ipynb/AntonovEtAl-2012-SSRN-SABR.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# AntonovEtAl-2012-SSRN-SABR"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "* Antonov, A., & Spector, M. (2012). Advanced analytics for the SABR model. Available at SSRN. https://ssrn.com/abstract=2026350\n",
    "* Antonov, A., Konikov, M., & Spector, M. (2013). SABR spreads its wings. Risk, 2013(Aug), 58–63.\n",
    "* Antonov, A., Konikov, M., & Spector, M. (2019). Modern SABR Analytics. Springer International Publishing. https://doi.org/10.1007/978-3-030-10656-0"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "import copy\n",
    "import pandas as pd\n",
    "import scipy as sp\n",
    "\n",
    "### Uncomment below if you want to run on your modified code\n",
    "#import sys\n",
    "#sys.path.insert(sys.path.index('')+1, 'D:/Github/PyFENG')\n",
    "import pyfeng as pf"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>sigma</th>\n",
       "      <th>vov</th>\n",
       "      <th>rho</th>\n",
       "      <th>beta</th>\n",
       "      <th>texp</th>\n",
       "      <th>spot</th>\n",
       "      <th>col_name</th>\n",
       "      <th>Reference</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Sheet</th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.8000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 1 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.8000</td>\n",
       "      <td>0.6</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 2 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.8000</td>\n",
       "      <td>0.9</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 3 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.5000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 4 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.5000</td>\n",
       "      <td>0.6</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 5 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.5000</td>\n",
       "      <td>0.9</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 6 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.2000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 7 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.2000</td>\n",
       "      <td>0.6</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 8 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.2000</td>\n",
       "      <td>0.9</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 9 in Antonov &amp; Spector (2012). https://s...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.8000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 10 in Antonov &amp; Spector (2012). https://...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>11</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.8000</td>\n",
       "      <td>0.6</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 11 in Antonov &amp; Spector (2012). https://...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>12</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.8000</td>\n",
       "      <td>0.9</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 12 in Antonov &amp; Spector (2012). https://...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>13</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.5000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 13 in Antonov &amp; Spector (2012). https://...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>14</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.5000</td>\n",
       "      <td>0.6</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 14 in Antonov &amp; Spector (2012) / Table A...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>15</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.5000</td>\n",
       "      <td>0.9</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 15 in Antonov &amp; Spector (2012). https://...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>16</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.2000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC</td>\n",
       "      <td>Table 16 in Antonov &amp; Spector (2012). https://...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>17</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.2000</td>\n",
       "      <td>0.6</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC2</td>\n",
       "      <td>Table 4.2 in Antonov et al. (2019) / Table 17 ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>18</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3000</td>\n",
       "      <td>-0.2000</td>\n",
       "      <td>0.9</td>\n",
       "      <td>20.00</td>\n",
       "      <td>1.00</td>\n",
       "      <td>IV MC2</td>\n",
       "      <td>Table 4.3 in Antonov et al. (2019) / Table 17 ...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>19</th>\n",
       "      <td>0.40</td>\n",
       "      <td>0.6000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.3</td>\n",
       "      <td>1.00</td>\n",
       "      <td>0.05</td>\n",
       "      <td>P FDM</td>\n",
