European_multi_step_tree.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "ecc9d140",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import math\n",
    "from scipy.stats import norm\n",
    "import matplotlib.pyplot as plt\n",
    "from matplotlib.pyplot import MultipleLocator\n",
    "from matplotlib.pyplot import figure\n",
    "import pandas as pd"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "id": "a04cc116",
   "metadata": {},
   "outputs": [],
   "source": [
    "### INSERT VARIABLES HERE ###\n",
    "assetLife = 20\n",
    "gearboxLife = 10\n",
    "tstrike = 10\n",
    "numberOfTurbines = 100 #number of turbines\n",
    "inflationRate = 1.05 #Assuming 5% inflation rate\n",
    "\n",
    "elecPriceSigma = 0.18\n",
    "gearboxCost = 1 #£MM per turbine\n",
    "gearboxSigma = 0.15\n",
    "\n",
    "totalSigma = 0.085\n",
    "\n",
    "#math.sqrt((elecPriceSigma**2)+(gearboxSigma**2))\n",
    "\n",
    "ratedCap = 8 #MW\n",
    "costPerMW = 0.9 #£1.1mil per MW\n",
    "capFactor = 0.3 #Output is 30% of RC\n",
    "availability = 0.95 #Assume turbines are on 95% of the time\n",
    "\n",
    "initElecPrice = 55 #£/MWh\n",
    "\n",
    "riskAdjRate = 0.07 #risk-adjusted discount rate\n",
    "riskFreeRate = 0.03"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "id": "78524bc0",
   "metadata": {},
   "outputs": [],
   "source": [
    "### FUNCTIONS FOR BAU CASE ###\n",
    "\n",
    "def BAUfindSetupCost(ratedCap, numberOfTurbines, costPerMW):\n",
    "    setupCost = numberOfTurbines * costPerMW * ratedCap\n",
    "    return setupCost\n",
    "\n",
    "def BAUfindNetYield(numberOfTurbines, ratedCap, capFactor, availability):\n",
    "    grossYield = numberOfTurbines * ratedCap * capFactor * 8760 #8760 hours in a year\n",
    "    netYield = availability * grossYield\n",
    "    return netYield\n",
    "\n",
    "def BAUfindCashIn(assetLife, gearboxLife, initElecPrice, inflationRate, netYield, tstrike):\n",
    "    \n",
    "    elecPrice = np.zeros(gearboxLife + tstrike) #initialise arrays\n",
    "    revenue = np.zeros(gearboxLife + tstrike)\n",
    "    opCosts = np.zeros(gearboxLife + tstrike)\n",
    "    profit = np.zeros(gearboxLife + tstrike)\n",
    "    elecPrice[0] = initElecPrice\n",
    "    \n",
    "    for i in range (0,assetLife):\n",
    "        if(i > 0):\n",
    "            elecPrice[i] = elecPrice[i-1]*inflationRate\n",
    "            \n",
    "        revenue[i] = netYield * elecPrice[i]\n",
    "        opCosts[i] = 0.3 * revenue[i] #Assuming operation costs are 30% of revenue\n",
    "        profit[i] = (revenue[i] - opCosts[i]) * pow(10, -6) #profit in £MM\n",
    "            \n",
    "    \n",
    "    return profit\n",
    "\n",
    "def BAUfindPV(r, setupCost, assetLife, profit):\n",
    "    PV = np.zeros(len(profit)) #initialise PV array\n",
    "    PV[0] = -setupCost #initial cash outflow due to setup\n",
    "    for i in range (1,tstrike):\n",
    "        PV[i] = profit[i] / pow((1 + r), i)\n",
    "        \n",
    "    print(\"BAU Present Values:\", np.around(PV, 2), '\\n')\n",
    "\n",
    "    return PV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "id": "4725b349",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "BAU Present Values: [-720.     75.46   74.05   72.66   71.31   69.97   68.66   67.38   66.12\n",
      "   64.89    0.      0.      0.      0.      0.      0.      0.      0.\n",
      "    0.      0.  ] \n",
      "\n",
      "BAU Net Present Value = £-89.50 million\n"
     ]
    }
   ],
   "source": [
    "### CALCULATIONS FOR BAU CASE ###\n",
    "\n",
    "### Calculate replacement cost ###\n",
    "BAUsetupCost = BAUfindSetupCost(ratedCap, numberOfTurbines, costPerMW)\n",
    "\n",
    "### Calculate net yield ###\n",
    "BAUnetYield = BAUfindNetYield(numberOfTurbines, ratedCap, capFactor, availability)\n",
    "\n",
    "### Calculate cash in-flows ###\n",
    "BAUprofit = BAUfindCashIn(assetLife, gearboxLife, initElecPrice, inflationRate, BAUnetYield, tstrike)\n",
    "\n",
    "### Calculate Present values ###\n",
    "BAUPV = BAUfindPV(riskAdjRate, BAUsetupCost, assetLife, BAUprofit)\n",
    "\n",
    "### Calculate NPV ###\n",
    "BAUNPV = np.sum(BAUPV)\n",
    "print(\"BAU Net Present Value = £%.2f million\" % BAUNPV)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "c294da0c",
   "metadata": {},
   "outputs": [],
   "source": [
    "def findReplacementCost(numberOfTurbines, gearboxCost):\n",
    "    replacementCost = gearboxCost * numberOfTurbines\n",
    "    return replacementCost"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "2521b034",
   "metadata": {},
   "outputs": [],
   "source": [
    "def findNetYield(numberOfTurbines, ratedCap, capFactor, availability):\n",
    "    grossYield = numberOfTurbines * ratedCap * capFactor * 8760 #8760 hours in a year\n",
    "    netYield = availability * grossYield\n",
    "    return netYield"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "fe92282e",
   "metadata": {},
   "outputs": [],
   "source": [
    "def findCashIn(assetLife, gearboxLife, initElecPrice, inflationRate, netYield):\n",
    "    \n",
    "    elecPrice = np.zeros(gearboxLife) #initialise arrays\n",
    "    revenue = np.zeros(gearboxLife)\n",
    "    opCosts = np.zeros(gearboxLife)\n",
    "    profit = np.zeros(gearboxLife)\n",
    "    elecPrice[0] = initElecPrice*pow(inflationRate,tstrike) # should move with inf rate at strike\n",
    "    \n",
    "    for i in range (0, gearboxLife):\n",
    "        if(i>0):\n",
    "            elecPrice[i] = elecPrice[i-1]*inflationRate\n",
    "        \n",
    "        revenue[i] = netYield * elecPrice[i]\n",
    "        opCosts[i] = 0.3 * revenue[i] #Assuming operation costs are 30% of revenue\n",
    "        profit[i] = (revenue[i] - opCosts[i]) * pow(10, -6) #profit in £MM\n",
    "        \n",
