ipynb/SchobelZhu1999-RF-OUSV.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 1,
   "id": "afa91be2",
   "metadata": {},
   "outputs": [],
   "source": [
    "%load_ext autoreload\n",
    "%autoreload 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "cfab1902",
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import scipy.stats as spst\n",
    "\n",
    "#import sys\n",
    "#sys.path.insert(sys.path.index('')+1, 'D:/Github/pyfeng')\n",
    "import pyfeng as pf\n",
    "\n",
    "np.set_printoptions(precision=3)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "88af4965",
   "metadata": {},
   "source": [
    "# OUSV Model by Schobel & Zhu (1999)\n",
    "\n",
    "Schöbel R, Zhu J (1999) Stochastic Volatility With an Ornstein–Uhlenbeck Process: An Extension. Rev Financ 3:23–46. https://doi.org/10.1023/A:1009803506170"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "f0fc4a07",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "\n",
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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>theta</th>\n",
       "      <th>vov</th>\n",
       "      <th>rho</th>\n",
       "      <th>mr</th>\n",
       "      <th>texp</th>\n",
       "      <th>spot</th>\n",
       "      <th>intr</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",
       "      <th></th>\n",
       "      <th></th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.7</td>\n",
       "      <td>4</td>\n",
       "      <td>1.0</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09531</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 2 in Li and Wu (2019)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.7</td>\n",
       "      <td>4</td>\n",
       "      <td>5.0</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09531</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 2 in Li and Wu (2019)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.7</td>\n",
       "      <td>4</td>\n",
       "      <td>10.0</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09531</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 2 in Li and Wu (2019)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>0.25</td>\n",
       "      <td>0.25</td>\n",
       "      <td>0.3</td>\n",
       "      <td>-0.6</td>\n",
       "      <td>8</td>\n",
       "      <td>1.0</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09531</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 3 in Li and Wu (2019)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.20</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09530</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 1A in Schobel &amp; Zhu (1999)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.10</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09530</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 1B in Schobel &amp; Zhu (1999)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>7</th>\n",
       "      <td>0.20</td>\n",
       "      <td>0.30</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09530</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 1C in Schobel &amp; Zhu (1999)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>8</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.5</td>\n",
       "      <td>4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09530</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 2E in Schobel &amp; Zhu (1999)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>9</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.1</td>\n",
       "      <td>0.0</td>\n",
       "      <td>4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09530</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 2D/F in Schobel &amp; Zhu (1999)</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>10</th>\n",
       "      <td>0.15</td>\n",
       "      <td>0.00</td>\n",
       "      <td>0.1</td>\n",
       "      <td>-0.5</td>\n",
       "      <td>4</td>\n",
       "      <td>0.5</td>\n",
       "      <td>100</td>\n",
       "      <td>0.09530</td>\n",
