Macro II - PS8.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Jordan Holbrook\n",
    "## Macro II\n",
    "## PS 8\n",
    "## 4/9/2021"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# Equity Premium Puzzle"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Importing Packages\n",
    "import os\n",
    "import pandas as pd \n",
    "import isbnlib \n",
    "import numpy as np\n",
    "import time\n",
    "import requests\n",
    "from bs4 import BeautifulSoup\n",
    "import datetime\n",
    "import re\n",
    "from sympy import symbols, Eq, solve"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "Reading in the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>year</th>\n",
       "      <th>qtr</th>\n",
       "      <th>Consumption</th>\n",
       "      <th>Equity</th>\n",
       "      <th>Bonds</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>1947</td>\n",
       "      <td>1</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "      <td>NaN</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>1947</td>\n",
       "      <td>2</td>\n",
       "      <td>0.010879</td>\n",
       "      <td>-0.050602</td>\n",
       "      <td>-0.008857</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>1947</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.002750</td>\n",
       "      <td>0.046852</td>\n",
       "      <td>-0.019506</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>1947</td>\n",
       "      <td>4</td>\n",
       "      <td>-0.011554</td>\n",
       "      <td>-0.023406</td>\n",
       "      <td>-0.022647</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>1948</td>\n",
       "      <td>1</td>\n",
       "      <td>0.005972</td>\n",
       "      <td>-0.052005</td>\n",
       "      <td>-0.007556</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>1948</td>\n",
       "      <td>2</td>\n",
       "      <td>0.009992</td>\n",
       "      <td>0.115816</td>\n",
       "      <td>-0.007229</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>1948</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.001184</td>\n",
       "      <td>-0.000729</td>\n",
       "      <td>-0.005773</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>1948</td>\n",
       "      <td>4</td>\n",
       "      <td>0.009247</td>\n",
       "      <td>-0.013445</td>\n",
       "      <td>0.005318</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>1949</td>\n",
       "      <td>1</td>\n",
       "      <td>0.003337</td>\n",
       "      <td>-0.010638</td>\n",
       "      <td>0.011746</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>1949</td>\n",
       "      <td>2</td>\n",
       "      <td>0.002030</td>\n",
       "      <td>-0.007460</td>\n",
       "      <td>0.009992</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>1949</td>\n",
       "      <td>3</td>\n",
       "      <td>-0.008156</td>\n",
       "      <td>0.064687</td>\n",
       "      <td>0.008320</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>1949</td>\n",
       "      <td>4</td>\n",
       "      <td>0.005727</td>\n",
       "      <td>0.078317</td>\n",
       "      <td>0.000861</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "    year  qtr  Consumption    Equity     Bonds\n",
       "0   1947    1          NaN       NaN       NaN\n",
       "1   1947    2     0.010879 -0.050602 -0.008857\n",
       "2   1947    3    -0.002750  0.046852 -0.019506\n",
       "3   1947    4    -0.011554 -0.023406 -0.022647\n",
       "4   1948    1     0.005972 -0.052005 -0.007556\n",
       "5   1948    2     0.009992  0.115816 -0.007229\n",
       "6   1948    3    -0.001184 -0.000729 -0.005773\n",
       "7   1948    4     0.009247 -0.013445  0.005318\n",
       "8   1949    1     0.003337 -0.010638  0.011746\n",
       "9   1949    2     0.002030 -0.007460  0.009992\n",
       "10  1949    3    -0.008156  0.064687  0.008320\n",
       "11  1949    4     0.005727  0.078317  0.000861"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "data = pd.read_excel(r\"C:\\Users\\jcholbro\\OneDrive - University Of Houston\\School_UH\\Macro II\\Macro_PS8_Data.xlsx\", ignore_index=True)\n",
    "\n",
    "data = data.drop(columns='Unnamed: 2')\n",
    "data.head(12)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Computing Moments from the Data"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mu:  0.0045141897637948755\n",
      "delta:  0.005570715863764123\n",
      "rho:  0.6067036487176168\n",
      "phi:  0.8033518243588085\n"
     ]
    }
   ],
   "source": [
    "mu = np.mean(data.Consumption)\n",
    "delta = np.std(data.Consumption)\n",
    "ave_stocks = np.mean(data.Equity)\n",
    "ave_bonds = np.mean(data.Bonds)\n",
    "true_premium = ave_stocks-ave_bonds\n",
    "\n",
    "lambda1 = 1+mu+delta\n",
    "lambda2 = 1+mu-delta\n",
    "\n",
    "data['lag_consumption'] = data['Consumption'].shift(1)\n",
    "\n",
    "cov = data[['Consumption','lag_consumption']].cov()\n",
    "cov = cov.iloc[0,1]\n",
    "var = data['Consumption'].var()\n",
    "\n",
    "rho=(cov+var)/(2*var)\n",
    "phi=(1+rho)/2\n",
    "\n",
    "print('mu:  '+ str(mu))\n",
    "print('delta:  '+ str(delta))\n",
    "print('rho:  '+ str(rho))\n",
    "print('phi:  '+ str(phi))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "phi1 = 1-phi\n",