    "        #if(i >= gearboxLife - 3):\n",
    "            #profit[i] = (revenue[i] - opCosts[i]) * pow(0.8, i - (gearboxLife - 4)) * pow(10, -6) #profit in £MM\n",
    "            #otherwise devides by decimals due to negative power ,  which grows values\n",
    "            \n",
    "           \n",
    "    return profit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "id": "999534fb",
   "metadata": {},
   "outputs": [],
   "source": [
    "def findPV(riskFreeRate, riskAdjRate, replacementCost, assetLife, gearboxLife, profit, tstrike):\n",
    "    PV = np.zeros(gearboxLife) #initialise PV array\n",
    "    \n",
    "    #PV[0] = -replacementCost\n",
    "    for i in range (1, assetLife - tstrike):\n",
    "        PV[i] = profit[i] / pow((1 + riskFreeRate), tstrike+i) # should start from tstrike not tstart\n",
    "\n",
    "    for i in range (assetLife - tstrike, gearboxLife):\n",
    "        PV[i] = profit[i] / pow((1 + riskAdjRate), tstrike+i)\n",
    "\n",
    "    print(\"Replacement case Present Values:\", np.around(PV, 2), '\\n')\n",
    "    return PV"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "id": "9867e81a",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Replacement case Present Values: [  0.    95.01  96.86  98.74 100.65 102.61 104.6  106.63 108.7  110.81] \n",
      "\n",
      "Net Present Value of replacement case = £924.61 million\n",
      "\n"
     ]
    }
   ],
   "source": [
    "### CALCULATIONS FOR OPTION CASES ###\n",
    "\n",
    "### Calculate replacement cost ###\n",
    "replacementCost = findReplacementCost(numberOfTurbines, gearboxCost)\n",
    "\n",
    "### Calculate net yield ###\n",
    "netYield = findNetYield(numberOfTurbines, ratedCap, capFactor, availability)\n",
    "\n",
    "### Calculate cash in-flows ###\n",
    "profitOption = findCashIn(assetLife, gearboxLife, initElecPrice, inflationRate, netYield)\n",
    "#print(profitOption)\n",
    "\n",
    "### Calculate Present Values ###\n",
    "PVOption = findPV(riskFreeRate, riskAdjRate, replacementCost, assetLife, gearboxLife, profitOption, tstrike)\n",
    "\n",
    "### Calculate NPVs ###\n",
    "NPVOption = np.around(np.sum(PVOption), 2)\n",
    "print(\"Net Present Value of replacement case = £%.2f million\\n\" % NPVOption)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "id": "bd652f5e",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "61.39132535407592\n"
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       "      <td>1303.613675</td>\n",
       "      <td>1369.183985</td>\n",
       "      <td>1438.052408</td>\n",
       "      <td>1510.384836</td>\n",
       "      <td>1586.355504</td>\n",
       "      <td>1666.147412</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>971.116849</td>\n",
       "      <td>1019.962940</td>\n",
       "      <td>1071.265936</td>\n",
       "      <td>1125.149414</td>\n",
       "      <td>1181.743172</td>\n",
       "      <td>1241.183531</td>\n",
       "      <td>1303.613675</td>\n",
       "      <td>1369.183985</td>\n",
       "      <td>1438.052408</td>\n",
       "      <td>1510.384836</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>880.330367</td>\n",
       "      <td>924.610000</td>\n",
       "      <td>971.116849</td>\n",
       "      <td>1019.962940</td>\n",
       "      <td>1071.265936</td>\n",
       "      <td>1125.149414</td>\n",
       "      <td>1181.743172</td>\n",
       "      <td>1241.183531</td>\n",
       "      <td>1303.613675</td>\n",
       "      <td>1369.183985</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>798.031211</td>\n",
       "      <td>838.171289</td>\n",
       "      <td>880.330367</td>\n",
       "      <td>924.610000</td>\n",
       "      <td>971.116849</td>\n",
       "      <td>1019.962940</td>\n",
       "      <td>1071.265936</td>\n",
       "      <td>1125.149414</td>\n",
       "      <td>1181.743172</td>\n",
       "      <td>1241.183531</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>723.425929</td>\n",
       "      <td>759.813445</td>\n",
       "      <td>798.031211</td>\n",
       "      <td>838.171289</td>\n",
       "      <td>880.330367</td>\n",
       "      <td>924.610000</td>\n",
       "      <td>971.116849</td>\n",
       "      <td>1019.962940</td>\n",
       "      <td>1071.265936</td>\n",
       "      <td>1125.149414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>655.795247</td>\n",
       "      <td>688.781015</td>\n",
       "      <td>723.425929</td>\n",
       "      <td>759.813445</td>\n",
       "      <td>798.031211</td>\n",
       "      <td>838.171289</td>\n",
       "      <td>880.330367</td>\n",
       "      <td>924.610000</td>\n",
       "      <td>971.116849</td>\n",
       "      <td>1019.962940</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>594.487132</td>\n",
       "      <td>624.389170</td>\n",
       "      <td>655.795247</td>\n",
       "      <td>688.781015</td>\n",
       "      <td>723.425929</td>\n",
       "      <td>759.813445</td>\n",
       "      <td>798.031211</td>\n",
       "      <td>838.171289</td>\n",
       "      <td>880.330367</td>\n",
       "      <td>924.610000</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>538.910509</td>\n",
       "      <td>566.017105</td>\n",
       "      <td>594.487132</td>\n",
       "      <td>624.389170</td>\n",
       "      <td>655.795247</td>\n",
       "      <td>688.781015</td>\n",
       "      <td>723.425929</td>\n",
       "      <td>759.813445</td>\n",
       "      <td>798.031211</td>\n",
       "      <td>838.171289</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>488.529559</td>\n",
       "      <td>513.102050</td>\n",
       "      <td>538.910509</td>\n",
       "      <td>566.017105</td>\n",
       "      <td>594.487132</td>\n",
       "      <td>624.389170</td>\n",
       "      <td>655.795247</td>\n",
       "      <td>688.781015</td>\n",