       "      <td>Table 7 (Case III.C) in Cai et al. (2017). htt...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>20</th>\n",
       "      <td>0.50</td>\n",
       "      <td>0.4000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.5</td>\n",
       "      <td>2.00</td>\n",
       "      <td>0.50</td>\n",
       "      <td>P ADI</td>\n",
       "      <td>Table A1, Figure 1 (Set I) in von Sydow et al....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>21</th>\n",
       "      <td>0.40</td>\n",
       "      <td>0.8000</td>\n",
       "      <td>-0.6000</td>\n",
       "      <td>0.5</td>\n",
       "      <td>10.00</td>\n",
       "      <td>0.07</td>\n",
       "      <td>P ADI</td>\n",
       "      <td>Table A2, Figure 2 (Set II) in von Sydow et al...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>22</th>\n",
       "      <td>0.68</td>\n",
       "      <td>0.3691</td>\n",
       "      <td>-0.0286</td>\n",
       "      <td>0.0</td>\n",
       "      <td>10.00</td>\n",
       "      <td>4.35</td>\n",
       "      <td>P New</td>\n",
       "      <td>Tables 1 and 2 (Case I) in Korn &amp; Tang (2013)....</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>23</th>\n",
       "      <td>1.00</td>\n",
       "      <td>0.5000</td>\n",
       "      <td>0.0000</td>\n",
       "      <td>0.0</td>\n",
       "      <td>30.00</td>\n",
       "      <td>3.50</td>\n",
       "      <td>P New</td>\n",
       "      <td>Tables 3 and 4 (Case II) in Korn &amp; Tang (2013)...</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>24</th>\n",
       "      <td>0.20</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>-0.7500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>0.25</td>\n",
       "      <td>1000.00</td>\n",
       "      <td>P</td>\n",
       "      <td>Table 8.6 (p 403) in Lewis (2016).</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>25</th>\n",
       "      <td>0.20</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>-0.7500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>1.00</td>\n",
       "      <td>1000.00</td>\n",
       "      <td>P</td>\n",
       "      <td>Table 8.6 (p 403) in Lewis (2016).</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>26</th>\n",
       "      <td>0.20</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>-0.7500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>2.00</td>\n",
       "      <td>1000.00</td>\n",
       "      <td>P</td>\n",
       "      <td>Table 8.6 (p 403) in Lewis (2016).</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>27</th>\n",
       "      <td>0.20</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>-0.7500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>5.00</td>\n",
       "      <td>1000.00</td>\n",
       "      <td>P</td>\n",
       "      <td>Table 8.6 (p 403) in Lewis (2016).</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>28</th>\n",
       "      <td>0.20</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>-0.7500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>10.00</td>\n",
       "      <td>1000.00</td>\n",
       "      <td>P</td>\n",
       "      <td>Table 8.4 (p 308) in Lewis (2016).</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>29</th>\n",
       "      <td>0.20</td>\n",
       "      <td>1.0000</td>\n",
       "      <td>-0.7500</td>\n",
       "      <td>1.0</td>\n",
       "      <td>50.00</td>\n",
       "      <td>1000.00</td>\n",
       "      <td>P</td>\n",
       "      <td>Table 8.6 (p 403) in Lewis (2016).</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       sigma     vov     rho  beta   texp     spot col_name  \\\n",
       "Sheet                                                         \n",
       "1       0.25  0.3000 -0.8000   0.3  10.00     1.00    IV MC   \n",
       "2       0.25  0.3000 -0.8000   0.6  10.00     1.00    IV MC   \n",
       "3       0.25  0.3000 -0.8000   0.9  10.00     1.00    IV MC   \n",
       "4       0.25  0.3000 -0.5000   0.3  10.00     1.00    IV MC   \n",
       "5       0.25  0.3000 -0.5000   0.6  10.00     1.00    IV MC   \n",
       "6       0.25  0.3000 -0.5000   0.9  10.00     1.00    IV MC   \n",
       "7       0.25  0.3000 -0.2000   0.3  10.00     1.00    IV MC   \n",
       "8       0.25  0.3000 -0.2000   0.6  10.00     1.00    IV MC   \n",
       "9       0.25  0.3000 -0.2000   0.9  10.00     1.00    IV MC   \n",
       "10      0.25  0.3000 -0.8000   0.3  20.00     1.00    IV MC   \n",
       "11      0.25  0.3000 -0.8000   0.6  20.00     1.00    IV MC   \n",
       "12      0.25  0.3000 -0.8000   0.9  20.00     1.00    IV MC   \n",
       "13      0.25  0.3000 -0.5000   0.3  20.00     1.00    IV MC   \n",
       "14      0.25  0.3000 -0.5000   0.6  20.00     1.00    IV MC   \n",
       "15      0.25  0.3000 -0.5000   0.9  20.00     1.00    IV MC   \n",
       "16      0.25  0.3000 -0.2000   0.3  20.00     1.00    IV MC   \n",
       "17      0.25  0.3000 -0.2000   0.6  20.00     1.00   IV MC2   \n",