       "      <td>Price</td>\n",
       "      <td>Table 2G in Schobel &amp; Zhu (1999)</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "       sigma  theta  vov  rho  mr  texp  spot     intr col_name  \\\n",
       "Sheet                                                             \n",
       "1       0.20   0.20  0.1 -0.7   4   1.0   100  0.09531    Price   \n",
       "2       0.20   0.20  0.1 -0.7   4   5.0   100  0.09531    Price   \n",
       "3       0.20   0.20  0.1 -0.7   4  10.0   100  0.09531    Price   \n",
       "4       0.25   0.25  0.3 -0.6   8   1.0   100  0.09531    Price   \n",
       "5       0.20   0.20  0.1  0.0   4   0.5   100  0.09530    Price   \n",
       "6       0.20   0.10  0.1  0.0   4   0.5   100  0.09530    Price   \n",
       "7       0.20   0.30  0.1  0.0   4   0.5   100  0.09530    Price   \n",
       "8       0.15   0.00  0.1  0.5   4   0.5   100  0.09530    Price   \n",
       "9       0.15   0.00  0.1  0.0   4   0.5   100  0.09530    Price   \n",
       "10      0.15   0.00  0.1 -0.5   4   0.5   100  0.09530    Price   \n",
       "\n",
       "                                Reference  \n",
       "Sheet                                      \n",
       "1             Table 2 in Li and Wu (2019)  \n",
       "2             Table 2 in Li and Wu (2019)  \n",
       "3             Table 2 in Li and Wu (2019)  \n",
       "4             Table 3 in Li and Wu (2019)  \n",
       "5        Table 1A in Schobel & Zhu (1999)  \n",
       "6        Table 1B in Schobel & Zhu (1999)  \n",
       "7        Table 1C in Schobel & Zhu (1999)  \n",
       "8        Table 2E in Schobel & Zhu (1999)  \n",
       "9      Table 2D/F in Schobel & Zhu (1999)  \n",
       "10       Table 2G in Schobel & Zhu (1999)  "
      ]
     },
     "execution_count": 3,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pf.OusvFft.init_benchmark()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "a21096b3",
   "metadata": {},
   "source": [
    "## Table 1A"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "99d47bc0",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Price</th>\n",
       "      <th>AVBS</th>\n",
       "      <th>SSBS</th>\n",
       "      <th>-1</th>\n",
       "      <th>-0.75</th>\n",
       "      <th>-0.5</th>\n",
       "      <th>-0.25</th>\n",
       "      <th>0</th>\n",
       "      <th>0.25</th>\n",
       "      <th>0.5</th>\n",
       "      <th>0.75</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>15.155</td>\n",
       "      <td>15.152</td>\n",
       "      <td>15.118</td>\n",
       "      <td>15.416</td>\n",
       "      <td>15.355</td>\n",
       "      <td>15.292</td>\n",
       "      <td>15.225</td>\n",
       "      <td>15.155</td>\n",
       "      <td>15.081</td>\n",
       "      <td>15.003</td>\n",
       "      <td>14.919</td>\n",
       "      <td>14.828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>11.379</td>\n",
       "      <td>11.391</td>\n",
       "      <td>11.342</td>\n",
       "      <td>11.617</td>\n",
       "      <td>11.562</td>\n",
       "      <td>11.503</td>\n",
       "      <td>11.443</td>\n",
       "      <td>11.379</td>\n",
       "      <td>11.313</td>\n",
       "      <td>11.243</td>\n",
       "      <td>11.169</td>\n",
       "      <td>11.092</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>8.176</td>\n",
       "      <td>8.203</td>\n",
       "      <td>8.142</td>\n",
       "      <td>8.307</td>\n",
       "      <td>8.275</td>\n",
       "      <td>8.243</td>\n",
       "      <td>8.210</td>\n",
       "      <td>8.176</td>\n",
       "      <td>8.141</td>\n",
       "      <td>8.106</td>\n",
       "      <td>8.070</td>\n",
       "      <td>8.034</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>105</td>\n",
       "      <td>5.617</td>\n",
       "      <td>5.650</td>\n",
       "      <td>5.584</td>\n",
       "      <td>5.576</td>\n",
       "      <td>5.585</td>\n",
       "      <td>5.595</td>\n",
       "      <td>5.606</td>\n",
       "      <td>5.617</td>\n",
       "      <td>5.628</td>\n",
