n",
        "'ST_over_S0_avg_k',\n",
        "'y_0T', 'y_0Td', 'p_0T', 'p_0Td' ,'L_0TdT_avg', 'L_TdTdT_avg', 'L_TdTdT_over_L_0TdT_avg', 'pi_avg', 'price'}}\n",
        "\n",
        "display_outputs_ordered = collections.OrderedDict()\n",
        "\n",
        "display_outputs_ordered['ST_over_S0_avg'] = display_outputs['ST_over_S0_avg']\n",
        "display_outputs_ordered['ST_over_S0_avg_k'] = display_outputs['ST_over_S0_avg_k']\n",
        "display_outputs_ordered['y_0T'] = display_outputs['y_0Td']\n",
        "display_outputs_ordered['p_0T'] = display_outputs['p_0T']\n",
        "display_outputs_ordered['p_0Td'] = display_outputs['p_0Td']\n",
        "display_outputs_ordered['L_0TdT_avg'] = display_outputs['L_0TdT_avg']\n",
        "display_outputs_ordered['L_TdTdT_avg'] = display_outputs['L_TdTdT_avg']\n",
        "display_outputs_ordered['L_TdTdT_over_L_0TdT_avg'] = display_outputs['L_TdTdT_over_L_0TdT_avg']\n",
        "display_outputs_ordered['pi_avg'] = display_outputs['pi_avg']\n",
        "display_outputs_ordered['price'] = display_outputs['price']\n",
        "\n",
        "print(\"Simulation Results:\")\n",
        "for k, v in display_outputs_ordered.items():\n",
        "    print (k, v)\n"
      ],
      "execution_count": 5,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Simulation Results:\n",
            "ST_over_S0_avg 0.98553392905389\n",
            "ST_over_S0_avg_k -0.014466070946109966\n",
            "y_0T 0.28\n",
            "p_0T 0.990445932897216\n",
            "p_0Td 0.9923295690574124\n",
            "L_0TdT_avg 0.007607224574839476\n",
            "L_TdTdT_avg 0.0033990630679548712\n",
            "L_TdTdT_over_L_0TdT_avg 0.44682039218312375\n",
            "pi_avg 0.06387512520111031\n",
            "price 0.06326485796874018\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 834
        },
        "id": "UfJZH6vIhxL0",
        "outputId": "89d49c86-05dc-4e76-a92e-6bb3a76d6bbf"
      },
      "source": [
        "#@title\n",
        "\n",
        "# stock_graph()\n",
        "\n",
        "ST_outcomes()\n",
        "ST_over_SO_outcomes()\n"
      ],
      "execution_count": 6,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "ST Average:  267.34787734491834\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": "stream",
          "text": [
            "(ST/S0) Average:  0.98553392905389\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"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "id": "igCAc7MuvvpV",
        "cellView": "form"
      },
      "source": [
        "#@title\n",
        "df_results = pd.DataFrame.from_dict([display_outputs_ordered])\n",
        "df_results\n",
        "df_results.to_excel(\"df_results.xlsx\", sheet_name='Sheet_name_1')"
      ],
      "execution_count": 7,
      "outputs": []
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 492
        },
        "id": "FkW2HI8IrnuS",
        "outputId": "798d829f-4dd1-4aed-ff11-7d4e31c9dd23"
      },
      "source": [
        "yield_curve_display()\n",
        "TS_info()"
      ],
      "execution_count": 8,
      "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"
          }
        },
        {
          "output_type": "stream",
          "text": [
            "y_0T: 0.32\n",
            "y_0Td: 0.28\n",
            "p_0T:  0.990445932897216\n",
            "L0:  0.0034\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 834
        },
        "id": "PQ5c3BO8rpOe",
        "outputId": "068fcb11-d822-4963-e02e-43f4aa3bfb0d"
      },
      "source": [
        "L_TdTdT_Outcomes()\n",
        "L_TdTdT_over_L_0TdT_Outcomes()\n"
      ],
      "execution_count": 9,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "(L(T-D,T-D,T) Average:  0.0033990630679548712\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": "stream",
          "text": [
            "(L(T-D,T-D,T) / L(0,T-D,T) Average:  0.44682039218312375\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"
          }
        }
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 448
        },
        "id": "PLAVIaqfln6q",
        "outputId": "3ef23345-ef0d-477a-b7ab-7c59cf2e9034"
      },
      "source": [
        "pi_outcomes()\n",
        "display_price()"
      ],
      "execution_count": 10,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "Average payoff is:  0.06387512520111031\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": "stream",
          "text": [
            "Discounted Price:  0.06326485796874018\n"
          ],
          "name": "stdout"
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "CiR_-AZmXvar"
      },
      "source": [
        "# Toggle Stock K from 0 to 2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 852
        },
        "id": "G060_qBm-4kw",
        "cellView": "form",
        "outputId": "2b1121f9-58df-4b55-d39e-3e18d31ca70a"
      },
      "source": [
        "#@title\n",
        "k_stock_values = np.arange(-2, 4.01, 0.01).tolist()\n",
        "toggle_k_stock = []\n",
        "\n",
        "# print(toggle_k_stock)\n",
        "\n",
        "for k in k_stock_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'k_stock_lognormal': k})\n",
        "  toggle_k_stock.append(inputs_k)\n",
        "\n",
        "# for d in toggle_k_stock:\n",
        "#   print(d)\n",
        "\n",
        "toggle_k_stock_outputs = []\n",
        "\n",
        "for i in toggle_k_stock:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_k_stock_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_k_stock_outputs\n",
        "\n",
        "# for d in toggle_k_stock_outputs:\n",
        "#   print(d['price'])\n",
        "\n",
        "# df_toggle_k_stock_outputs = pd.DataFrame[x.pop() for x in mwe]\n",
        "\n",
        "toggle_k_stock_prices = [d['price'] for d in toggle_k_stock_outputs]\n",
        "# toggle_k_stock_prices\n",
        "\n",
        "\n",
        "k_stock_values\n",
        "plt.plot(k_stock_values, toggle_k_stock_prices )\n",
        "plt.title('Impact of Changes in K Stock on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('K Stock') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('k_stock_plots1.png')\n",
        "\n",
        "toggle_k_stock_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_k_stock_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in K Stock on (ST/S0 Avg - k)')\n",