       "      <td>723.425929</td>\n",
       "      <td>759.813445</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>442.858557</td>\n",
       "      <td>465.133847</td>\n",
       "      <td>488.529559</td>\n",
       "      <td>513.102050</td>\n",
       "      <td>538.910509</td>\n",
       "      <td>566.017105</td>\n",
       "      <td>594.487132</td>\n",
       "      <td>624.389170</td>\n",
       "      <td>655.795247</td>\n",
       "      <td>688.781015</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>401.457184</td>\n",
       "      <td>421.650032</td>\n",
       "      <td>442.858557</td>\n",
       "      <td>465.133847</td>\n",
       "      <td>488.529559</td>\n",
       "      <td>513.102050</td>\n",
       "      <td>538.910509</td>\n",
       "      <td>566.017105</td>\n",
       "      <td>594.487132</td>\n",
       "      <td>624.389170</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>363.926288</td>\n",
       "      <td>382.231374</td>\n",
       "      <td>401.457184</td>\n",
       "      <td>421.650032</td>\n",
       "      <td>442.858557</td>\n",
       "      <td>465.133847</td>\n",
       "      <td>488.529559</td>\n",
       "      <td>513.102050</td>\n",
       "      <td>538.910509</td>\n",
       "      <td>566.017105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>329.904031</td>\n",
       "      <td>346.497835</td>\n",
       "      <td>363.926288</td>\n",
       "      <td>382.231374</td>\n",
       "      <td>401.457184</td>\n",
       "      <td>421.650032</td>\n",
       "      <td>442.858557</td>\n",
       "      <td>465.133847</td>\n",
       "      <td>488.529559</td>\n",
       "      <td>513.102050</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>314.104905</td>\n",
       "      <td>329.904031</td>\n",
       "      <td>346.497835</td>\n",
       "      <td>363.926288</td>\n",
       "      <td>382.231374</td>\n",
       "      <td>401.457184</td>\n",
       "      <td>421.650032</td>\n",
       "      <td>442.858557</td>\n",
       "      <td>465.133847</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>299.062401</td>\n",
       "      <td>314.104905</td>\n",
       "      <td>329.904031</td>\n",
       "      <td>346.497835</td>\n",
       "      <td>363.926288</td>\n",
       "      <td>382.231374</td>\n",
       "      <td>401.457184</td>\n",
       "      <td>421.650032</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>284.740283</td>\n",
       "      <td>299.062401</td>\n",
       "      <td>314.104905</td>\n",
       "      <td>329.904031</td>\n",
       "      <td>346.497835</td>\n",
       "      <td>363.926288</td>\n",
       "      <td>382.231374</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>271.104053</td>\n",
       "      <td>284.740283</td>\n",
       "      <td>299.062401</td>\n",
       "      <td>314.104905</td>\n",
       "      <td>329.904031</td>\n",
       "      <td>346.497835</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>258.120862</td>\n",
       "      <td>271.104053</td>\n",
       "      <td>284.740283</td>\n",
       "      <td>299.062401</td>\n",
       "      <td>314.104905</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>245.759437</td>\n",
       "      <td>258.120862</td>\n",
       "      <td>271.104053</td>\n",
       "      <td>284.740283</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>233.990002</td>\n",
       "      <td>245.759437</td>\n",
       "      <td>258.120862</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>222.784205</td>\n",
       "      <td>233.990002</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.00</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>212.115055</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>31 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "        0           1            2            3            4            5   \\\n",
       "0   924.61  971.116849  1019.962940  1071.265936  1125.149414  1181.743172   \n",
       "1     0.00  880.330367   924.610000   971.116849  1019.962940  1071.265936   \n",
       "2     0.00    0.000000   838.171289   880.330367   924.610000   971.116849   \n",
       "3     0.00    0.000000     0.000000   798.031211   838.171289   880.330367   \n",
       "4     0.00    0.000000     0.000000     0.000000   759.813445   798.031211   \n",
       "5     0.00    0.000000     0.000000     0.000000     0.000000   723.425929   \n",
       "6     0.00    0.000000     0.000000     0.000000     0.000000     0.000000   \n",
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       "8     0.00    0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "9     0.00    0.000000     0.000000     0.000000     0.000000     0.000000   \n",
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       "\n",
       "             6            7            8            9   ...           21  \\\n",
       "0   1241.183531  1303.613675  1369.183985  1438.052408  ...  2591.370739   \n",
       "1   1125.149414  1181.743172  1241.183531  1303.613675  ...  2349.112114   \n",
       "2   1019.962940  1071.265936  1125.149414  1181.743172  ...  2129.501441   \n",
       "3    924.610000   971.116849  1019.962940  1071.265936  ...  1930.421439   \n",
       "4    838.171289   880.330367   924.610000   971.116849  ...  1749.952764   \n",
       "5    759.813445   798.031211   838.171289   880.330367  ...  1586.355504   \n",
       "6    688.781015   723.425929   759.813445   798.031211  ...  1438.052408   \n",
       "7      0.000000   655.795247   688.781015   723.425929  ...  1303.613675   \n",
       "8      0.000000     0.000000   624.389170   655.795247  ...  1181.743172   \n",
       "9      0.000000     0.000000     0.000000   594.487132  ...  1071.265936   \n",
       "10     0.000000     0.000000     0.000000     0.000000  ...   971.116849   \n",