       "      <td>5.640</td>\n",
       "      <td>5.652</td>\n",
       "      <td>5.665</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>110</td>\n",
       "      <td>3.694</td>\n",
       "      <td>3.722</td>\n",
       "      <td>3.658</td>\n",
       "      <td>3.468</td>\n",
       "      <td>3.525</td>\n",
       "      <td>3.582</td>\n",
       "      <td>3.638</td>\n",
       "      <td>3.694</td>\n",
       "      <td>3.749</td>\n",
       "      <td>3.803</td>\n",
       "      <td>3.856</td>\n",
       "      <td>3.909</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>115</td>\n",
       "      <td>2.333</td>\n",
       "      <td>2.349</td>\n",
       "      <td>2.293</td>\n",
       "      <td>1.966</td>\n",
       "      <td>2.063</td>\n",
       "      <td>2.156</td>\n",
       "      <td>2.246</td>\n",
       "      <td>2.333</td>\n",
       "      <td>2.416</td>\n",
       "      <td>2.497</td>\n",
       "      <td>2.576</td>\n",
       "      <td>2.653</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>1.420</td>\n",
       "      <td>1.422</td>\n",
       "      <td>1.377</td>\n",
       "      <td>0.995</td>\n",
       "      <td>1.110</td>\n",
       "      <td>1.218</td>\n",
       "      <td>1.321</td>\n",
       "      <td>1.420</td>\n",
       "      <td>1.514</td>\n",
       "      <td>1.605</td>\n",
       "      <td>1.693</td>\n",
       "      <td>1.777</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Strike   Price    AVBS    SSBS      -1   -0.75    -0.5   -0.25       0  \\\n",
       "0      90  15.155  15.152  15.118  15.416  15.355  15.292  15.225  15.155   \n",
       "1      95  11.379  11.391  11.342  11.617  11.562  11.503  11.443  11.379   \n",
       "2     100   8.176   8.203   8.142   8.307   8.275   8.243   8.210   8.176   \n",
       "3     105   5.617   5.650   5.584   5.576   5.585   5.595   5.606   5.617   \n",
       "4     110   3.694   3.722   3.658   3.468   3.525   3.582   3.638   3.694   \n",
       "5     115   2.333   2.349   2.293   1.966   2.063   2.156   2.246   2.333   \n",
       "6     120   1.420   1.422   1.377   0.995   1.110   1.218   1.321   1.420   \n",
       "\n",
       "     0.25     0.5    0.75       1  \n",
       "0  15.081  15.003  14.919  14.828  \n",
       "1  11.313  11.243  11.169  11.092  \n",
       "2   8.141   8.106   8.070   8.034  \n",
       "3   5.628   5.640   5.652   5.665  \n",
       "4   3.749   3.803   3.856   3.909  \n",
       "5   2.416   2.497   2.576   2.653  \n",
       "6   1.514   1.605   1.693   1.777  "
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_no = 5\n",
    "m, p, rv = pf.OusvFft.init_benchmark(sheet_no)\n",
    "m0, *_ = pf.OusvUncorrBallRoma1994.init_benchmark(sheet_no)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "id": "274b2a37",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[-0.001  0.     0.     0.     0.     0.     0.   ]\n",
      "[ 0.    -0.001  0.     0.     0.     0.     0.   ]\n",
      "[-0.001  0.     0.     0.     0.     0.     0.   ]\n",
      "[ 0.    -0.001  0.     0.     0.     0.     0.   ]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[ 0.    -0.001  0.     0.     0.     0.     0.   ]\n",
      "[ 0.    -0.001  0.     0.     0.     0.     0.   ]\n",
      "[-0.001  0.     0.     0.     0.     0.     0.   ]\n",
      "[ 0.    -0.001  0.     0.     0.     0.     0.   ]\n"
     ]
    }
   ],
   "source": [
    "rhos = [-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1]\n",
    "\n",
    "for rho in rhos:\n",
    "    m.rho = rho\n",
    "    print(np.round(m.price(**rv['args_pricing']), 3) - p[rho].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "id": "286cc07d",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### AVBS price\n",
    "np.round(m0.price(**rv['args_pricing']), 3) - p['AVBS'].values"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "f9f68d58",
   "metadata": {},
   "outputs": [],
   "source": []
  },
  {
   "cell_type": "markdown",
   "id": "cf924306",
   "metadata": {},
   "source": [