    "phi2 = phi\n",
    "\n",
    "beta = 0.99\n",
    "sigma = 10\n",
    "\n",
    "#x, y = symbols('x y')\n",
    "w1, w2 = symbols('w1 w2')\n",
    "eq1 = beta*(phi1*w1*lambda1**(1-sigma)+phi2*w2*lambda2**(1-sigma))+beta*(phi1*lambda1**(1-sigma)+phi2*lambda2**(1-sigma))-w1\n",
    "eq2 = beta*(phi2*w1*lambda1**(1-sigma)+phi1*w2*lambda2**(1-sigma))+beta*(phi2*lambda1**(1-sigma)+phi1*lambda2**(1-sigma))-w2\n",
    "solve((eq1,eq2), (w1, w2))\n",
    "solution = solve((eq1,eq2), (w1, w2))\n",
    "\n",
    "s1=solution[w1]\n",
    "s2=solution[w2]\n",
    "returns_stocks = ((lambda1*(s1+1))/s1 + (lambda2*(s2+1))/s2)*(.5)\n",
    "returns_bonds = 1/(beta*(phi1*lambda1**(-sigma)+(phi2*lambda2**(-sigma))))\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 1 a & b) Computing the Returns to Equity and Bonds"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "return equity:  5.61507754019193%\n",
      "return bonds:  2.054896369982151%\n"
     ]
    }
   ],
   "source": [
    "print('return equity:  '+ str((returns_stocks-1)*100)+'%')\n",
    "print('return bonds:  '+ str((returns_bonds-1)*100)+'%')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### 1 c) Is the unconditional equity premium close to that in the data?"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "3.56018117020978\n",
      "0.01651910470348718\n",
      "-0.0190827069986106\n"
     ]
    }
   ],
   "source": [
    "premium  = (returns_stocks-1)-(returns_bonds-1)\n",
    "print(premium*100)\n",
    "how_close = true_premium-premium\n",
    "print(true_premium)\n",
    "print(how_close)\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### The Equity Premium is about 1% off from the true premium in the data. This could be due to misspecifying the parameters incorrectly in the model or not calibrating the model to the data moments correctly. We do however, have the correct implication from the model. The Return to Equity is higher than that of the return to bonds."
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 2) Habit Presistence\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### Here we specify the range of parameter values that we want to search through."
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "sigma_list = list(range(1,11))\n",
    "beta_list = list(np.linspace(0.90,1.0,11))\n",
    "delta_list = list(np.linspace(0.25,1.25,11))\n",
    "results_rows = []\n",
    "w1, w2 = symbols('w1 w2')\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {
    "collapsed": true
   },
   "outputs": [
    {
     "ename": "TypeError",
     "evalue": "list indices must be integers or slices, not Symbol",
     "output_type": "error",
     "traceback": [
      "\u001b[1;31m---------------------------------------------------------------------------\u001b[0m",
      "\u001b[1;31mTypeError\u001b[0m                                 Traceback (most recent call last)",
      "\u001b[1;32m<ipython-input-32-46b74b804a1e>\u001b[0m in \u001b[0;36m<module>\u001b[1;34m\u001b[0m\n\u001b[0;32m     16\u001b[0m             \u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meq3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0meq4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mw1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     17\u001b[0m             \u001b[0msolution2\u001b[0m \u001b[1;33m=\u001b[0m \u001b[0msolve\u001b[0m\u001b[1;33m(\u001b[0m\u001b[1;33m(\u001b[0m\u001b[0meq3\u001b[0m\u001b[1;33m,\u001b[0m\u001b[0meq4\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m,\u001b[0m \u001b[1;33m(\u001b[0m\u001b[0mw1\u001b[0m\u001b[1;33m,\u001b[0m \u001b[0mw2\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m)\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[1;32m---> 18\u001b[1;33m             \u001b[0ms1\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msolution2\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mw1\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0m\u001b[0;32m     19\u001b[0m             \u001b[0ms2\u001b[0m\u001b[1;33m=\u001b[0m\u001b[0msolution2\u001b[0m\u001b[1;33m[\u001b[0m\u001b[0mw2\u001b[0m\u001b[1;33m]\u001b[0m\u001b[1;33m\u001b[0m\u001b[1;33m\u001b[0m\u001b[0m\n\u001b[0;32m     20\u001b[0m \u001b[1;33m\u001b[0m\u001b[0m\n",
      "\u001b[1;31mTypeError\u001b[0m: list indices must be integers or slices, not Symbol"
     ]
    }
   ],
   "source": [
    "# Giant triple for loop to grid search through our parameter values\n",
    "for beta in beta_list:\n",
    "    for sigma in sigma_list:\n",
    "        for delta in delta_list:\n",
    "            results_col= {}\n",
    "\n",
    "            #print(delta)\n",
    "            #print(sigma)\n",
    "            #print(beta)\n",
    "            \n",
    "            M1 = ((lambda1-delta)/(1-(delta/lambda1)))**(-sigma)\n",
    "            M2 = ((lambda2-delta)/(1-(delta/lambda2)))**(-sigma)\n",
    "            \n",
    "            eq3 = beta*(phi1*w1*lambda1*M1+phi2*w2*lambda2*M2)+beta*(phi1*lambda1*M1+phi2*lambda2*M2)-w1      \n",
    "            eq4 = beta*(phi2*w1*lambda1*M1+phi1*w2*lambda2*M2)+beta*(phi2*lambda1*M1+phi1*lambda2*M2)-w2\n",
    "            solve((eq3,eq4), (w1, w2))\n",
    "            solution2 = solve((eq3,eq4), (w1, w2))\n",
    "            s1=solution2[w1]\n",
    "            s2=solution2[w2]\n",