        "plt.plot(k_stock_values, toggle_k_stock_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('K Stock') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('k_stock_plots2.png')\n",
        "toggle_k_stock_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_k_stock_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in K Stock on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(k_stock_values, toggle_k_stock_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('K Stock') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('k_stock_plots3.png')\n",
        "\n",
        "df_toggle_k_stock = pd.DataFrame(list(zip(k_stock_values, toggle_k_stock_prices)),\n",
        "               columns =['k', 'price'])\n",
        "df_toggle_k_stock\n",
        "df_toggle_k_stock.to_excel(\"df_toggle_k_stock.xlsx\", sheet_name='Sheet_name_1')"
      ],
      "execution_count": 11,
      "outputs": [
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "vOfDX4PwXzpi"
      },
      "source": [
        "# Toggle Libor K from 0 to 2"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 852
        },
        "id": "brRnWAtuXbLa",
        "cellView": "form",
        "outputId": "d763d765-259f-48a6-c741-59be3e413326"
      },
      "source": [
        "#@title\n",
        "k_libor_values = np.arange(-2, 3.01, 0.01).tolist()\n",
        "toggle_k_libor = []\n",
        "\n",
        "# print(toggle_k_libor)\n",
        "\n",
        "for k in k_libor_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'k_libor_lognormal': k})\n",
        "  toggle_k_libor.append(inputs_k)\n",
        "\n",
        "# Uncomment to print all output results\n",
        "# for d in toggle_k_libor:\n",
        "#   print(d)\n",
        "\n",
        "toggle_k_libor_outputs = []\n",
        "\n",
        "for i in toggle_k_libor:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_k_libor_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_k_libor_outputs\n",
        "\n",
        "# for d in toggle_k_libor_outputs:\n",
        "#   print(d['price'])\n",
        "\n",
        "toggle_k_libor_prices = [d['price'] for d in toggle_k_libor_outputs]\n",
        "# toggle_k_libor_prices\n",
        "\n",
        "k_libor_values\n",
        "plt.plot(k_libor_values, toggle_k_libor_prices )\n",
        "plt.title('Impact of Changes in K Libor on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('K LIBOR') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('k_libor_plots1.png')\n",
        "\n",
        "toggle_k_libor_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_k_libor_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in K Libor on (ST/S0 Avg - k)')\n",
        "plt.plot(k_libor_values, toggle_k_libor_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('K Libor') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('k_libor_plots2.png')\n",
        "toggle_k_libor_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_k_libor_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in K Libor on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(k_libor_values, toggle_k_libor_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('K Libor') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('k_libor_plots3.png')\n",
        "\n",
        "df_toggle_k_libor = pd.DataFrame(list(zip(k_libor_values, toggle_k_libor_prices)),\n",
        "               columns =['k', 'price'])\n",
        "df_toggle_k_libor\n",
        "df_toggle_k_libor.to_excel(\"df_toggle_k_libor.xlsx\", sheet_name='Sheet_name_1')"
      ],
      "execution_count": 12,
      "outputs": [
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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FnTk9oUmlzNMKxHHo16UZf+7bllfmb+ST5du8jmOMCVMfLNnKpC/TuczXiqtPi6+0+bpaIERkgIisFpF0EbkrSP/rRWSpiKSJyPci0iWg393OeKtF5Hw3cx6PuwZ2okfL+tzx5hIysw95HccYE2aWZe7ltjmL8bVpyPiLuiLi3knp4lwrECISCUwBBgJdgOTAAuCYrqrdVTUReAyY6IzbBRgOdAUGAM840ws50VER/Cu5F4VFypgZi8gvLPI6kjEmTGTl5HLdtBQa1Y7m2St6ExNVuZtBN/cg+gDpqrpeVfOAmcCQwAFUdV/AyzrAkd+KDwFmqmquqm4A0p3phaQ2jevwyCXdSd20hyc/W+N1HGNMGMgtKOT611PJPpjPCyN9xMXGVHoGNwtECyCw4aIMp9uviMhNIrIO/x7EmGMcd5SIpIhISlZWVoUFL48LezYnuU8rnvl6Hd+u8TaLMaZqU1Xue2cZqZv28MSlPenavL4nOTw/Sa2qU1S1HXAncN8xjjtVVX2q6ouLi3Mn4DG4/w9d6dCsLmNnp7Ej57DXcYwxVdTL8zYyJzWDMecmcEGPEz3L4WaByARaBbxu6XQryUzgonKOGxJqRUcyZUQS+3MLuHVWGoUutK5ojAlv367J4u8fruD8rs245dwET7O4WSAWAAki0lZEovGfdJ4bOICIBC79BcBa5/lcYLiIxIhIWyAB+MnFrBUmoVks4wd3Y176Lp79Ot3rOMaYKmR91n5GT19Ih2axTByW6EoLrcciyq0Jq2qBiIwGPgEigZdUdbmIjAdSVHUuMFpE+gH5wB5gpDPuchGZDawACoCbVLXK/Fz5Ul9L5q3bycTP1nDKSY05Ob6R15GMMSFu3+F8rp2WQlRkBC9c5aNOjGub5zKTcLlDms/n05SUFK9j/GJ/bgF/mPQduQVFfDTmDBrWifY6kjEmRBUWKde8uoDv1+7kjWtP4ZSTGlfavEUkVVV9wfp5fpI6XNWNiWLyiCR27c/jtjmL7ValxpgSPfafVXy9OovxQ7pVanEojRUIF3VrUZ97BnXii1U7eGneRq/jGGNC0FupGTz/7XquOrUNI05p7XWcX7EC4bKRp8VzXpdmPPrxSpZkZHsdxxgTQhZu3sPdby/l1JMa839/KN7QhPesQLhMRHhsaA+axtbkrzMWkXM43+tIxpgQsG3vYf7yWion1K/JM5cnUSMy9DbHoZcoDDWoHc2k5EQy9hzi7reX2vkIY6q5w/mFjHothYO5Bbw40heyF7FYgagkvds0Ymz/Dnyw5GdmLthS+gjGmLCkqtz51hKWZu7l6eG96NAs1utIJbICUYluOKsdZyQ0Ydzc5azeluN1HGOMB577Zj3vpW3ltvM60q9LM6/jHJUViEoUESFMHJZIvVo1GD19IYfyqsxv/4wxFeDzFdt57JNVXNizOTee3c7rOKWyAlHJ4mJjeOqyRNKz9jNu7nKv4xhjKsma7TncPHMR3ZrX57E/9qjUG/+UlxUID/Rt34Sbzm7PrJQtvJcW8m0QGmOO054DeVz7agq1Y6KYelVvakWH5P3PfsMKhEdu6ZfAyfENueftpWzYecDrOMYYl+QXFnHT9IVs23uY56/szYn1a3kdqcysQHgkKjKCp4f3okZUBH+dsZDcAjsfYUw4evjDlcxft4sJl3QnqXVDr+McEysQHmreoBZPDO3Jssx9PPLRKq/jGGMq2IyfNvPK/I1cd0ZbhvZu6XWcY2YFwmP9ujTjz33b8sr8jXy6fJvXcYwxFeTH9bv4v3eXcVaHOO4a2NnrOOViBSIE3DmwI91b1Of2N5eQmX3I6zjGmOOUsecgN7yxkNaNazMpuReRHt/4p7ysQISAmKhIJo/oRWGRMmbGIvILi7yOZIwppwO5BVz7agr5hUW8eJWP+rVqeB2p3KxAhIg2jesw4ZLupG7aw5OfrfE6jjGmHIqKlNvmLGbN9hwmj0jipLi6Xkc6LlYgQsjgns1J7tOKZ79Zx3drs7yOY4w5RpO+XMvHy7Zxz6DOnNUhzus4x80KRIi5/w9dSWhal1tnpbEj57DXcYwxZfTx0p956vO1DO3dkmtOb+t1nAphBSLE1IqOZMqIJPbnFnDrrDQKi6xpcGNC3fKtexk7ezFJrRvw8MXdqkQzGmXhaoEQkQEislpE0kXkriD9x4rIChFZIiJfiEibgH6FIpLmPOa6mTPUJDSL5cHBXZmXvotnv073Oo4x5ih27s9l1LRUGtSuwXNX9iYmqmo0o1EWrhUIEYkEpgADgS5AsogUv6feIsCnqj2AN4HHAvodUtVE5zHYrZyhapivFYN7NmfiZ2tYsHG313GMMUHkFRRxw+up7DqQywtX+WgaW9PrSBXKzT2IPkC6qq5X1TxgJjAkcABV/UpVDzovfwCq3k8NXSIiPHxxN1o3qs2YGYvYcyDP60jGmACqyv3vLWPBxj08PrQn3VrU9zpShXOzQLQAAm+dluF0K8k1wMcBr2uKSIqI/CAiFwUbQURGOcOkZGWF31U/sTVrMHlEErv253H7m0vsVqXGhJBX529k5oItjP59ey7s2dzrOK4IiZPUInIF4AMeD+jcRlV9wAjgKRH5zd01