    "## Table 1B"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "id": "0c9f9089",
   "metadata": {},
   "outputs": [
    {
     "data": {
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       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Price</th>\n",
       "      <th>AVBS</th>\n",
       "      <th>-1</th>\n",
       "      <th>-0.75</th>\n",
       "      <th>-0.5</th>\n",
       "      <th>-0.25</th>\n",
       "      <th>0</th>\n",
       "      <th>0.25</th>\n",
       "      <th>0.5</th>\n",
       "      <th>0.75</th>\n",
       "      <th>1</th>\n",
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       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>14.515</td>\n",
       "      <td>14.501</td>\n",
       "      <td>14.730</td>\n",
       "      <td>14.679</td>\n",
       "      <td>14.626</td>\n",
       "      <td>14.572</td>\n",
       "      <td>14.515</td>\n",
       "      <td>14.456</td>\n",
       "      <td>14.395</td>\n",
       "      <td>14.330</td>\n",
       "      <td>14.261</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>10.346</td>\n",
       "      <td>10.348</td>\n",
       "      <td>10.600</td>\n",
       "      <td>10.541</td>\n",
       "      <td>10.480</td>\n",
       "      <td>10.415</td>\n",
       "      <td>10.346</td>\n",
       "      <td>10.271</td>\n",
       "      <td>10.191</td>\n",
       "      <td>10.103</td>\n",
       "      <td>10.005</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>6.803</td>\n",
       "      <td>6.829</td>\n",
       "      <td>6.976</td>\n",
       "      <td>6.936</td>\n",
       "      <td>6.894</td>\n",
       "      <td>6.849</td>\n",
       "      <td>6.803</td>\n",
       "      <td>6.753</td>\n",
       "      <td>6.701</td>\n",
       "      <td>6.645</td>\n",
       "      <td>6.587</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>105</td>\n",
       "      <td>4.093</td>\n",
       "      <td>4.132</td>\n",
       "      <td>4.057</td>\n",
       "      <td>4.066</td>\n",
       "      <td>4.075</td>\n",
       "      <td>4.085</td>\n",
       "      <td>4.093</td>\n",
       "      <td>4.102</td>\n",
       "      <td>4.110</td>\n",
       "      <td>4.117</td>\n",
       "      <td>4.125</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>110</td>\n",
       "      <td>2.254</td>\n",
       "      <td>2.282</td>\n",
       "      <td>1.977</td>\n",
       "      <td>2.051</td>\n",
       "      <td>2.121</td>\n",
       "      <td>2.189</td>\n",
       "      <td>2.254</td>\n",
       "      <td>2.316</td>\n",
       "      <td>2.376</td>\n",
       "      <td>2.433</td>\n",
       "      <td>2.489</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>115</td>\n",
       "      <td>1.144</td>\n",
       "      <td>1.150</td>\n",
       "      <td>0.739</td>\n",
       "      <td>0.853</td>\n",
       "      <td>0.957</td>\n",
       "      <td>1.053</td>\n",
       "      <td>1.144</td>\n",
       "      <td>1.230</td>\n",
       "      <td>1.311</td>\n",
       "      <td>1.389</td>\n",
       "      <td>1.463</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>0.542</td>\n",
       "      <td>0.530</td>\n",
       "      <td>0.179</td>\n",
       "      <td>0.279</td>\n",
       "      <td>0.371</td>\n",
       "      <td>0.458</td>\n",
       "      <td>0.542</td>\n",
       "      <td>0.621</td>\n",
       "      <td>0.698</td>\n",
       "      <td>0.773</td>\n",
       "      <td>0.845</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Strike   Price    AVBS      -1   -0.75    -0.5   -0.25       0    0.25  \\\n",
       "0      90  14.515  14.501  14.730  14.679  14.626  14.572  14.515  14.456   \n",
       "1      95  10.346  10.348  10.600  10.541  10.480  10.415  10.346  10.271   \n",
       "2     100   6.803   6.829   6.976   6.936   6.894   6.849   6.803   6.753   \n",
       "3     105   4.093   4.132   4.057   4.066   4.075   4.085   4.093   4.102   \n",
       "4     110   2.254   2.282   1.977   2.051   2.121   2.189   2.254   2.316   \n",