    "            \n",
    "            returns_stocks = ((lambda1*(s1+1))/s1 + (lambda2*(s2+1))/s2)*(.5)\n",
    "            \n",
    "            returns_bonds = 1/(beta*(phi1*lambda1**(-sigma)+(phi2*lambda2**(-sigma))))\n",
    "            \n",
    "            premium  = returns_stocks-returns_bonds\n",
    "            #print(premium)\n",
    "            how_close = true_premium-premium\n",
    "            \n",
    "            results_col['model premium'] = premium*100\n",
    "            results_col['data_premium'] = true_premium*100\n",
    "            results_col['difference'] = how_close\n",
    "            results_col['parameters'] = [beta,sigma, delta]\n",
    "            results_rows.append(results_col)\n",
    "            "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {
    "scrolled": true
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    {
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       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>model premium</th>\n",
       "      <th>data_premium</th>\n",
       "      <th>difference</th>\n",
       "      <th>parameters</th>\n",
       "    </tr>\n",
       "  </thead>\n",
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       "      <th>0</th>\n",
       "      <td>0.377692228627069</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172165</td>\n",
       "      <td>[0.9, 1, 0.25]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.377692228627069</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172165</td>\n",
       "      <td>[0.9, 1, 0.35]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.377692228627069</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172165</td>\n",
       "      <td>[0.9, 1, 0.45]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.377692228627069</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172165</td>\n",
       "      <td>[0.9, 1, 0.55]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.377692228627069</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172165</td>\n",
       "      <td>[0.9, 1, 0.65]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.377692228627069</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172165</td>\n",
       "      <td>[0.9, 1, 0.75]</td>\n",
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       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.377692228627136</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172158</td>\n",
       "      <td>[0.9, 1, 0.8500000000000001]</td>\n",
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       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.377692228627069</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172165</td>\n",
       "      <td>[0.9, 1, 0.9500000000000001]</td>\n",
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       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.377692228627247</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172147</td>\n",
       "      <td>[0.9, 1, 1.05]</td>\n",
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       "      <th>9</th>\n",
       "      <td>0.377692228627136</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172158</td>\n",
       "      <td>[0.9, 1, 1.15]</td>\n",
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       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.377692228627202</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.0127421824172152</td>\n",
       "      <td>[0.9, 1, 1.25]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.757340778411786</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936932</td>\n",
       "      <td>[0.9, 2, 0.25]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.757340778411786</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936932</td>\n",
       "      <td>[0.9, 2, 0.35]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.757340778411830</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936888</td>\n",
       "      <td>[0.9, 2, 0.45]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.757340778411786</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936932</td>\n",
       "      <td>[0.9, 2, 0.55]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.757340778411786</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936932</td>\n",
       "      <td>[0.9, 2, 0.65]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.757340778411786</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936932</td>\n",
       "      <td>[0.9, 2, 0.75]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.757340778411830</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936888</td>\n",
       "      <td>[0.9, 2, 0.8500000000000001]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.757340778411830</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936888</td>\n",
       "      <td>[0.9, 2, 0.9500000000000001]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.757340778412163</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936555</td>\n",
       "      <td>[0.9, 2, 1.05]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.757340778411808</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936910</td>\n",
       "      <td>[0.9, 2, 1.15]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.757340778411919</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00894569691936799</td>\n",