       "11     0.000000     0.000000     0.000000     0.000000  ...   880.330367   \n",
       "12     0.000000     0.000000     0.000000     0.000000  ...   798.031211   \n",
       "13     0.000000     0.000000     0.000000     0.000000  ...   723.425929   \n",
       "14     0.000000     0.000000     0.000000     0.000000  ...   655.795247   \n",
       "15     0.000000     0.000000     0.000000     0.000000  ...   594.487132   \n",
       "16     0.000000     0.000000     0.000000     0.000000  ...   538.910509   \n",
       "17     0.000000     0.000000     0.000000     0.000000  ...   488.529559   \n",
       "18     0.000000     0.000000     0.000000     0.000000  ...   442.858557   \n",
       "19     0.000000     0.000000     0.000000     0.000000  ...   401.457184   \n",
       "20     0.000000     0.000000     0.000000     0.000000  ...   363.926288   \n",
       "21     0.000000     0.000000     0.000000     0.000000  ...   329.904031   \n",
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       "23     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
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       "26     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
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       "\n",
       "             22           23           24           25           26  \\\n",
       "0   2721.713789  2858.612949  3002.397983  3153.415244  3312.028504   \n",
       "1   2467.269826  2591.370739  2721.713789  2858.612949  3002.397983   \n",
       "2   2236.612982  2349.112114  2467.269826  2591.370739  2721.713789   \n",
       "3   2027.519478  2129.501441  2236.612982  2349.112114  2467.269826   \n",
       "4   1837.973431  1930.421439  2027.519478  2129.501441  2236.612982   \n",
       "5   1666.147412  1749.952764  1837.973431  1930.421439  2027.519478   \n",
       "6   1510.384836  1586.355504  1666.147412  1749.952764  1837.973431   \n",
       "7   1369.183985  1438.052408  1510.384836  1586.355504  1666.147412   \n",
       "8   1241.183531  1303.613675  1369.183985  1438.052408  1510.384836   \n",
       "9   1125.149414  1181.743172  1241.183531  1303.613675  1369.183985   \n",
       "10  1019.962940  1071.265936  1125.149414  1181.743172  1241.183531   \n",
       "11   924.610000   971.116849  1019.962940  1071.265936  1125.149414   \n",
       "12   838.171289   880.330367   924.610000   971.116849  1019.962940   \n",
       "13   759.813445   798.031211   838.171289   880.330367   924.610000   \n",
       "14   688.781015   723.425929   759.813445   798.031211   838.171289   \n",
       "15   624.389170   655.795247   688.781015   723.425929   759.813445   \n",
       "16   566.017105   594.487132   624.389170   655.795247   688.781015   \n",
       "17   513.102050   538.910509   566.017105   594.487132   624.389170   \n",
       "18   465.133847   488.529559   513.102050   538.910509   566.017105   \n",
       "19   421.650032   442.858557   465.133847   488.529559   513.102050   \n",
       "20   382.231374   401.457184   421.650032   442.858557   465.133847   \n",
       "21   346.497835   363.926288   382.231374   401.457184   421.650032   \n",
       "22   314.104905   329.904031   346.497835   363.926288   382.231374   \n",
       "23     0.000000   299.062401   314.104905   329.904031   346.497835   \n",
       "24     0.000000     0.000000   284.740283   299.062401   314.104905   \n",
       "25     0.000000     0.000000     0.000000   271.104053   284.740283   \n",
       "26     0.000000     0.000000     0.000000     0.000000   258.120862   \n",
       "27     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "28     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "29     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "30     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "\n",
       "             27           28           29           30  \n",
       "0   3478.619834  3653.590522  3837.362039  4030.377058  \n",
       "1   3153.415244  3312.028504  3478.619834  3653.590522  \n",
       "2   2858.612949  3002.397983  3153.415244  3312.028504  \n",
       "3   2591.370739  2721.713789  2858.612949  3002.397983  \n",
       "4   2349.112114  2467.269826  2591.370739  2721.713789  \n",
       "5   2129.501441  2236.612982  2349.112114  2467.269826  \n",
       "6   1930.421439  2027.519478  2129.501441  2236.612982  \n",
       "7   1749.952764  1837.973431  1930.421439  2027.519478  \n",
       "8   1586.355504  1666.147412  1749.952764  1837.973431  \n",
       "9   1438.052408  1510.384836  1586.355504  1666.147412  \n",
       "10  1303.613675  1369.183985  1438.052408  1510.384836  \n",
       "11  1181.743172  1241.183531  1303.613675  1369.183985  \n",
       "12  1071.265936  1125.149414  1181.743172  1241.183531  \n",
       "13   971.116849  1019.962940  1071.265936  1125.149414  \n",
       "14   880.330367   924.610000   971.116849  1019.962940  \n",
       "15   798.031211   838.171289   880.330367   924.610000  \n",
       "16   723.425929   759.813445   798.031211   838.171289  \n",
       "17   655.795247   688.781015   723.425929   759.813445  \n",
       "18   594.487132   624.389170   655.795247   688.781015  \n",
       "19   538.910509   566.017105   594.487132   624.389170  \n",
       "20   488.529559   513.102050   538.910509   566.017105  \n",
       "21   442.858557   465.133847   488.529559   513.102050  \n",
       "22   401.457184   421.650032   442.858557   465.133847  \n",
       "23   363.926288   382.231374   401.457184   421.650032  \n",
       "24   329.904031   346.497835   363.926288   382.231374  \n",
       "25   299.062401   314.104905   329.904031   346.497835  \n",
       "26   271.104053   284.740283   299.062401   314.104905  \n",
       "27   245.759437   258.120862   271.104053   284.740283  \n",
       "28     0.000000   233.990002   245.759437   258.120862  \n",