       "5     115   1.144   1.150   0.739   0.853   0.957   1.053   1.144   1.230   \n",
       "6     120   0.542   0.530   0.179   0.279   0.371   0.458   0.542   0.621   \n",
       "\n",
       "      0.5    0.75       1  \n",
       "0  14.395  14.330  14.261  \n",
       "1  10.191  10.103  10.005  \n",
       "2   6.701   6.645   6.587  \n",
       "3   4.110   4.117   4.125  \n",
       "4   2.376   2.433   2.489  \n",
       "5   1.311   1.389   1.463  \n",
       "6   0.698   0.773   0.845  "
      ]
     },
     "execution_count": 7,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_no = 6\n",
    "m, p, rv = pf.OusvFft.init_benchmark(sheet_no)\n",
    "m0, *_ = pf.OusvUncorrBallRoma1994.init_benchmark(sheet_no)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "id": "b42a14ca",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "rhos = [-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1]\n",
    "\n",
    "for rho in rhos:\n",
    "    m.rho = rho\n",
    "    print(np.round(m.price(**rv['args_pricing']), 3) - p[rho].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "id": "822782c4",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### AVBS price\n",
    "np.round(m0.price(**rv['args_pricing']), 3) - p['AVBS'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "7f1edbbb",
   "metadata": {},
   "source": [
    "## Table 1C"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "id": "35fa6703",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Price</th>\n",
       "      <th>AVBS</th>\n",
       "      <th>-1</th>\n",
       "      <th>-0.75</th>\n",
       "      <th>-0.5</th>\n",
       "      <th>-0.25</th>\n",
       "      <th>0</th>\n",
       "      <th>0.25</th>\n",
       "      <th>0.5</th>\n",
       "      <th>0.75</th>\n",
       "      <th>1</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>16.106</td>\n",
       "      <td>16.111</td>\n",
       "      <td>16.357</td>\n",
       "      <td>16.298</td>\n",
       "      <td>16.236</td>\n",
       "      <td>16.172</td>\n",
       "      <td>16.106</td>\n",
       "      <td>16.037</td>\n",
       "      <td>15.964</td>\n",
       "      <td>15.889</td>\n",
       "      <td>15.810</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>12.651</td>\n",
       "      <td>12.666</td>\n",
       "      <td>12.846</td>\n",
       "      <td>12.800</td>\n",
       "      <td>12.751</td>\n",
       "      <td>12.702</td>\n",
       "      <td>12.651</td>\n",
       "      <td>12.598</td>\n",
       "      <td>12.544</td>\n",
       "      <td>12.489</td>\n",
       "      <td>12.432</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>9.687</td>\n",
       "      <td>9.711</td>\n",
       "      <td>9.777</td>\n",
       "      <td>9.755</td>\n",
       "      <td>9.732</td>\n",
       "      <td>9.710</td>\n",
       "      <td>9.687</td>\n",
       "      <td>9.665</td>\n",
       "      <td>9.642</td>\n",
       "      <td>9.620</td>\n",
       "      <td>9.598</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>105</td>\n",
       "      <td>7.237</td>\n",
       "      <td>7.264</td>\n",
       "      <td>7.186</td>\n",
       "      <td>7.198</td>\n",
       "      <td>7.210</td>\n",
       "      <td>7.223</td>\n",
       "      <td>7.237</td>\n",
       "      <td>7.251</td>\n",
       "      <td>7.265</td>\n",
       "      <td>7.280</td>\n",
       "      <td>7.296</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>110</td>\n",
       "      <td>5.279</td>\n",
       "      <td>5.305</td>\n",
       "      <td>5.084</td>\n",
       "      <td>5.133</td>\n",
       "      <td>5.182</td>\n",
       "      <td>5.230</td>\n",
       "      <td>5.279</td>\n",
       "      <td>5.328</td>\n",
       "      <td>5.377</td>\n",
       "      <td>5.426</td>\n",
       "      <td>5.475</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>115</td>\n",
       "      <td>3.768</td>\n",
       "      <td>3.786</td>\n",
       "      <td>3.449</td>\n",
       "      <td>3.531</td>\n",
       "      <td>3.611</td>\n",