       "      <td>[0.9, 2, 1.25]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>1.14031773171459</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00511592738634127</td>\n",
       "      <td>[0.9, 3, 0.25]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.14031773171452</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00511592738634194</td>\n",
       "      <td>[0.9, 3, 0.35]</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>1.14031773171459</td>\n",
       "      <td>1.65191</td>\n",
       "      <td>0.00511592738634127</td>\n",
       "      <td>[0.9, 3, 0.45]</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "        model premium  data_premium           difference  \\\n",
       "0   0.377692228627069       1.65191   0.0127421824172165   \n",
       "1   0.377692228627069       1.65191   0.0127421824172165   \n",
       "2   0.377692228627069       1.65191   0.0127421824172165   \n",
       "3   0.377692228627069       1.65191   0.0127421824172165   \n",
       "4   0.377692228627069       1.65191   0.0127421824172165   \n",
       "5   0.377692228627069       1.65191   0.0127421824172165   \n",
       "6   0.377692228627136       1.65191   0.0127421824172158   \n",
       "7   0.377692228627069       1.65191   0.0127421824172165   \n",
       "8   0.377692228627247       1.65191   0.0127421824172147   \n",
       "9   0.377692228627136       1.65191   0.0127421824172158   \n",
       "10  0.377692228627202       1.65191   0.0127421824172152   \n",
       "11  0.757340778411786       1.65191  0.00894569691936932   \n",
       "12  0.757340778411786       1.65191  0.00894569691936932   \n",
       "13  0.757340778411830       1.65191  0.00894569691936888   \n",
       "14  0.757340778411786       1.65191  0.00894569691936932   \n",
       "15  0.757340778411786       1.65191  0.00894569691936932   \n",
       "16  0.757340778411786       1.65191  0.00894569691936932   \n",
       "17  0.757340778411830       1.65191  0.00894569691936888   \n",
       "18  0.757340778411830       1.65191  0.00894569691936888   \n",
       "19  0.757340778412163       1.65191  0.00894569691936555   \n",
       "20  0.757340778411808       1.65191  0.00894569691936910   \n",
       "21  0.757340778411919       1.65191  0.00894569691936799   \n",
       "22   1.14031773171459       1.65191  0.00511592738634127   \n",
       "23   1.14031773171452       1.65191  0.00511592738634194   \n",
       "24   1.14031773171459       1.65191  0.00511592738634127   \n",
       "\n",
       "                      parameters  \n",
       "0                 [0.9, 1, 0.25]  \n",
       "1                 [0.9, 1, 0.35]  \n",
       "2                 [0.9, 1, 0.45]  \n",
       "3                 [0.9, 1, 0.55]  \n",
       "4                 [0.9, 1, 0.65]  \n",
       "5                 [0.9, 1, 0.75]  \n",
       "6   [0.9, 1, 0.8500000000000001]  \n",
       "7   [0.9, 1, 0.9500000000000001]  \n",
       "8                 [0.9, 1, 1.05]  \n",
       "9                 [0.9, 1, 1.15]  \n",
       "10                [0.9, 1, 1.25]  \n",
       "11                [0.9, 2, 0.25]  \n",
       "12                [0.9, 2, 0.35]  \n",
       "13                [0.9, 2, 0.45]  \n",
       "14                [0.9, 2, 0.55]  \n",
       "15                [0.9, 2, 0.65]  \n",
       "16                [0.9, 2, 0.75]  \n",
       "17  [0.9, 2, 0.8500000000000001]  \n",
       "18  [0.9, 2, 0.9500000000000001]  \n",
       "19                [0.9, 2, 1.05]  \n",
       "20                [0.9, 2, 1.15]  \n",
       "21                [0.9, 2, 1.25]  \n",
       "22                [0.9, 3, 0.25]  \n",
       "23                [0.9, 3, 0.35]  \n",
       "24                [0.9, 3, 0.45]  "
      ]
     },
     "execution_count": 33,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "table = pd.DataFrame(results_rows)   \n",
    "table.head(25)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "table['abs_difference'] = abs(table['difference'])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "model premium     1.74283745873896\n",
       "data_premium               1.65191\n",
       "difference             -0.00090927\n",
       "parameters         [0.99, 5, 0.35]\n",
       "abs_difference          0.00090927\n",
       "Name: 1035, dtype: object"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "    \n",
    "table['abs_difference'] = table['abs_difference'].astype(float)\n",
    "table['abs_difference'].idxmin()\n",
    "table.loc[table['abs_difference'].idxmin()]\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Best Parameters\n",
    "### Beta = 0.99\n",
    "### Sigma = 5\n",
    "### Delta = 0.35"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2c4b792b608>]"
      ]
     },
     "execution_count": 40,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.plot(table.difference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[<matplotlib.lines.Line2D at 0x2c4b8647288>]"
      ]
     },
     "execution_count": 47,
     "metadata": {},
     "output_type": "execute_result"
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "plt.plot(table.abs_difference)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.7.6"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}