VHWqqvpU1RcXV/UvKQumW4v63D2oE5+v3M7L8zZ6HccYA3y/dicPfbiS/l2aMbZ/B6/juMbNApEJtAp43dLp9isi0g+4FxisqrlHuqtqpvN3PfA10MvFrCHt6tPi6d+lGY98vJIlGdlexzGmWtu48wA3TV9I+7i6PHlZIhFVtBmNsnCzQCwAEkSkrYhEA8OBX12NJCK9gOfxF4cdAd0bikiM87wJ0BdY4WLWkCYiPD60B3F1Y/jrjEXkHM73OpIx1VLO4XyunZZChMCLI33UjYnyOpKrXCsQqloAjAY+AVYCs1V1uYiMF5EjVyU9DtQF5hS7nLUzkCIii4GvgEdVtdoWCIAGtaOZlNyLjD2HuOedZXY+wphKVlik3DwzjY07D/DM5b1p1ai215Fc52r5U9WPgI+Kdbs/4Hm/EsabD3R3M1tV5ItvxNj+HXj8k9X0bdeY4X1aex3JmGrjiU9X8+WqHTx0UTdObdfY6ziVIiROUpuyu+GsdpyR0IRx7y9nzfYcr+MYUy28uyiTZ79ex+WntObK37UpfYQwYQWiiomIECYOS6RuTA1uemMhh/LsVqXGuGnxlmzueGsJp7RtxLjBXb2OU6msQFRBcbExPHVZIulZ+xk3d7nXcYwJW9v3HWbUayk0jY3h2St6UyOyem0yq9fShpHTE5pw09ntmZWyhffSfnP1sDHmOB3OL2TUa6nkHC7gxZE+GtWJ9jpSpbMCUYXd0i+Bk+Mbcs/bS9m484DXcYwJG6rKPW8vZfGWbJ68LJFOJ9TzOpInrEBUYVGRETw9vBc1oiIYPWMhuQV2PsKYijD12/W8vSiTv/XvwPldT/A6jmesQFRxzRvU4vGhPVmWuY9HP17ldRxjqryvVu3g0f+s4oLuJzL6nPZex/GUFYgw0L9LM/7UN56X523k0+XbvI5jTJWVviOHMTMW0eXEejxxac+wufFPeVmBCBN3DexEtxb1uP3NJWRmH/I6jjFVzt6D+Vz7agoxNSJ44SoftaLD58Y/5WUFIkzEREUyOTnJ3xzAjEUUFBZ5HcmYKqOgsIjRMxaSmX2I56/sTfMGtbyOFBKsQISR+CZ1mHBJd1I27eHJz9d4HceYKmPCR6v4bu1OHr6oO73bNPI6TsiwAhFmBvdszvCTW/HM1+v4bm343UTJmIo2e8EWXpq3gT/3bcuwk1uVPkI1YgUiDD1wYVcSmtbl1llp7Mg57HUcY0JWysbd3PvuUs5IaMI9gzp5HSfkWIEIQ7WiI5k8Ion9uQWMnbWYoiJrGtyY4jKzD3H966m0bFibyclJRFWzZjTKwt6RMNWhWSwPDu7K9+k7efabdV7HMSakHMwr4LpXU8jNL+KFq3zUr13D60ghyQpEGBvma8Xgns2Z+NkaUjbu9jqOMSFBVbl9zhJWbtvHpBG9aN+0rteRQpYViDAmIjx8cTdaNqzFmBmLyD6Y53UkYzz3ry/T+XDpz9w9sBO/79jU6zghzQpEmIutWYPJyUlk7c/ltjlL7Falplr7z7JtTPxsDZf0asF1Z5zkdZyQZwWiGujesj53D+zM5yu38/K8jV7HMcYTK3/ex9jZaSS2asCES7pX+2Y0ysIKRDXxp77x9OvcjEc+XsnSjL1exzGmUu3an8u1r6YQWzOKqVf2pmYNa0ajLFwtECIyQERWi0i6iNwVpP9YEVkhIktE5AsRaRPQb6SIrHUeI93MWR2ICE9c2oO4ujGMnrGQnMP5XkcyplLkFRRxwxsL2bk/l6lX+mhar6bXkaoM1wqEiEQCU4CBQBcgWUS6FBtsEeBT1R7Am8BjzriNgAeAU4A+wAMi0tCtrNVFg9rRTEruRcaeQ9z7zjI7H2HCnqoy7v3l/LRhN48N7UHPVg28jlSluLkH0QdIV9X1qpoHzASGBA6gql+p6kHn5Q9AS+f5+cBnqrpbVfcAnwEDXMxabfjiGzG2fwfmLt7K7JQtXscxxlWv/7CJ6T9u5oaz2zEksYXXcaocNwtECyBwC5ThdCvJNcDHxzKuiIwSkRQRScnKsnaHyuqGs9pxevsmPDB3OWu253gdxxhXzE/fybj3V3Bup6bcdl5Hr+NUSSFxklpErgB8wOPHMp6qTlVVn6r64uLi3AkXhiIihImX9aRuTA1uemMhh/LsVqUmvGzedZAbpy/kpCZ1eGp4IpERdsVSebhZIDKBwKYRWzrdfkVE+gH3AoNVNfdYxjXl1zS2Jk9dlkh61n4efH+513GMqTD7cwu4dtoCVOHFkT5ia1ozGuXlZoFYACSISFsRiQaGA3MDBxCRXsDz+IvDjoBenwDniUhD5+T0eU43U4FOT2jCjWe3Y+aCLcxdvNXrOMYct6Ii5ZaZaazLOsAzlyfRpnEdryNVaa4VCFUtAEbj37CvBGar6nIRGS8ig53BHgfqAnNEJE1E5jrj7gYewl9kFgDjnW6mgt3arwO+Ng255+2lbNx5wOs4xhyXf362ms9Xbuf+P3Shb/smXsep8iRcLnX0+XyakpLidYwqKTP7EIOe/o5WjWrx1g2nERNlPyIyVc97aZncPDON5D6tmHCx/VK6rEQkVVV9wfqFxElq460WDWrxxKU9WZa5j0c/XuV1HGOO2dKMvdzx5hL6xDfiwcHdrDhUkDIVCBHp4PzSeZnzuoeI3OduNFOZ+ndpxp/6xvPyvI18tmK713GMKbMdOYe5bloKTerG8OwVSURH2ffeilLWd/IF4G4gH0BVl+A/6WzCyF0DO9GtRT1uf3MxW7MPeR3HmFLlFhTyl9dS2Xsonxeu8tG4bozXkcJKWQtEbVX9qVi3gooOY7wVExXJ5OQkCgqVMTMWUVBY5HUkY0qkqtzz9jIWbc5m4rCedGlez+tIYaesBWKniLQDFEBEhgI/u5bKeCa+SR0evrgbKZv28OTna7yOY0yJ/v39Bt5amMEt/RIY2P1Er+OEpagyDncTMBXoJCKZwAbgCtdSGU8NSWzB/PRdPPP1Ok49qQmnJ9jlgia0fL16BxM+WsnAbicw5pwEr+OErTLtQTgN7vUD4oBOqnq6qm50NZnx1LjBXWkfV5dbZqWRlZNb+gjGVJJ1Wfv564xFdDyhHv8c1pMIa0bDNWW9immCiDRQ1QOqmuP8wvnvbocz3qkVHcmUy5PYn5vP2NlpFBWFx+9lTNW291A+172aQnRkBC9c1Zva0WU9CGLKo6znIAaqavaRF04T3IPciWRCRYdmsYy7sCvfrd3Js9+s8zqOqeYKi5S/zljElj0Hee7K3rRsWNvrSGGvrAUiUkR+uX5MRGoBdj1ZNXDZya24sGdzJn62hpSN1tqJ8c4jH63k2zVZPDSkGyfHN/I6TrVQ1gLxBvCFiFwjItfgv4HPq+7FMqFCRJhwcTdaNqzFmBmLyD6Y53UkUw3NSdnCi99v4OrT4hnep7XXcaqNsp6k/gfwMNDZeTykqo+5GcyEjtiaNZicnETW/lxum7PEblVqKlXqpj3c+84y+rZvzH0XdPY6TrVS5t+kq+rHqnqb87Cmt6uZ7uNqiWsAABq2SURBVC3rc/fAzny+cjuvzN/odRxTTfy89xB/eS2VExvUZMqIJKIirRmNynTUd1tEvnf+5ojIvoBHjojsq5yIJlT8qW88/To345GPVrEsc6/XcUyYO5RXyKhpqRzOL+TFq3w0qB3tdaRq56gFQlVPd/7Gqmq9gEesqtrv2qsZEeHxoT1oXDea0dMXknM43+tIJkypKne8tYRlW/fy9PBEEprFeh2pWip1f01EIkXE2oA2ADSsE82k5F5s2XOIe99ZZucjjCue+Xod7y/eyh3nd+Lczs28jlNtlVogVLUQWC0idumAAeDk+EaM7d+BuYu3Mjtli9dxTJj5dPk2Hv9kNRclNuf6s07yOk61VtafITYElovIT8Av96VU1cElj2LC2Q1nteO/63bxwNzl9GrdkA52CMBUgNXbcrh1Vho9W9bn0T/2sBv/eKysBeL/XE1hqpyICGHiZT0Z9PR3jJ6+kPduOp1a0XarUlN+ew7kce20BdSJieL5K33UrGHrk9dKu4qppojcAlwKdALmqeo3Rx6VktCErKaxNXnyskTW7tjP+A+Wex3HVGH5hUXc+MZCtu/L5fkre3NC/ZpeRzKUfg7iVcAHLAUGAv88lomLyAARWS0i6SJyV5D+Z4rIQhEpcO4xEdivUETSnMfcY5mvqTxnJMRxw1ntmPHTFuYu3up1HFNFjX9/Bf9dv4tHL+lOr9YNvY5jHKUdYuqiqt0BROTfQPG7ypVIRCKBKUB/IANYICJzVXVFwGCbgauB24JM4pCqJpZ1fsY7Y/t34KcNu7nn7aX0aFGf+CZ1vI5kqpDXf9jEaz9s4i9nnsQlSS29jmMClLYH8cuF7qp6rLcY7QOkO/eSyANmAkMCB1DVjc79re3ellVYVGQETyf3IjJC+OuMReQWFHodyVQRP6zfxbi5y/l9xzjuGNDJ6zimmNIKRM/AX08DPY7hl9QtgMBrIDOcbmVVU0RSROQHEbko2AAiMsoZJiUrK+sYJm0qWosGtXji0p4szdzLPz5e7XUcUwVs2X2QG15PpU3j2r98wTChpbRfUkcW+/V0VCX+krqNqvqAEcBTzj2xi+ebqqo+VfXFxcW5HMeUpn+XZlx9WjwvzdvAZyu2ex3HhLADuQVcNy2FwiLlxZEnU69mDa8jmSDcbPkqE2gV8Lql061MVDXT+bse+BroVZHhjDvuHtSJbi3qcfubi9mafcjrOCYEFRUpt85KY832HKZcnkRbO2cVstwsEAuABBFpKyLRwHCgTFcjObc0jXGeNwH6AiuOPpYJBTFRkfwrOYn8giLGzFhEQaGdXjK/9tTna/h0xXbuu6ALZyTYnn8oc61AOCe1RwOfACuB2aq6XETGi8hgABE5WUQy8P/O4nkROXIxfWcgRUQWA18Bjxa7+smEsLZN6jDhku6kbNrDU5+v9TqOCSEfLNnKpC/TGeZryZ/6xnsdx5TC1Tt+q+pHwEfFut0f8HwB/kNPxcebD3R3M5tx15DEFsxP38WUr9P53UmNOT2hideRjMeWZe7ltjmL8bVpyEMXdbNmNKoAu/uGcc24wV1pH1eXW2alkZWT63Uc46GsnFxGTUuhUe1onr2iNzFR1oxGVWAFwrimVnQkk0ckkXM4n7Gz0ygqsqbBq6PcgkKufz2V3QfzmHqVj7jYGK8jmTKyAmFc1fGEWMYN7sp3a3fy7DfrvI5jKpmq8n/vLiN10x7+eWki3VrU9zqSOQZWIIzrhp/cigt7NmfiZ2tI2bjb6zimEr08byOzUzIYc057LuhxotdxzDGyAmFcJyJMuLgbLRvWYsyMRWQfzPM6kqkE367J4u8fruD8rs24pV8Hr+OYcrACYSpFbM0a/Cu5F1n7c7njzSV2q9Iwt2HnAUZPX0iHZrFMHJZIhDWjUSVZgTCVpkfLBtw1sDOfrtjOq/M3eh3HuGTf4XyufXUBUZERvHCVjzoxrl5Nb1xkBcJUqj/3jadf56ZM+GgVyzL3eh3HVLDCImXMjEVs2nWQZy5PolWj2l5HMsfBCoSpVCLC40N70rhuNKOnL2R/7rG2Im9C2WP/WcXXq7N4cEhXfndSY6/jmONkBcJUuoZ1opmU3Istew5x7ztL7XxEmHh7YQbPf7ueK3/XhstPaeN1HFMBrEAYT5wc34hb+yXwXtpW5qRkeB3HHKdFm/dw19tLOfWkxtx/YRev45gKYgXCeOaGs9vTt31j7p+7jLXbc7yOY8pp297D/OW1VJrVi+GZy5OoEWmblXBh/0njmcgI4cnLEqkbE8VN0xdyKM9uVVrVHM4v5C+vpXAgt4AXrzqZhnWivY5kKpAVCOOpprE1efKyRNbu2M/4D5aXPoIJGarKnW8tYUnmXp4a3ouOJ8R6HclUMCsQxnNnJMRxw1ntmPHTFt5fvNXrOKaMnvtmPe+lbeW28zrSv0szr+MYF1iBMCFhbP8O9G7TkLvfXsqmXQe8jmNK8cXK7Tz2ySou7NmcG8/+ze3iTZiwAmFCQlRkBJOSexEZIYyevojcAjsfEarWbs/h5plpdGten8f+2MNu/BPGrECYkNGiQS0eG9qDpZl7+cfHq72OY4LIPpjHtdNSqFkjkqlX9aZWtN34J5xZgTAh5fyuJ3D1afG8NG8Dn6/Y7nUcEyC/sIibpi/k5+zDPH9lb06sX8vrSMZlViBMyLl7UCe6tajHbW8uZmv2Ia/jGMfDH65kXvouJlzSnd5tGnodx1QCVwuEiAwQkdUiki4idwXpf6aILBSRAhEZWqzfSBFZ6zxGupnThJaYqEj+lZxEfkERN89cREFhkdeRqr0ZP23mlfkbufb0tgzt3dLrOKaSuFYgRCQSmAIMBLoAySJS/Df4m4GrgenFxm0EPACcAvQBHhAR+8pSjbRtUocJl3RnwcY9PP3FWq/jVGs/bdjN/e8t46wOcdw9qLPXcUwlcnMPog+QrqrrVTUPmAkMCRxAVTeq6hKg+FfE84HPVHW3qu4BPgMGuJjVhKAhiS0Y5mvJ5K/S+X7tTq/jVEsZew5yw+uptGpY+5erzEz14WaBaAFsCXid4XSrsHFFZJSIpIhISlZWVrmDmtA1bnBX2sXV5ZZZaWTl5Hodp1o5mFfAddNSySss4oWRPurXquF1JFPJqvRJalWdqqo+VfXFxcV5Hce4oHZ0FFNGJJFzOJ+xs9MoKrKmwStDUZHyt9mLWb1tH5NHJNEurq7XkYwH3CwQmUCrgNctnW5uj2vCTMcTYhk3uCvfrd3Jc9+u8zpOtTDpy7V8vGwb9wzqzFkd7MtXdeVmgVgAJIhIWxGJBoYDc8s47ifAeSLS0Dk5fZ7TzVRTw09uxR96nMg/P11D6qbdXscJax8v/ZmnPl/L0N4tueb0tl7HMR5yrUCoagEwGv+GfSUwW1WXi8h4ERkMICIni0gGcCnwvIgsd8bdDTyEv8gsAMY73Uw1JSI8ckl3WjSoxZgZaWQfzPM6UlhasXUfY2cvJql1Ax6+uJs1o1HNSbjc7tHn82lKSorXMYzLlmRk88dn5/P7jk15/sretgGrQDv35zJk8jyKVHlvdF+axtb0OpKpBCKSqqq+YP2q9ElqU/30aNmAuwZ25tMV23l1/kav44SNvIIibnx9ITv35zL1Sp8VBwNYgTBV0J/7xtOvc1MmfLSKZZl7vY5T5akq97+3jJ827ubxS3vSvWV9ryOZEGEFwlQ5IsLjQ3vSuG40o6cvZH9ugdeRqrRp/93EzAVbuOn37Rjcs7nXcUwIsQJhqqSGdaJ5engvNu8+yL3vLCVczqVVtnnpOxn/wQr6d2nG3/p39DqOCTFWIEyV1adtI27t14H30rYyJyXD6zhVzqZdB7jxjYW0i6vDk5clEmHNaJhirECYKu3G37enb/vG3D93GWu353gdp8rIOZzPta+mIAIvXnUydWOivI5kQpAVCFOlRUYIT16WSN2YKEZPX8ThfLtVaWkKi5RbZqaxfucBnrk8idaNa3sdyYQoKxCmymsaW5OJwxJZvT2HB99f4XWckPfEp6v5YtUOxl3YhdPaNfE6jglhViBMWDizQxw3nN2OGT9t5v3FW72OE7LeS8vk2a/XMeKU1lzxuzZexzEhzgqECRtj+3cgqXUD7n57KZt2HfA6TshZvCWbO95cwiltGzHuwq72K3RTKisQJmzUiIz45aY2f52xiLwCu1XpETv2HWbUaynExcbwzOVJREfZR9+UztYSE1ZaNqzNY0N7sCRjL//4zyqv44SEw/mFXPdaKjmHC3jhKh+N68Z4HclUEVYgTNg5v+sJXH1aPP/+fgNfrNzudRxPqSr3vL2UxVuymTgskc4n1vM6kqlCrECYsHT3oE50bV6Pv81ZzM97D3kdxzMvfLeetxdlMrZ/BwZ0O8HrOKaKsQJhwlJMVCSTRySRX1DEmBmLKCisfucjvlq1g0c+XsUF3U/kr+e09zqOqYKsQJiw1bZJHSZc0p0FG/fw9BdrvY5TqdJ37GfMjEV0ObEej1/aw65YMuViBcKEtSGJLRjma8nkr9KZl77T6ziVYu/BfK6blkJMjQimXuWjdrQ1o2HKxwqECXvjBnelXVxdbpmVRlZOrtdxXFVQWMToGQvJ2HOQ567oTYsGtbyOZKowKxAm7NWOjmLKiCT2Hcpn7Ow0iorCt2nwCR+t4ru1O3n4ou744ht5HcdUcVYgTLXQ8YRYHriwK9+t3clz367zOo4rZi/YwkvzNvCnvvEMO7mV13FMGHC1QIjIABFZLSLpInJXkP4xIjLL6f+jiMQ73eNF5JCIpDmP59zMaaqH5D6tuKDHifzz0zWkbtrtdZwKlbJxN/e+u5QzEppw76DOXscxYcK1AiEikcAUYCDQBUgWkS7FBrsG2KOq7YEngX8E9FunqonO43q3cprqQ0R45JLutGhQizEz0sg+mOd1pAqRmX2I619PpUWDWkxOTiIq0g4MmIrh5prUB0hX1fWqmgfMBIYUG2YI8Krz/E3gXLHr8YyL6tWsweQRvdiRc5g73lxS5W9VejCvgFHTUsjNL+LFkT7q167hdSQTRtwsEC2ALQGvM5xuQYdR1QJgL9DY6ddWRBaJyDcickawGYjIKBFJEZGUrKysik1vwlaPlg24c0AnPl2xnWn/3eR1nHJTVW6fs4QVP+9jUnIv2jeN9TqSCTOhui/6M9BaVXsBY4HpIvKbRmRUdaqq+lTVFxcXV+khTdV1zeltObdTUx7+cCXLMvd6HadcJn+ZzodLf+auAZ34faemXscxYcjNApEJBF5K0dLpFnQYEYkC6gO7VDVXVXcBqGoqsA7o4GJWU82ICI9f2pNGdaIZPX0h+3MLvI50TP6zbBv//GwNl/RqwagzT/I6jglTbhaIBUCCiLQVkWhgODC32DBzgZHO86HAl6qqIhLnnORGRE4CEoD1LmY11VCjOtFMSu7F5t0Hue+dpVXmfMSqbfsYOzuNnq0aMOGS7taMhnGNawXCOacwGvgEWAnMVtXlIjJeRAY7g/0baCwi6fgPJR25FPZMYImIpOE/eX29qobXdYkmJPRp24hb+3Xg3bStzEnN8DpOqXYfyOPaV1OIrRnF1Ct7U7NGpNeRTBiTqvKtqTQ+n09TUlK8jmGqoMIi5cp//8iizdm8/9e+IXuyN6+gyJ9zSzZz/nIqPVs18DqSCQMikqqqvmD9QvUktTGVJjJCeOqyRGpHR3LTG4s4nF/odaSgHnx/OT9u2M1jf+xhxcFUCisQxgBN69Vk4mWJrN6ew4Pvr/A6zm+89sMm3vhxM9ef1Y6LehW/WtwYd1iBMMZxVoc4bji7HTN+2swHS7Z6HecX89ft5MG5yzm3U1NuP7+j13FMNWIFwpgAY/t3IKl1A+5+aymbdx30Og6bdx3kpjcWEt+kDk8NTyQywq5YMpXHCoQxAWpERjApuRciMHrGQvIKvLtVac7hfK6dtoAihRev8hFb05rRMJXLCoQxxbRsWJvHL+3Jkoy9PPafVZ5kKCxSbpmZxrqsAzx7eRLxTep4ksNUb1YgjAni/K4nMPLUNrz4/Qa+WLm90uf/+Cer+WLVDsZd2IXT2jep9PkbA1YgjCnR3YM607V5Pf42ZzE/7z1UafN9e2EGz32zjit+15orT42vtPkaU5wVCGNKULNGJJNHJJFfUMTNM9IoKHT/fMTCzXu4662lnHpSYx64sKvr8zPmaKxAGHMUbZvU4eGLu/PTxt1M+mKtq/Pamn2IUdNSOaF+TZ65PIkaduMf4zFbA40pxUW9WnBp75b866t05qfvdGUeh/IKGfVaCofzC3lxpI+GdaJdmY8xx8IKhDFl8OCQrrSLq8vNs9LIysmt0GmrKrfNWczyrfuYlJxIh2ah2RaUqX6sQBhTBrWjo5g8ohf7DuUzdnYaRUUV18jlpC/+d+Ofczo1q7DpGnO8rEAYU0adTqjHAxd25bu1O3n+24q5Pcl7aZk8+bnd+MeEJisQxhyD5D6tuKDHiTzx6WpSN+05rmn9sH4Xt89ZwiltG/HIH+3GPyb0WIEw5hiICI9c0p0WDWoxZsYi9h7ML9d00nfkMGpaCq0b12bqlT5iouzGPyb0WIEw5hjVq1mDfyX3YkfOYe54a/Ex36p0a/YhRr60gOioSF6++mTq17Y2lkxosgJhTDn0bNWAOwd04pPl24/pfMT2fYcZ8cIP7DuUz8tXn0yrRrVdTGnM8YnyOoAxVdU1p7clbUs2j368isZ1ornU1+qow2/YeYA/v7KArJxcpl1zCt1b1q+kpMaUj6t7ECIyQERWi0i6iNwVpH+MiMxy+v8oIvEB/e52uq8WkfPdzGlMeYgIE4clckZCE+56eymzFmwucdj56Tu5+Jl57D2Uz7RrTqF3m4aVmNSY8nGtQIhIJDAFGAh0AZJFpEuxwa4B9qhqe+BJ4B/OuF2A4UBXYADwjDM9Y0JKdFQEz13Rm9PaNebOt5Zy88xFbNx5APD/AC59x37ufHMJI178kUZ1onnnxtOsOJgqw81DTH2AdFVdDyAiM4EhQOANf4cA45znbwKTxX+t3xBgpqrmAhtEJN2Z3n9dzGtMudSJieLlq09m0pfpPPfNOt5L20rT2BiKVNm5P4/oyAiuPb0tY8/rQO1oO6prqg4319YWwJaA1xnAKSUNo6oFIrIXaOx0/6HYuHandhOyoiIjGNu/A8l9WvHR0m2s+nkfAN1a1GdQ9xOJi43xOKExx65Kf50RkVHAKIDWrVt7nMYYOLF+La45va3XMYypEG6epM4EAi/raOl0CzqMiEQB9YFdZRwXVZ2qqj5V9cXFxVVgdGOMMW4WiAVAgoi0FZFo/Ced5xYbZi4w0nk+FPhS/b86mgsMd65yagskAD+5mNUYY0wxrh1ics4pjAY+ASKBl1R1uYiMB1JUdS7wb+A15yT0bvxFBGe42fhPaBcAN6lqoVtZjTHG/JYcazMBocrn82lKSorXMYwxpkoRkVRV9QXrZ01tGGOMCcoKhDHGmKCsQBhjjAnKCoQxxpigwuYktYhkAZuOYxJNgJ0VFKeqqG7LXN2WF2yZq4vjWeY2qhr0h2RhUyCOl4iklHQmP1xVt2WubssLtszVhVvLbIeYjDHGBGUFwhhjTFBWIP5nqtcBPFDdlrm6LS/YMlcXriyznYMwxhgTlO1BGGOMCcoKhDHGmKCsQDhE5HERWSUiS0TkHRFp4HUmt4nIpSKyXESKRCSsLwsUkQEislpE0kXkLq/zuE1EXhKRHSKyzOsslUVEWonIVyKywlmvb/Y6k9tEpKaI/CQii51lfrAip28F4n8+A7qpag9gDXC3x3kqwzLgEuBbr4O4SUQigSnAQKALkCwiXbxN5bpXgAFeh6hkBcDfVLUL8Dvgpmrwf84FzlHVnkAiMEBEfldRE7cC4VDVT1W1wHn5A/672IU1VV2pqqu9zlEJ+gDpqrpeVfOAmcAQjzO5SlW/xX+PlWpDVX9W1YXO8xxgJWF+L3v12++8rOE8KuzKIysQwf0Z+NjrEKbCtAC2BLzOIMw3HNWdiMQDvYAfvU3iPhGJFJE0YAfwmapW2DK7dke5UCQinwMnBOl1r6q+5wxzL/5d1TcqM5tbyrLMxoQTEakLvAXcoqr7vM7jNudum4nOedN3RKSbqlbIuadqVSBUtd/R+ovI1cAfgHM1TH4gUtoyVxOZQKuA1y2dbibMiEgN/MXhDVV92+s8lUlVs0XkK/znniqkQNghJoeIDADuAAar6kGv85gKtQBIEJG2IhKN/97ncz3OZCqYiAj++9yvVNWJXuepDCISd+SKSxGpBfQHVlXU9K1A/M9kIBb4TETSROQ5rwO5TUQuFpEM4FTgQxH5xOtMbnAuPhgNfIL/xOVsVV3ubSp3icgM4L9ARxHJEJFrvM5UCfoCVwLnOJ/hNBEZ5HUol50IfCUiS/B/EfpMVT+oqIlbUxvGGGOCsj0IY4wxQVmBMMYYE5QVCGOMMUFZgTDGGBOUFQhjjDFBWYEwpgQisj/g+SARWSMibYoNc7WITA4y7kYRaeI8L3QuuVwsIgtF5LSA4U53WuNc5TxGBfQbJyKZzrgrRCTZnSU1Jrhq9UtqY8pDRM4FJgHnq+qmckzikKomOtM6H3gEOEtETgCmAxep6kKnoHwiIpmq+qEz7pOq+oSIJACpIvKmquYf/1IZUzrbgzDmKETkTOAF4A+quq4CJlkP2OM8vwl4JaAF0p34f83/m/tVqOpa4CDQsAIyGFMmtgdhTMligHeBs1X1eJovqOW0tlkT/y9fz3G6dwVeLTZsitP9V0QkCVirqjuOI4cxx8T2IIwpWT4wHzjeZioOqWqiqnbC35DaNKfdoLK4VUSW42+2+uHjzGHMMbECYUzJioBhQB8RuaciJqiq/wWaAHHACqB3sUF6A4HtRD2pql2BPwL/FpGaFZHDmLKwAmHMUTgt+14AXF4RDd6JSCcgEtiF/zaoV4vIkRPYjYF/AI8FyTEX/+GnkcebwZiysnMQxpRCVXc7zcF/KyJZzsY60NUiclHA6+L3BD5yDgJAgJHOTV5+FpErgBdEJNbp95Sqvl9ClPHAdBF5QVWLjm+pjCmdteZqjDEmKDvEZIwxJigrEMYYY4KyAmGMMSYoKxDGGGOCsgJhjDEmKCsQxhhjgrICYYwxJqj/B11Y3XtZnIrpAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        },