       "29     0.000000     0.000000   222.784205   233.990002  \n",
       "30     0.000000     0.000000     0.000000   212.115055  \n",
       "\n",
       "[31 rows x 31 columns]"
      ]
     },
     "execution_count": 23,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### BINOMIAL TREE\n",
    "\n",
    "\n",
    "S = NPVOption\n",
    "K = replacementCost / pow(inflationRate, tstrike)#Equivalent of exercise price in B-S\n",
    "sigma = totalSigma\n",
    "N = 30\n",
    "dt = tstrike/N\n",
    "u = np.exp(sigma*np.sqrt(dt))\n",
    "d = 1/u\n",
    "r = riskFreeRate\n",
    "p = (np.exp(r*dt) - d)/(u-d)\n",
    "q = 1-p\n",
    "\n",
    "print(K)\n",
    "\n",
    "\n",
    "stock_prices = np.zeros((N+1, N+1))\n",
    "option_values = np.zeros((N+1, N+1))\n",
    "\n",
    "for i in range(N+1):\n",
    "    for j in range(i+1):\n",
    "        stock_prices[j][i] = S*(u**(i-j))*(d**j)\n",
    "\n",
    "df = pd.DataFrame(stock_prices)\n",
    "df"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "id": "ea19163a",
   "metadata": {},
   "outputs": [
    {
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       "      <th>1</th>\n",
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       "      <td>971.670814</td>\n",
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       "      <td>1075.881722</td>\n",
       "      <td>1131.980330</td>\n",
       "      <td>...</td>\n",
       "      <td>2073.393994</td>\n",
       "      <td>2179.941646</td>\n",
       "      <td>2291.871221</td>\n",
       "      <td>2409.453653</td>\n",
       "      <td>2532.973504</td>\n",
       "      <td>2662.729652</td>\n",
       "      <td>2799.036011</td>\n",
       "      <td>2942.222288</td>\n",
       "      <td>3092.634773</td>\n",
       "      <td>3250.637179</td>\n",
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       "      <td>1874.313992</td>\n",
       "      <td>1970.848143</td>\n",
       "      <td>2072.260548</td>\n",
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       "      <td>831.552896</td>\n",
       "      <td>875.342307</td>\n",
       "      <td>921.354008</td>\n",
       "      <td>...</td>\n",
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       "      <td>2530.590267</td>\n",
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       "      <td>0.000000</td>\n",
       "      <td>675.614317</td>\n",
       "      <td>711.521318</td>\n",
       "      <td>749.253740</td>\n",
       "      <td>788.903596</td>\n",
       "      <td>830.567526</td>\n",
       "      <td>...</td>\n",
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       "      <td>1609.476076</td>\n",
       "      <td>1692.711871</td>\n",
       "      <td>1780.157258</td>\n",
       "      <td>1872.024204</td>\n",
       "      <td>1968.535341</td>\n",
       "      <td>2069.924503</td>\n",
       "      <td>2176.437286</td>\n",
       "      <td>2288.331642</td>\n",
       "      <td>2405.878500</td>\n",
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       "      <th>6</th>\n",
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       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>640.488888</td>\n",
       "      <td>674.648458</td>\n",
       "      <td>710.545752</td>\n",
       "      <td>748.268370</td>\n",
       "      <td>...</td>\n",
       "      <td>1381.944962</td>\n",
       "      <td>1453.713500</td>\n",
       "      <td>1529.114612</td>\n",
       "      <td>1608.331239</td>\n",
       "      <td>1691.555529</td>\n",
       "      <td>1778.989294</td>\n",
       "      <td>1870.844501</td>\n",
       "      <td>1967.343783</td>\n",
       "      <td>2068.720969</td>\n",
       "      <td>2175.221656</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>607.017776</td>\n",
       "      <td>639.513322</td>\n",
       "      <td>673.663088</td>\n",
       "      <td>...</td>\n",
       "      <td>1247.506228</td>\n",
       "      <td>1312.512649</td>\n",
       "      <td>1380.811516</td>\n",
       "      <td>1452.568663</td>\n",
       "      <td>1527.958269</td>\n",
       "      <td>1607.163275</td>\n",
       "      <td>1690.375826</td>\n",
       "      <td>1777.797735</td>\n",
       "      <td>1869.640967</td>\n",
       "      <td>1966.128153</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>575.121477</td>\n",
       "      <td>606.032406</td>\n",
       "      <td>...</td>\n",
       "      <td>1125.635725</td>\n",
       "      <td>1184.512196</td>\n",
       "      <td>1246.372783</td>\n",
       "      <td>1311.367812</td>\n",
       "      <td>1379.655173</td>\n",
       "      <td>1451.400699</td>\n",
       "      <td>1526.778567</td>\n",
       "      <td>1605.971717</td>\n",
       "      <td>1689.172292</td>\n",
       "      <td>1776.582105</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>544.724291</td>\n",
       "      <td>...</td>\n",
       "      <td>1015.158489</td>\n",
       "      <td>1068.478078</td>\n",
       "      <td>1124.502279</td>\n",
       "      <td>1183.367359</td>\n",
       "      <td>1245.216440</td>\n",
       "      <td>1310.199848</td>\n",
       "      <td>1378.475471</td>\n",
       "      <td>1450.209141</td>\n",
       "      <td>1525.575033</td>\n",
       "      <td>1604.756087</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>915.009402</td>\n",
       "      <td>963.291605</td>\n",
       "      <td>1014.025043</td>\n",
       "      <td>1067.333241</td>\n",
       "      <td>1123.345936</td>\n",
       "      <td>1182.199394</td>\n",
       "      <td>1244.036738</td>\n",
       "      <td>1309.008289</td>\n",
       "      <td>1377.271937</td>\n",
       "      <td>1448.993511</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>824.222920</td>\n",
       "      <td>867.938664</td>\n",
       "      <td>913.875957</td>\n",
       "      <td>962.146768</td>\n",