       "18      0.25  0.3000 -0.2000   0.9  20.00     1.00   IV MC2   \n",
       "19      0.40  0.6000  0.0000   0.3   1.00     0.05    P FDM   \n",
       "20      0.50  0.4000  0.0000   0.5   2.00     0.50    P ADI   \n",
       "21      0.40  0.8000 -0.6000   0.5  10.00     0.07    P ADI   \n",
       "22      0.68  0.3691 -0.0286   0.0  10.00     4.35    P New   \n",
       "23      1.00  0.5000  0.0000   0.0  30.00     3.50    P New   \n",
       "24      0.20  1.0000 -0.7500   1.0   0.25  1000.00        P   \n",
       "25      0.20  1.0000 -0.7500   1.0   1.00  1000.00        P   \n",
       "26      0.20  1.0000 -0.7500   1.0   2.00  1000.00        P   \n",
       "27      0.20  1.0000 -0.7500   1.0   5.00  1000.00        P   \n",
       "28      0.20  1.0000 -0.7500   1.0  10.00  1000.00        P   \n",
       "29      0.20  1.0000 -0.7500   1.0  50.00  1000.00        P   \n",
       "\n",
       "                                               Reference  \n",
       "Sheet                                                     \n",
       "1      Table 1 in Antonov & Spector (2012). https://s...  \n",
       "2      Table 2 in Antonov & Spector (2012). https://s...  \n",
       "3      Table 3 in Antonov & Spector (2012). https://s...  \n",
       "4      Table 4 in Antonov & Spector (2012). https://s...  \n",
       "5      Table 5 in Antonov & Spector (2012). https://s...  \n",
       "6      Table 6 in Antonov & Spector (2012). https://s...  \n",
       "7      Table 7 in Antonov & Spector (2012). https://s...  \n",
       "8      Table 8 in Antonov & Spector (2012). https://s...  \n",
       "9      Table 9 in Antonov & Spector (2012). https://s...  \n",
       "10     Table 10 in Antonov & Spector (2012). https://...  \n",
       "11     Table 11 in Antonov & Spector (2012). https://...  \n",
       "12     Table 12 in Antonov & Spector (2012). https://...  \n",
       "13     Table 13 in Antonov & Spector (2012). https://...  \n",
       "14     Table 14 in Antonov & Spector (2012) / Table A...  \n",
       "15     Table 15 in Antonov & Spector (2012). https://...  \n",
       "16     Table 16 in Antonov & Spector (2012). https://...  \n",
       "17     Table 4.2 in Antonov et al. (2019) / Table 17 ...  \n",
       "18     Table 4.3 in Antonov et al. (2019) / Table 17 ...  \n",
       "19     Table 7 (Case III.C) in Cai et al. (2017). htt...  \n",
       "20     Table A1, Figure 1 (Set I) in von Sydow et al....  \n",
       "21     Table A2, Figure 2 (Set II) in von Sydow et al...  \n",
       "22     Tables 1 and 2 (Case I) in Korn & Tang (2013)....  \n",
       "23     Tables 3 and 4 (Case II) in Korn & Tang (2013)...  \n",
       "24                    Table 8.6 (p 403) in Lewis (2016).  \n",
       "25                    Table 8.6 (p 403) in Lewis (2016).  \n",
       "26                    Table 8.6 (p 403) in Lewis (2016).  \n",
       "27                    Table 8.6 (p 403) in Lewis (2016).  \n",
       "28                    Table 8.4 (p 308) in Lewis (2016).  \n",
       "29                    Table 8.6 (p 403) in Lewis (2016).  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "# This is the list of parameters\n",
    "sheets = list(range(1, 19))\n",
    "pf.SabrHagan2002.init_benchmark() #.loc[sheets,]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "      K  IV HL-P  IV Hagan\n",
      "0   0.1   0.7898    0.7176\n",
      "1   0.2   0.5992    0.5725\n",
      "2   0.3   0.4999    0.4886\n",
      "3   0.4   0.4339    0.4293\n",
      "4   0.5   0.3849    0.3835\n",
      "5   0.6   0.3461    0.3462\n",
      "6   0.7   0.3141    0.3148\n",
      "7   0.8   0.2869    0.2876\n",
      "8   0.9   0.2634    0.2638\n",
      "9   1.0   0.2427    0.2427\n",
      "10  1.1   0.2244    0.2238\n",
      "11  1.2   0.2080    0.2068\n",
      "12  1.3   0.1936    0.1916\n",
      "13  1.4   0.1808    0.1781\n",
      "14  1.5   0.1697    0.1663\n",
      "15  1.6   0.1602    0.1562\n",
      "16  1.7   0.1523    0.1478\n",
      "17  1.8   0.1460    0.1412\n",
      "18  1.9   0.1411    0.1360\n",
      "19  2.0   0.1373    0.1322\n"
     ]
    }
   ],
   "source": [
    "# Select sheet number from above\n",
    "sheet_no = 1\n",
    "assert sheet_no in sheets\n",
    "# Hagan2002 implementation\n",
    "m, df, rv = pf.SabrHagan2002.init_benchmark(sheet_no)\n",
    "print(df.iloc[:,[0, 2, 3]])\n",
    "v_ref = df['IV Hagan'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Compare the reference values with the pyfeng implementation\n",
    "v_pf = m.vol_for_price(**rv['args_pricing'])\n",
    "np.testing.assert_almost_equal(v_ref, np.round(v_pf, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [],
   "source": [
    "m, df, rv = pf.SabrChoiWu2021P.init_benchmark(sheet_no)\n",
    "m._base_beta = 1.0\n",
    "v_ref = df['IV HL-P'].values\n",
    "v_pf = m.vol_for_price(**rv['args_pricing'])\n",
    "np.testing.assert_almost_equal(v_ref, np.round(v_pf, 4))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
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