        {
          "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"
          }
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "MGthNYewa3u4"
      },
      "source": [
        "# Toggle L0 from 0.0001 to 0.0040"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 852
        },
        "id": "FRzldIBxa8eA",
        "cellView": "form",
        "outputId": "67b7ccef-b2a8-4806-921f-e98613bd8517"
      },
      "source": [
        "#@title\n",
        "L0_values = np.arange(0.0001, 0.004, 0.00005).tolist()\n",
        "toggle_L0 = []\n",
        "\n",
        "# print(toggle_L0)\n",
        "\n",
        "for k in L0_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'L0': k})\n",
        "  toggle_L0.append(inputs_k)\n",
        "\n",
        "# Uncomment to print all output results\n",
        "# for d in toggle_L0:\n",
        "#   print(d)\n",
        "\n",
        "toggle_L0_outputs = []\n",
        "\n",
        "for i in toggle_L0:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_L0_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_L0_outputs\n",
        "\n",
        "# for d in toggle_L0_outputs:\n",
        "#   print(d['price'])\n",
        "\n",
        "toggle_L0_prices = [d['price'] for d in toggle_L0_outputs]\n",
        "# toggle_L0_prices\n",
        "\n",
        "L0_values\n",
        "plt.plot(L0_values, toggle_L0_prices)\n",
        "plt.title('Impact of Changes in L0 on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('L0') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('L0_plots1.png')\n",
        "toggle_L0_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_L0_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in L0 on (ST/S0 Avg - k)')\n",
        "plt.plot(L0_values, toggle_L0_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('L0') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('L0_plots2.png')\n",
        "\n",
        "toggle_L0_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_L0_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in L0 on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(L0_values, toggle_L0_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('L0') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('L0_plots3.png')\n",
        "\n",
        "df_toggle_L0 = pd.DataFrame(list(zip(L0_values, toggle_L0_prices)),\n",
        "               columns =['L0', 'price'])\n",
        "df_toggle_L0\n",
        "df_toggle_L0.to_excel(\"df_toggle_L0.xlsx\", sheet_name='Sheet_name_1')\n"
      ],
      "execution_count": 13,
      "outputs": [
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "mhP_2v2temhu"
      },
      "source": [
        "# Toggle rho_SL from -1 to 1"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 874
        },
        "id": "yScODD7QemP_",
        "cellView": "form",
        "outputId": "69c02006-3548-4075-9a35-fbcb19e02e99"
      },
      "source": [
        "#@title\n",
        "rho_sl_values = np.arange(-1.0, 1.01, 0.01).tolist()\n",
        "toggle_rho_sl = []\n",
        "\n",
        "# print(toggle_rho_sl)\n",
        "\n",
        "for k in rho_sl_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'rho_sl': k})\n",
        "  toggle_rho_sl.append(inputs_k)\n",
        "\n",
        "# Uncomment to print all output results\n",
        "# for d in toggle_rho_sl:\n",
        "#   print(d)\n",
        "\n",
        "toggle_rho_sl_outputs = []\n",
        "\n",
        "for i in toggle_rho_sl:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_rho_sl_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_rho_sl_outputs\n",
        "\n",
        "# for d in toggle_rho_sl_outputs:\n",
        "#   print(d['price'])\n",
        "\n",
        "toggle_rho_sl_prices = [d['price'] for d in toggle_rho_sl_outputs]\n",
        "# toggle_rho_sl_prices\n",
        "\n",
        "rho_sl_values\n",
        "plt.plot(rho_sl_values, toggle_rho_sl_prices)\n",
        "plt.title('Impact of Changes in rho_sl on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('rho_sl') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('rho_SL_plots1.png')\n",
        "\n",
        "toggle_rho_sl_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_rho_sl_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in rho_sl on (ST/S0 Avg - k)')\n",
        "plt.plot(rho_sl_values, toggle_rho_sl_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('rho_sl') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('rho_SL_plots2.png')\n",
        "toggle_rho_sl_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_rho_sl_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in rho_sl on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(rho_sl_values, toggle_rho_sl_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('rho_sl') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('rho_SL_plots3.png')\n",
        "df_toggle_rho_sl = pd.DataFrame(list(zip(rho_sl_values, toggle_rho_sl_prices)),\n",
        "               columns =['rho_sl', 'price'])\n",
        "df_toggle_rho_sl\n",
        "df_toggle_rho_sl.to_excel(\"df_toggle_rho_sl.xlsx\", sheet_name='Sheet_name_1')\n",
        "\n"
      ],
      "execution_count": 14,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:58: RuntimeWarning: invalid value encountered in sqrt\n"
          ],
          "name": "stderr"
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "J16teuJ_hQlf"
      },
      "source": [
        "# Toggle sigma_l from 0 to 100"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 852
        },
        "id": "cd1RA_mchPWR",
        "outputId": "04721592-92fd-4dca-d126-9622c07513a6"
      },
      "source": [
        "#@title\n",
        "sigma_l_values = np.arange(0, 1.01, 0.01).tolist()\n",
        "toggle_sigma_l = []\n",
        "\n",
        "# print(toggle_sigma_l)\n",
        "\n",
        "for k in sigma_l_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'sigma_l': k})\n",
        "  toggle_sigma_l.append(inputs_k)\n",
        "\n",
        "# Uncomment to print all output results\n",
        "# for d in toggle_sigma_l:\n",
        "#   print(d)\n",
        "\n",
        "toggle_sigma_l_outputs = []\n",
        "\n",
        "for i in toggle_sigma_l:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_sigma_l_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_sigma_l_outputs\n",