       "      <td>1012.868701</td>\n",
       "      <td>1066.165277</td>\n",
       "      <td>1122.166234</td>\n",
       "      <td>1181.007836</td>\n",
       "      <td>1242.833204</td>\n",
       "      <td>1307.792660</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>741.923764</td>\n",
       "      <td>781.499953</td>\n",
       "      <td>823.089475</td>\n",
       "      <td>866.793827</td>\n",
       "      <td>912.719614</td>\n",
       "      <td>960.978803</td>\n",
       "      <td>1011.688998</td>\n",
       "      <td>1064.973719</td>\n",
       "      <td>1120.962700</td>\n",
       "      <td>1179.792206</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>667.318483</td>\n",
       "      <td>703.142109</td>\n",
       "      <td>740.790319</td>\n",
       "      <td>780.355116</td>\n",
       "      <td>821.933132</td>\n",
       "      <td>865.625863</td>\n",
       "      <td>911.539911</td>\n",
       "      <td>959.787245</td>\n",
       "      <td>1010.485464</td>\n",
       "      <td>1063.758089</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>599.687800</td>\n",
       "      <td>632.109679</td>\n",
       "      <td>666.185037</td>\n",
       "      <td>701.997272</td>\n",
       "      <td>739.633976</td>\n",
       "      <td>779.187152</td>\n",
       "      <td>820.753430</td>\n",
       "      <td>864.434304</td>\n",
       "      <td>910.336378</td>\n",
       "      <td>958.571615</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>538.379685</td>\n",
       "      <td>567.717834</td>\n",
       "      <td>598.554355</td>\n",
       "      <td>630.964842</td>\n",
       "      <td>665.028694</td>\n",
       "      <td>700.829308</td>\n",
       "      <td>738.454274</td>\n",
       "      <td>777.995593</td>\n",
       "      <td>819.549896</td>\n",
       "      <td>863.218675</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>482.803062</td>\n",
       "      <td>509.345769</td>\n",
       "      <td>537.246240</td>\n",
       "      <td>566.572997</td>\n",
       "      <td>597.398012</td>\n",
       "      <td>629.796878</td>\n",
       "      <td>663.848992</td>\n",
       "      <td>699.637749</td>\n",
       "      <td>737.250740</td>\n",
       "      <td>776.779963</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>432.422112</td>\n",
       "      <td>456.430714</td>\n",
       "      <td>481.669616</td>\n",
       "      <td>508.200932</td>\n",
       "      <td>536.089897</td>\n",
       "      <td>565.405033</td>\n",
       "      <td>596.218310</td>\n",
       "      <td>628.605319</td>\n",
       "      <td>662.645458</td>\n",
       "      <td>698.422119</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>386.751110</td>\n",
       "      <td>408.462511</td>\n",
       "      <td>431.288667</td>\n",
       "      <td>455.285877</td>\n",
       "      <td>480.513274</td>\n",
       "      <td>507.032968</td>\n",
       "      <td>534.910195</td>\n",
       "      <td>564.213474</td>\n",
       "      <td>595.014776</td>\n",
       "      <td>627.389689</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>345.349737</td>\n",
       "      <td>364.978696</td>\n",
       "      <td>385.617664</td>\n",
       "      <td>407.317674</td>\n",
       "      <td>430.132324</td>\n",
       "      <td>454.117913</td>\n",
       "      <td>479.333571</td>\n",
       "      <td>505.841409</td>\n",
       "      <td>533.706661</td>\n",
       "      <td>562.997845</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>307.818841</td>\n",
       "      <td>325.560038</td>\n",
       "      <td>344.216292</td>\n",
       "      <td>363.833859</td>\n",
       "      <td>384.461322</td>\n",
       "      <td>406.149710</td>\n",
       "      <td>428.952622</td>\n",
       "      <td>452.926354</td>\n",
       "      <td>478.130037</td>\n",
       "      <td>504.625779</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>273.796584</td>\n",
       "      <td>289.826499</td>\n",
       "      <td>306.685396</td>\n",
       "      <td>324.415201</td>\n",
       "      <td>343.059949</td>\n",
       "      <td>362.665895</td>\n",
       "      <td>383.281619</td>\n",
       "      <td>404.958151</td>\n",
       "      <td>427.749088</td>\n",
       "      <td>451.710724</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>257.433569</td>\n",
       "      <td>272.663138</td>\n",
       "      <td>288.681662</td>\n",
       "      <td>305.529053</td>\n",
       "      <td>323.247236</td>\n",
       "      <td>341.880247</td>\n",
       "      <td>361.474336</td>\n",
       "      <td>382.078085</td>\n",
       "      <td>403.742521</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>241.821509</td>\n",
       "      <td>256.288732</td>\n",
       "      <td>271.506796</td>\n",
       "      <td>287.513698</td>\n",
       "      <td>304.349351</td>\n",
       "      <td>322.055678</td>\n",
       "      <td>340.676713</td>\n",
       "      <td>360.258706</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>226.924110</td>\n",
       "      <td>240.665166</td>\n",
       "      <td>255.120768</td>\n",
       "      <td>270.327093</td>\n",
       "      <td>286.322139</td>\n",
       "      <td>303.145817</td>\n",
       "      <td>320.840048</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>212.706817</td>\n",
       "      <td>225.756146</td>\n",
       "      <td>239.485464</td>\n",
       "      <td>253.929210</td>\n",
       "      <td>269.123559</td>\n",
       "      <td>285.106509</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>199.136725</td>\n",
       "      <td>211.527115</td>\n",
       "      <td>224.564588</td>\n",
       "      <td>238.281930</td>\n",
       "      <td>252.713580</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>186.182500</td>\n",
       "      <td>197.945166</td>\n",