        "\n",
        "# for d in toggle_sigma_l_outputs:\n",
        "#   print(d['price'])\n",
        "\n",
        "toggle_sigma_l_prices = [d['price'] for d in toggle_sigma_l_outputs]\n",
        "# toggle_sigma_l_prices\n",
        "\n",
        "sigma_l_values\n",
        "plt.plot(sigma_l_values, toggle_sigma_l_prices)\n",
        "plt.title('Impact of Changes in sigma_l on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('sigma_l') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('sigma_l_plots1.png')\n",
        "toggle_sigma_l_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_sigma_l_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in sigma_l on (ST/S0 Avg - k)')\n",
        "plt.plot(sigma_l_values, toggle_sigma_l_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('sigma_l') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('sigma_l_plots2.png')\n",
        "toggle_sigma_l_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_sigma_l_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in sigma_l on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(sigma_l_values, toggle_sigma_l_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('sigma_l') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('sigma_l_plots3.png')\n",
        "df_toggle_sigma_l = pd.DataFrame(list(zip(sigma_l_values, toggle_sigma_l_prices)),\n",
        "               columns =['sigma_l', 'price'])\n",
        "df_toggle_sigma_l\n",
        "df_toggle_sigma_l.to_excel(\"df_toggle_sigma_l.xlsx\", sheet_name='Sheet_name_1')\n",
        "# print(toggle_sigma_l_outputs_L_TdTdT_over_L_0TdT_avg)"
      ],
      "execution_count": 15,
      "outputs": [
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "xMhYPYrLjs0I"
      },
      "source": [
        "# Toggle sigma_p from 0 to 200"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 852
        },
        "id": "2sT8djaLjViZ",
        "outputId": "b6352a94-df4c-424f-cb1c-7b80dc5fd539"
      },
      "source": [
        "#@title\n",
        "sigma_p_values = np.arange(0, 2, 0.01).tolist()\n",
        "toggle_sigma_p = []\n",
        "\n",
        "# print(toggle_sigma_p)\n",
        "\n",
        "for k in sigma_p_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'sigma_p': k})\n",
        "  toggle_sigma_p.append(inputs_k)\n",
        "\n",
        "# Uncomment to print all output results\n",
        "# for d in toggle_sigma_p:\n",
        "#   print(d)\n",
        "\n",
        "toggle_sigma_p_outputs = []\n",
        "\n",
        "for i in toggle_sigma_p:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_sigma_p_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_sigma_p_outputs\n",
        "\n",
        "# for d in toggle_sigma_p_outputs:\n",
        "#   print(d['price'])\n",
        "\n",
        "toggle_sigma_p_prices = [d['price'] for d in toggle_sigma_p_outputs]\n",
        "# toggle_sigma_p_prices\n",
        "\n",
        "sigma_p_values\n",
        "plt.plot(sigma_p_values, toggle_sigma_p_prices)\n",
        "plt.title('Impact of Changes in sigma_p on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('sigma_p') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('sigma_p_plots1.png')\n",
        "toggle_sigma_p_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_sigma_p_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in sigma_p on (ST/S0 Avg - k)')\n",
        "plt.plot(sigma_p_values, toggle_sigma_p_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('sigma_p') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('sigma_p_plots2.png')\n",
        "toggle_sigma_p_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_sigma_p_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in sigma_p on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(sigma_p_values, toggle_sigma_p_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('sigma_p') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('sigma_p_plots3.png')\n",
        "df_toggle_sigma_p = pd.DataFrame(list(zip(sigma_p_values, toggle_sigma_p_prices)),\n",
        "               columns =['sigma_p', 'price'])\n",
        "df_toggle_sigma_p\n",
        "df_toggle_sigma_p.to_excel(\"df_toggle_sigma_p.xlsx\", sheet_name='Sheet_name_1')"
      ],
      "execution_count": 16,
      "outputs": [
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "output_type": "display_data",
          "data": {
            "image/png": 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2s4DxknaStAkwBZhZrCBpVGF0ElDrKnsUOEjSUEkbky4OWK8bzczMBofKrkaLiLWSpgM3AUOASyNivqSzgM6ImAmcImkSsBZYBUzNzWcAhwDzSBcL/CwirqsqVjMzq5Yior9j6BUdHR3hh6eZmXWPpNkR0VH1cvr7AgEzM/sT4GRjZmaVc7IxM7PKOdmYmVnlnGzMzKxyTjZmZlY5JxszM6uck42ZmVXOycbMzCrnZGNmZpVzsjEzs8o52ZiZWeWcbMzMrHJONmZmVjknGzMzq5yTjZmZVc7JxszMKudkY2ZmlXOyMTOzyjnZmJlZ5ZxszMysck42ZmZWOScbMzOr3NCyCpL2A/4WOBAYBTwH3AtcD1wREU9VGqGZmQ16TY9sJN0InADcBEwkJZvdgDOATYGfSJpUdZBmZja4lR3Z/F1EPF5Xtga4Ow/nShpRSWRmZtY2mh7Z1CcaSZtJGtKsjpmZWb2ybrSNJH1Q0vWS/gjcDyyXdJ+kr0rapaT9REkLJS2SdGqD6VMlrZA0Jw8n5PKDC2VzJD0v6agNWVEzM+s/Zd1otwH/A3wauDciXgGQtA1wMPAVSddExBX1DfMR0AXAYcBSYJakmRFxX13VqyNierEgIm4D3lxY1iLg5u6unJmZDQxlyebQiHipvjAiVgE/An4kaeMu2u4DLIqIxQCSrgImA/XJpszfADdGxLPdbGdmZgNE2e9s7iybQaNklI0GlhTGl+ayekdLmitphqQxDaZPAa5stABJ0yR1SupcsWJFWahmZtZPypKNKl7+dcC4iJgA3AJcvs7CpVHAHqRLr9cTERdFREdEdIwcObLiUM3MrKfKutFGSvpEVxMj4utN2i4DikcqO+SyYvuVhdFLgHPq5vF+4JomR09mZjYIlB3ZDAE2B7boYmhmFjBe0k6SNiF1h80sVshHLjWTgAV18ziGLrrQzMxs8Cg7slkeEWf1ZMYRsVbSdFIX2BDg0oiYL+ksoDMiZgKn5DsQrAVWAVNr7SWNIx0Z/aInyzczs4FDEdH1ROm3EbFnH8bTYx0dHdHZ2dnfYZiZDSqSZkdER9XLKetGe2fVAZiZWfsru13NqkblkhbkYXqj6WZmZkWljxhoJCLeKGlbYN9ejsfMzNpQS8lG0tbA+Dz6QEQ8lS9bvr6yyMzMrG00TTaShgHfAY4CHiL9yHNHSdcAJ0bEi9WHaGZmg13ZBQKnAxsDYyJiz4h4MzCWlKQ+U3VwZmbWHsqSzfuAv4+I1bWC/Pok4L1VBmZmZu2jLNm80uhuyxGxBuj6BzpmZmYFZRcIhKThNL4h5ysVxGNmZm2oLNlsBcymcbLxkY2ZmbWkabKJiHF9FIeZmbWxsnM265F0ZgVxmJlZG+t2siE9CsDMzKxlTZONpPc1Kq4oFjMza1NlRzZnNCjbu4pAzMysfXW7Gy0ifMmzmZl1S9mlz7tKmtugXEBExIQKYjIzszZTlmweAo7si0DMzKx9lSWbFyPikT6JxMzM2lbZOZtf9UkUZmbW1soeC93wsc+SJkt6azUhmZlZu+nRY6GBtwJ7SBoaEYf3ZkBmZtZ+epRsIuK03g7EzMzaV2mykbQrMBkYnYuWATMjYkGVgZmZWfsou13Np4CrSL+ruSsPAq6UdGr14ZmZWTsoO7I5Htg9Il4qFkr6OjAfOLuqwMzMrH2UPhYa2L5B+Sj8pE4zM2tRWbL5R+Dnkm6UdFEefgb8HPiHsplLmihpoaRFjbrdJE2VtELSnDycUJg2VtLNkhZIuk/SuO6tmpmZDRRlT+r8maS/BPZh3QsEZkXEy83aShoCXAAcBiwFZkmaGRH31VW9uovf83wX+FJE3CJpc3wkZWY2aDVNNpI2j4g1wB0t1Km3D7AoIhbneleRrmqrTzaN5rkbMDQibgHoYv5mZjZIlHWj/UTSuZLeLmmzWqGknSUdL+kmYGIXbUcDSwrjS3nt6KjoaElzJc2QNCaX/SXwpKQfS/qtpK/mI6V1SJomqVNS54oVK0pWxczM+kvZ7WreSTo/81FgvqSnJa0ErgBeDxwXETM2YPnXAePyowpuAS7P5UOBA4FPAm8BdgamNojvoojoiIiOkSNHbkAYZmZWpdIfdUbEDcAN9eWSto+I3zdpugwYUxjfIZcV572yMHoJcE5+vRSYU+iCuxbYF/jPsnjNzGzg6faTOgu6PI+TzQLGS9pJ0ibAFGBmsYKkUYXRScCCQtutJdUOVw6hhXM9ZmY2MPX0RpyQ7iTQpYhYK2k6cBMwBLg0IuZLOgvojIiZwCmSJgFrgVXkrrKIeFnSJ0mXXQuYDVy8AbGamVk/UkT0rKH0aESM7eV4eqyjoyM6Ozv7Owwzs0FF0uyI6Kh6OWWXPv870CgbCdi6kojMzKztlHWjNTtU8GGEmZm1pOwOApc3m25mZtaKDbkazczMrCVONmZmVrmyh6cdI2nbvgrGzMzaU9kFAmOBH0ramHTbmhuBu6Kn10ubmdmfpLJ7o30lIg4BjgDuAT4C3C3p+5I+JGm7vgjSzMwGt5buIBARq4Fr8lB7BMDhpGfOvLuy6MzMrC306HY1+QFo9wHn9m44ZmbWjnw1mpmZVc7JxszMKtdyN5qk4cD2wHPAwxHxSmVRmZlZWym7EedWwMeBY4BNgBXApsB2ku4ALoyI2yqP0szMBrWyI5sZpCvODoyIJ4sTJO0N/J2knSPCT9A0M7MulSWbEyLikUYTImI26aFmZmZmTZVdIHBNn0RhZmZtrezIpumjn9vF56+bz32PPd3fYZiZ9chu22/J547cvb/DaKos2YyWdF5XEyPilF6Ox8zM2lBZsnmOP4HzMgP9G4GZ2WBXlmxW+mmdZma2ocouEHixT6IwM7O2VvaIgX0blUsaJWlYNSGZmVm76em90f4buF/S13ozGDMza089fcTAoZIE7NbL8ZiZWRtqKdlI2gPYNY8uiIh786Oh51cWmZmZtY2m3WiStpJ0O3At8EHgWOAnkm6TtGXZzCVNlLRQ0iJJpzaYPlXSCklz8nBCYdrLhfKZ3V4zMzMbMMqObL4AdAKH1B4pIGkj4GzgS8DJXTWUNAS4ADgMWArMkjQzP+Wz6OqImN5gFs9FxJtbWw0zMxvIypLNocCE4rNrIuIVSacB80ra7gMsiojFAJKuAiaTHidtZmZ/Qkp/ZxMRa+sLc9kLJW1HA0sK40tzWb2jJc2VNEPSmEL5ppI6Jd0h6aiSZZmZ2QBWdmSzqaQ9Wf+GnAJ643c21wFXRsQLkj4KXA4ckqftGBHLJO0M3CppXkQ8uE4Q0jRgGsDYsWN7IRwzM6tCWbJZDny9i2m/L2m7DCgeqeyQy14VESsLo5cA5xSmLct/F+eLFPYEHqxrfxFwEUBHR0eUxGNmZv2kabKJiIM3YN6zgPGSdiIlmSmkK9peJWlURCzPo5OABbl8OPBsPuIZAbyNQiIyM7PBpds/6pR0UURMK6sXEWslTQduAoYAl0bEfElnAZ0RMRM4RdIkYC2wCpiam78R+I6kV0jnlc5ucBWbmZkNEkq/zexGA+nuiNironh6rKOjIzo7O/s7DDOzQUXS7IjoqHo5ZT/qbPT7lz9WFIuZmbWpskufP1JfEBETK4rFzMzaVE/v+mxmZtaysgsEJkh6ukG5gIiI0vujmZmZlSWbeRGxZ59EYmZmbcvdaGZmVrmyZPPDPonCzMzaWtNkExFfblQu6SRJH5DUoyd9mpnZn5aedqMJOAD4cS/GYmZmbapHRyYRcUFvB2JmZu2rNNlIegPpNv675qIFwEUR8UCVgZmZWfsou13NfsDtwGrSrfwvBp4Bbpe0b+XRmZlZWyg7svkscExE3F4ou1bSrcDngMOrCszMzNpH2QUCf1GXaACIiF8AO1cSkZmZtZ2yZLO6ybRnejMQMzNrX2XdaGMkndegXMDoCuIxM7M2VJZs/qXJND+pzMzMWtI02UTE5fVlkl4fEb+vLiQzM2s3PbmDwA29HoWZmbW1niQb9XoUZmbW1sp+1Hlzg+KLK4rFzMzaVNmRzcj6goi4sKJYzMysTZVdjbaVpPd1NTEifNdnMzMrVZpsgL+m8XmawI8YMDOzFpQlm0ci4iN9EomZmbWtsnM2vvLMzMw2WFmy+VDZDCQ5IZmZWVNlyebfJZ0saWyxUNImkg6RdDlwXFeNJU2UtFDSIkmnNpg+VdIKSXPycELd9C0lLZV0fndWyszMBpayczYTgY8AV0raCXgS2BQYAtwMfDMiftuooaQhwAXAYcBSYJakmRFxX13VqyNiehfL/wLwy5bWxMzMBqyye6M9D1wIXChpY2AE8FxEPNnCvPcBFkXEYgBJVwGTgfpk05CkvYHtgJ8BHa20MTOzganl29VExEsRsbyWaCQ9WtJkNLCkML6Uxo8lOFrSXEkzJI3J894IOBf4ZLMFSJomqVNS54oVK1pdFTMz62M9uTdaTW9cGHAdMC4iJgC3ALW7TJ8E3BARS5s1joiLIqIjIjpGjlzvZgdmZjZAlJ2zaSZKpi8DxhTGd8hlr80gYmVh9BLgnPx6P+BASScBmwObSFoTEetdZGBmZgNf02Qj6RNdTSIlgWZmAePzhQXLgCnAB+vmPyoilufRScACgIg4tlBnKtDhRGNmNniVHdls0WTat5o1jIi1kqYDN5GuXrs0IuZLOgvojIiZwCmSJgFrgVXA1JYjNzOzQUMRZb1hg0NHR0d0dvpJ1WZm3SFpdkRUfsVv2fNszpA0vMn0QyT9de+HZWZm7aSsG20e8FNJzwN3AytIP+ocD7wZ+B/gy5VGaGZmg17Zjzp/AvxE0njgbcAo4GngCmBaRDxXfYhmZjbYtXTpc0T8DvhdxbGYmVmb2pAfdZqZmbXEycbMzCrnZGNmZpXrdrKRdHcVgZiZWfvqyZGNn8xpZmbd0pNkc32vR2FmZm2t28kmIs6oIhAzM2tfvkDAzMwq52RjZmaVaynZSNq7QZlvwGlmZi1p9cjmYkl/VRuRdAzwmWpCMjOzdtPqY6H/Bpgh6YPAgcCHgHdVFpWZmbWVVm/EuVjSFOBa4FHgXb7js5mZtappspE0Dyg+ynMb0iOe75REREyoMjgzM2sPZUc2vgjAzMw2WNnD0x7pq0DMzKx9+Xc2ZmZWOScbMzOrnJONmZlVzsnGzMwq52RjZmaVc7IxM7PKOdmYmVnlKk02kiZKWihpkaRTG0yfKmmFpDl5OCGX7yjp7lw2X9KJVcZpZmbVavVGnN0maQhwAXAYsBSYJWlmRNxXV/XqiJheV7Yc2C8iXpC0OXBvbvtYVfGamVl1qjyy2QdYFBGLI+JF4CpgcisNI+LFiHghjw7D3X1mZoNalR/io4ElhfGluaze0ZLmSpohaUytUNIYSXPzPL7S6KhG0jRJnZI6V6xY0dvxm5lZL+nvI4brgHH57tG3AJfXJkTEkly+C3CcpO3qG0fERRHREREdI0eO7LOgzcyse6pMNsuAMYXxHXLZqyJiZaG77BJgvcdP5yOae0kPbTMzs0GoymQzCxgvaSdJmwBTgJnFCpJGFUYnAQty+Q6S/iy/Hg4cACysMFYzM6tQZVejRcRaSdOBm0gPXLs0IuZLOgvojIiZwCmSJgFrgVXA1Nz8jcC5kgIQ8LWImFdVrGZmVi1FRHmtQaCjoyM6Ozv7Owwzs0FF0uyI6Kh6Of19gYCZmf0JcLIxM7PKOdmYmVnlnGzMzKxyTjZmZlY5JxszM6uck42ZmVXOycbMzCrnZGNmZpVzsjEzs8o52ZiZWeWcbMzMrHJONmZmVjknGzMzq5yTjZmZVc7JxszMKudkY2ZmlXOyMTOzyjnZmJlZ5ZxszMyscoqI/o6hV0haATyyAbMYATzeS+H0JsfVPQM1Lhi4sTmu7hmocUHPYtsxIkZWEUxR2ySbDSWpMyI6+juOeo6rewZqXDBwY3Nc3TNQ44KBHZu70czMrHJONmZmVjknm9dc1N8BdMFxdc9AjQsGbmyOq3sGalwwgGPzORszM6ucj2zMzKxyTjZmZla5tk82kiZKWihpkaRTG0wfJunqPP1OSeMK0z6dyxdKencfx/UJSfdJmivp55J2LEx7WdKcPMzszbhajG2qpBWFGE4oTDtO0u/ycFwfx/WNQkwPSHqyMF45qL8AAAaUSURBVK2ybSbpUkl/lHRvF9Ml6bwc91xJexWmVbm9yuI6NsczT9KvJb2pMO3hXD5HUmcfx/UOSU8V3q/PFqY13QcqjutfCjHdm/epbfK0KrfXGEm35c+D+ZL+oUGdftnHuiUi2nYAhgAPAjsDmwD3ALvV1TkJ+HZ+PQW4Or/eLdcfBuyU5zOkD+M6GHhdfv2xWlx5fE0/b7OpwPkN2m4DLM5/h+fXw/sqrrr6JwOX9tE2ezuwF3BvF9OPAG4EBOwL3Fn19moxrv1rywMOr8WVxx8GRvTT9noH8NMN3Qd6O666ukcCt/bR9hoF7JVfbwE80OB/sl/2se4M7X5ksw+wKCIWR8SLwFXA5Lo6k4HL8+sZwDslKZdfFREvRMRDwKI8vz6JKyJui4hn8+gdwA69tOwNjq2JdwO3RMSqiHgCuAWY2E9xHQNc2UvLbioifgmsalJlMvDdSO4AtpY0imq3V2lcEfHrvFzow32she3VlQ3ZN3s7rr7cv5ZHxN359WpgATC6rlq/7GPd0e7JZjSwpDC+lPXfpFfrRMRa4Clg2xbbVhlX0fGkby01m0rqlHSHpKN6KabuxnZ0PlyfIWlMN9tWGRe5y3En4NZCcZXbrExXsVe5vbqrfh8L4GZJsyVN64d49pN0j6QbJe2eywbE9pL0OtIH9o8KxX2yvZS6+fcE7qybNOD3saH9sVBrnaS/BTqAgwrFO0bEMkk7A7dKmhcRD/ZhWNcBV0bEC5I+SjoyPKQPl19mCjAjIl4ulPX3NhuwJB1MSjYHFIoPyNvrz4FbJN2fv/n3hbtJ79caSUcA1wLj+2jZrTgS+FVEFI+CKt9ekjYnJbh/jIine3PefaHdj2yWAWMK4zvksoZ1JA0FtgJWtti2yriQdChwOjApIl6olUfEsvx3MXA76ZtObymNLSJWFuK5BNi71bZVxlUwhboujoq3WZmuYq9ye7VE0gTSezg5IlbWygvb64/ANfReF3KpiHg6Itbk1zcAG0sawQDYXlmz/auS7SVpY1Ki+V5E/LhBlQG7j72qP04U9dVAOnJbTOpSqZ1Q3L2uzsdZ9wKBH+TXu7PuBQKL6b0LBFqJa0/SydDxdeXDgWH59Qjgd/TuSdJWYhtVeP1e4I78ehvgoRzj8Px6m76KK9fblXSyVn21zfJ8x9H1Ce/3sO7J27uq3l4txjWWdC5y/7ryzYAtCq9/DUzsw7heX3v/SB/aj+Zt19I+UFVcefpWpPM6m/XV9srr/l3gm03q9Ns+1vJ69MdC+3QF01UaD5A+uE/PZWeRjhYANgV+mP/p7gJ2LrQ9PbdbCBzex3H9D/AHYE4eZuby/YF5+R9tHnB8P2yzfwPm5xhuA3YttP1I3paLgA/3ZVx5/Ezg7Lp2lW4z0rfc5cBLpD7x44ETgRPzdAEX5LjnAR19tL3K4roEeKKwj3Xm8p3ztronv8+n93Fc0wv71x0UkmGjfaCv4sp1ppIuHCq2q3p7HUA6JzS38F4dMRD2se4Mvl2NmZlVrt3P2ZiZ2QDgZGNmZpVzsjEzs8o52ZiZWeWcbMzMrHJONmZmVjknG7MWSbpE0m79HYfZYOTf2ZiZWeV8ZGPWgKTNJF2f7zx8r6QPSLpdUkeefnx+QNtdki6WdH4uv0zSf+S7Sy/ODwK7VNICSZcV5v8f+S7U8yV9viSWhyWdkx/OdZekXSpdebMKONmYNTYReCwi3hQRfwX8rDZB0vbAZ0j3oHob6X5sRcOB/YB/AmYC3yDda28PSW/OdU6PiA5gAnBQviFmM09FxB7A+cA3N2jNzPqBk41ZY/OAwyR9RdKBEfFUYdo+wC8iPZDqJdK99Yqui9Q/PQ/4Q0TMi4hXSPfNGpfrvF/S3cBvSYmo7FzQlYW/+/V4rcz6iZ9nY9ZARDyQn+N+BPBFST/vRvPa4xdeKbyujQ+VtBPwSeAtEfFE7l7btCykLl6bDQo+sjFrIHeVPRsRVwBfJT2bvmYWqetreH4G0tHdnP2WwDPAU5K2Aw5voc0HCn9/083lmfU7H9mYNbYH8FVJr5BuOf8x4GuQHpQl6cukR1KsAu4nPU68JRFxj6Tf5nZLgF+10Gy4pLmkI6VjurMiZgOBL3026wFJm0d6bPFQ0pMZL42Iaypa1sOk55M8XsX8zfqCu9HMeuZMSXOAe0lPP7y2n+MxG9B8ZGM2QEi6hvTI46JPRcRN/RGPWW9ysjEzs8q5G83MzCrnZGNmZpVzsjEzs8o52ZiZWeX+PykeflN9ABdvAAAAAElFTkSuQmCC\n",
            "text/plain": [
              "<Figure size 432x288 with 1 Axes>"
            ]
          },
          "metadata": {
            "tags": [],
            "needs_background": "light"
          }
        }
      ]
    },
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "UiVcjoJolNhk"
      },
      "source": [
        "# Toggle T from 0 to 3.5"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 874
        },
        "id": "fAi-gAUOlPmO",
        "outputId": "6b308d7b-c71d-4b1d-845c-f5a930f5b438"
      },
      "source": [
        "#@title\n",
        "T_values = np.arange(0, 3.5, 0.02).tolist()\n",
        "toggle_T = []\n",
        "\n",
        "# print(toggle_T)\n",
        "\n",
        "for k in T_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'T': k})\n",
        "  toggle_T.append(inputs_k)\n",
        "\n",
        "# Uncomment to print all output results\n",
        "# for d in toggle_T:\n",
        "#   print(d)\n",
        "\n",
        "toggle_T_outputs = []\n",
        "\n",
        "for i in toggle_T:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_T_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_T_outputs\n",
        "\n",
        "# for d in toggle_T_outputs:\n",
        "#   print(d['price'])\n",
        "\n",
        "toggle_T_prices = [d['price'] for d in toggle_T_outputs]\n",
        "# toggle_T_prices\n",
        "\n",
        "T_values\n",
        "plt.plot(T_values, toggle_T_prices)\n",
        "plt.title('Impact of Changes in T on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('T') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('T_plots1.png')\n",
        "toggle_T_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_T_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in T on (ST/S0 Avg - k)')\n",
        "plt.plot(T_values, toggle_T_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('T') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('T_plots2.png')\n",
        "toggle_T_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_T_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in T on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(T_values, toggle_T_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('T') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('T_plots3.png')\n",
        "df_toggle_T = pd.DataFrame(list(zip(T_values, toggle_T_prices)),\n",
        "               columns =['T', 'price'])\n",
        "df_toggle_T\n",
        "df_toggle_T.to_excel(\"df_toggle_T.xlsx\", sheet_name='Sheet_name_1')"
      ],
      "execution_count": 17,
      "outputs": [
        {
          "output_type": "stream",
          "text": [
            "/usr/local/lib/python3.7/dist-packages/ipykernel_launcher.py:110: RuntimeWarning: invalid value encountered in sqrt\n"
          ],
          "name": "stderr"
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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": "markdown",
      "metadata": {
        "id": "wLp0gDnrnDGB"
      },
      "source": [
        "# Toggle Q from 0% to 50%"
      ]
    },
    {
      "cell_type": "code",
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/",
          "height": 852
        },
        "id": "GIhOZDdknF2u",
        "outputId": "f6c7227e-1f37-49d9-bc59-ea7ed85aea08"
      },
      "source": [
        "#@title\n",
        "q_values = np.arange(0, 0.5, 0.01).tolist()\n",
        "toggle_q = []\n",
        "\n",
        "# print(toggle_q)\n",
        "\n",
        "for k in q_values:\n",
        "  inputs_k = inputs.copy()\n",
        "  inputs_k.update({'q': k})\n",
        "  toggle_q.append(inputs_k)\n",
        "\n",
        "# Uncomment to print all output results\n",
        "# for d in toggle_q:\n",
        "#   print(d)\n",
        "\n",
        "toggle_q_outputs = []\n",
        "\n",
        "for i in toggle_q:\n",
        "  outputs = lognormalPricer(i)\n",
        "  toggle_q_outputs.append(outputs)\n",
        "\n",
        "# df_toggle_q_outputs\n",
        "\n",
        "# for d in toggle_q_outputs:\n",
        "#   print(d)\n",
        "\n",
        "toggle_q_prices = [d['price'] for d in toggle_q_outputs]\n",
        "# toggle_q_prices\n",
        "\n",
        "q_values\n",
        "plt.subplots(1)\n",
        "plt.plot(q_values, toggle_q_prices)\n",
        "plt.title('Impact of Changes in q on Contract Price') # Add a title to the plot.\n",
        "plt.xlabel('q') # Add an x-label to the axes.\n",
        "plt.ylabel('Price') # Add a y-label to the axes.\n",
        "plt.savefig('q_plots1.png')\n",
        "toggle_q_outputs_ST_over_S0_avg = [d['ST_over_S0_avg_k'] for d in toggle_q_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in q on (ST/S0 Avg - k)')\n",
        "plt.plot(q_values, toggle_q_outputs_ST_over_S0_avg )\n",
        "plt.xlabel('q') # Add an x-label to the axes.\n",
        "plt.ylabel('ST_over_S0_avg_k') # Add a y-label to the axes.\n",
        "plt.savefig('q_plots2.png')\n",
        "toggle_q_outputs_L_TdTdT_over_L_0TdT_avg = [d['k_L_TdTdT_over_L_0TdT_avg'] for d in toggle_q_outputs]\n",
        "plt.subplots(1)\n",
        "plt.title('Impact of Changes in q on k - (L(T-D,T-D,T) / L(0,T-D,T))')\n",
        "plt.plot(q_values, toggle_q_outputs_L_TdTdT_over_L_0TdT_avg )\n",
        "plt.xlabel('q') # Add an x-label to the axes.\n",
        "plt.ylabel('k - (L(T-D,T-D,T) / L(0,T-D,T))') # Add a y-label to the axes.\n",
        "plt.savefig('q_plots3.png')\n",
        "df_toggle_q = pd.DataFrame(list(zip(q_values, toggle_q_prices)),\n",
        "               columns =['q', 'price'])\n",
        "df_toggle_q\n",
        "df_toggle_q.to_excel(\"df_toggle_q.xlsx\", sheet_name='Sheet_name_1')"
      ],
      "execution_count": 18,
      "outputs": [
        {
          "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"
          }
        },
        {
          "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"
          }
        },
        {
          "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"
          }
        }
      ]
    }
  ]
}