       "      <td>210.323581</td>\n",
       "      <td>223.348958</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>173.814306</td>\n",
       "      <td>184.978966</td>\n",
       "      <td>196.729537</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>162.003734</td>\n",
       "      <td>172.598676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>30</th>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>...</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>0.000000</td>\n",
       "      <td>150.723730</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "<p>31 rows × 31 columns</p>\n",
       "</div>"
      ],
      "text/plain": [
       "            0           1           2            3            4            5   \\\n",
       "0   879.130188  925.179957  973.564375  1024.401057  1077.813536  1133.931559   \n",
       "1     0.000000  834.393475  878.211434   924.251970   972.627062  1023.454323   \n",
       "2     0.000000    0.000000  791.772723   833.465488   877.274121   923.305237   \n",
       "3     0.000000    0.000000    0.000000   751.166332   790.835410   832.518755   \n",
       "4     0.000000    0.000000    0.000000     0.000000   712.477566   750.219599   \n",
       "5     0.000000    0.000000    0.000000     0.000000     0.000000   675.614317   \n",
       "6     0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "7     0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "8     0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "9     0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "10    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "11    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "12    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "13    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "14    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "15    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "16    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "17    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "18    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "19    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "20    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "21    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "22    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "23    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "24    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "25    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "26    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "27    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "28    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "29    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "30    0.000000    0.000000    0.000000     0.000000     0.000000     0.000000   \n",
       "\n",
       "             6            7            8            9   ...           21  \\\n",
       "0   1192.891405  1254.836204  1319.916292  1388.289567  ...  2535.263292   \n",
       "1   1076.857287  1132.965701  1191.915839  1253.850834  ...  2293.004667   \n",
       "2    971.670814  1022.488465  1075.881722  1131.980330  ...  2073.393994   \n",
       "3    876.317873   922.339378   970.695248  1021.503095  ...  1874.313992   \n",
       "4    789.879162   831.552896   875.342307   921.354008  ...  1693.845317   \n",
       "5    711.521318   749.253740   788.903596   830.567526  ...  1530.248058   \n",
       "6    640.488888   674.648458   710.545752   748.268370  ...  1381.944962   \n",
       "7      0.000000   607.017776   639.513322   673.663088  ...  1247.506228   \n",
       "8      0.000000     0.000000   575.121477   606.032406  ...  1125.635725   \n",
       "9      0.000000     0.000000     0.000000   544.724291  ...  1015.158489   \n",
       "10     0.000000     0.000000     0.000000     0.000000  ...   915.009402   \n",
       "11     0.000000     0.000000     0.000000     0.000000  ...   824.222920   \n",
       "12     0.000000     0.000000     0.000000     0.000000  ...   741.923764   \n",
       "13     0.000000     0.000000     0.000000     0.000000  ...   667.318483   \n",
       "14     0.000000     0.000000     0.000000     0.000000  ...   599.687800   \n",
       "15     0.000000     0.000000     0.000000     0.000000  ...   538.379685   \n",
       "16     0.000000     0.000000     0.000000     0.000000  ...   482.803062   \n",
       "17     0.000000     0.000000     0.000000     0.000000  ...   432.422112   \n",
       "18     0.000000     0.000000     0.000000     0.000000  ...   386.751110   \n",
       "19     0.000000     0.000000     0.000000     0.000000  ...   345.349737   \n",
       "20     0.000000     0.000000     0.000000     0.000000  ...   307.818841   \n",
       "21     0.000000     0.000000     0.000000     0.000000  ...   273.796584   \n",
       "22     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "23     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "24     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "25     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "26     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "27     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "28     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "29     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "30     0.000000     0.000000     0.000000     0.000000  ...     0.000000   \n",
       "\n",
       "             22           23           24           25           26  \\\n",
       "0   2665.042453  2801.372056  2944.581810  3095.018009  3253.044367   \n",
       "1   2410.598490  2534.129846  2663.897616  2800.215714  2943.413846   \n",
       "2   2179.941646  2291.871221  2409.453653  2532.973504  2662.729652   \n",
       "3   1970.848143  2072.260548  2178.796809  2290.714878  2408.285689   \n",
       "4   1781.302095  1873.180547  1969.703306  2071.104206  2177.628845   \n",
       "5   1609.476076  1692.711871  1780.157258  1872.024204  1968.535341   \n",
       "6   1453.713500  1529.114612  1608.331239  1691.555529  1778.989294   \n",
       "7   1312.512649  1380.811516  1452.568663  1527.958269  1607.163275   \n",
       "8   1184.512196  1246.372783  1311.367812  1379.655173  1451.400699   \n",
       "9   1068.478078  1124.502279  1183.367359  1245.216440  1310.199848   \n",
       "10   963.291605  1014.025043  1067.333241  1123.345936  1182.199394   \n",
       "11   867.938664   913.875957   962.146768  1012.868701  1066.165277   \n",
       "12   781.499953   823.089475   866.793827   912.719614   960.978803   \n",
       "13   703.142109   740.790319   780.355116   821.933132   865.625863   \n",
       "14   632.109679   666.185037   701.997272   739.633976   779.187152   \n",
       "15   567.717834   598.554355   630.964842   665.028694   700.829308   \n",
       "16   509.345769   537.246240   566.572997   597.398012   629.796878   \n",
       "17   456.430714   481.669616   508.200932   536.089897   565.405033   \n",
       "18   408.462511   431.288667   455.285877   480.513274   507.032968   \n",
       "19   364.978696   385.617664   407.317674   430.132324   454.117913   \n",
       "20   325.560038   344.216292   363.833859   384.461322   406.149710   \n",
       "21   289.826499   306.685396   324.415201   343.059949   362.665895   \n",
       "22   257.433569   272.663138   288.681662   305.529053   323.247236   \n",
       "23     0.000000   241.821509   256.288732   271.506796   287.513698   \n",
       "24     0.000000     0.000000   226.924110   240.665166   255.120768   \n",
       "25     0.000000     0.000000     0.000000   212.706817   225.756146   \n",
       "26     0.000000     0.000000     0.000000     0.000000   199.136725   \n",
       "27     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "28     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "29     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "30     0.000000     0.000000     0.000000     0.000000     0.000000   \n",
       "\n",
       "             27           28           29           30  \n",
       "0   3419.042897  3593.414826  3776.581568  3968.985733  \n",
       "1   3093.838307  3251.852809  3417.839363  3592.199196  \n",
       "2   2799.036011  2942.222288  3092.634773  3250.637179  \n",
       "3   2531.793801  2661.538093  2797.832477  2941.006658  \n",
       "4   2289.535176  2407.094130  2530.590267  2660.322464  \n",
       "5   2069.924503  2176.437286  2288.331642  2405.878500  \n",
       "6   1870.844501  1967.343783  2068.720969  2175.221656  \n",
       "7   1690.375826  1777.797735  1869.640967  1966.128153  \n",
       "8   1526.778567  1605.971717  1689.172292  1776.582105  \n",
       "9   1378.475471  1450.209141  1525.575033  1604.756087  \n",
       "10  1244.036738  1309.008289  1377.271937  1448.993511  \n",
       "11  1122.166234  1181.007836  1242.833204  1307.792660  \n",
       "12  1011.688998  1064.973719  1120.962700  1179.792206  \n",
       "13   911.539911   959.787245  1010.485464  1063.758089  \n",
       "14   820.753430   864.434304   910.336378   958.571615  \n",
       "15   738.454274   777.995593   819.549896   863.218675  \n",
       "16   663.848992   699.637749   737.250740   776.779963  \n",
       "17   596.218310   628.605319   662.645458   698.422119  \n",
       "18   534.910195   564.213474   595.014776   627.389689  \n",
       "19   479.333571   505.841409   533.706661   562.997845  \n",
       "20   428.952622   452.926354   478.130037   504.625779  \n",
       "21   383.281619   404.958151   427.749088   451.710724  \n",
       "22   341.880247   361.474336   382.078085   403.742521  \n",
       "23   304.349351   322.055678   340.676713   360.258706  \n",
       "24   270.327093   286.322139   303.145817   320.840048  \n",
       "25   239.485464   253.929210   269.123559   285.106509  \n",
       "26   211.527115   224.564588   238.281930   252.713580  \n",
       "27   186.182500   197.945166   210.323581   223.348958  \n",
       "28     0.000000   173.814306   184.978966   196.729537  \n",
       "29     0.000000     0.000000   162.003734   172.598676  \n",
       "30     0.000000     0.000000     0.000000   150.723730  \n",
       "\n",
       "[31 rows x 31 columns]"
      ]
     },
     "execution_count": 24,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "for i in range(N+1):\n",
    "    option_values[i][N] = max(0, stock_prices[i][N] - K)\n",
    "\n",
    "\n",
    "for i in range(N-1, -1, -1):\n",
    "    for j in range(i+1):\n",
    "        option_values[j][i] = (p*option_values[j][i+1] + (1-p)*option_values[j+1][i+1])*np.exp(-r*dt)\n",
    "        \n",
    "df2 = pd.DataFrame(option_values)\n",
    "df2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "id": "a2343d4f",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "Present Value of NPV of option case = £924.61 million\n",
      "\n",
      "Total volitility = 0.09\n",
      "\n",
      "Option value = £879.13 million\n",
      "\n",
      "Total value of project = £159.13 million\n",
      "\n"
     ]
    }
   ],
   "source": [
    "Co = option_values[0][0]\n",
    "\n",
    "#Add NPV of the BAU case with the option value to find total value of the project\n",
    "totalValue = Co - BAUsetupCost\n",
    "\n",
    "print(\"Present Value of NPV of option case = £%.2f million\\n\" % S)\n",
    "print(\"Total volitility = %.2f\\n\" % totalSigma)\n",
    "print(\"Option value = £%.2f million\\n\" % Co)\n",
    "print(\"Total value of project = £%.2f million\\n\" % totalValue)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "21e75451",
   "metadata": {},
   "outputs": [],
   "source": []
  }
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