       "      <td>3.690</td>\n",
       "      <td>3.768</td>\n",
       "      <td>3.844</td>\n",
       "      <td>3.919</td>\n",
       "      <td>3.993</td>\n",
       "      <td>4.065</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>2.635</td>\n",
       "      <td>2.646</td>\n",
       "      <td>2.235</td>\n",
       "      <td>2.340</td>\n",
       "      <td>2.441</td>\n",
       "      <td>2.540</td>\n",
       "      <td>2.635</td>\n",
       "      <td>2.728</td>\n",
       "      <td>2.819</td>\n",
       "      <td>2.908</td>\n",
       "      <td>2.994</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Strike   Price    AVBS      -1   -0.75    -0.5   -0.25       0    0.25  \\\n",
       "0      90  16.106  16.111  16.357  16.298  16.236  16.172  16.106  16.037   \n",
       "1      95  12.651  12.666  12.846  12.800  12.751  12.702  12.651  12.598   \n",
       "2     100   9.687   9.711   9.777   9.755   9.732   9.710   9.687   9.665   \n",
       "3     105   7.237   7.264   7.186   7.198   7.210   7.223   7.237   7.251   \n",
       "4     110   5.279   5.305   5.084   5.133   5.182   5.230   5.279   5.328   \n",
       "5     115   3.768   3.786   3.449   3.531   3.611   3.690   3.768   3.844   \n",
       "6     120   2.635   2.646   2.235   2.340   2.441   2.540   2.635   2.728   \n",
       "\n",
       "      0.5    0.75       1  \n",
       "0  15.964  15.889  15.810  \n",
       "1  12.544  12.489  12.432  \n",
       "2   9.642   9.620   9.598  \n",
       "3   7.265   7.280   7.296  \n",
       "4   5.377   5.426   5.475  \n",
       "5   3.919   3.993   4.065  \n",
       "6   2.819   2.908   2.994  "
      ]
     },
     "execution_count": 10,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_no = 7\n",
    "m, p, rv = pf.OusvFft.init_benchmark(sheet_no)\n",
    "m0, *_ = pf.OusvUncorrBallRoma1994.init_benchmark(sheet_no)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "id": "9fb73139",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "rhos = [-1, -0.75, -0.5, -0.25, 0, 0.25, 0.5, 0.75, 1]\n",
    "\n",
    "for rho in rhos:\n",
    "    m.rho = rho\n",
    "    print(np.round(m.price(**rv['args_pricing']), 3) - p[rho].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "id": "a1a5fc81",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([0., 0., 0., 0., 0., 0., 0.])"
      ]
     },
     "execution_count": 12,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "### AVBS price\n",
    "np.round(m0.price(**rv['args_pricing']), 3) - p['AVBS'].values"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "daa52bfc",
   "metadata": {},
   "source": [
    "## Table 2E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "id": "4b369805",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Price</th>\n",
       "      <th>0</th>\n",
       "      <th>0.1</th>\n",
       "      <th>0.2</th>\n",
       "      <th>0.3</th>\n",
       "      <th>AVBS-0</th>\n",
       "      <th>AVBS-0.1</th>\n",
       "      <th>AVBS-0.2</th>\n",
       "      <th>AVBS-0.3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>14.200</td>\n",
       "      <td>14.200</td>\n",
       "      <td>14.351</td>\n",
       "      <td>14.871</td>\n",
       "      <td>15.754</td>\n",
       "      <td>14.194</td>\n",
       "      <td>14.333</td>\n",
       "      <td>14.864</td>\n",
       "      <td>15.757</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>9.527</td>\n",
       "      <td>9.527</td>\n",
       "      <td>9.997</td>\n",
       "      <td>10.952</td>\n",
       "      <td>12.198</td>\n",
       "      <td>9.510</td>\n",
       "      <td>9.990</td>\n",
       "      <td>10.962</td>\n",
       "      <td>12.213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>5.269</td>\n",
       "      <td>5.269</td>\n",
       "      <td>6.254</td>\n",
       "      <td>7.632</td>\n",
       "      <td>9.161</td>\n",
       "      <td>5.277</td>\n",
       "      <td>6.282</td>\n",
       "      <td>7.662</td>\n",
       "      <td>9.187</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>105</td>\n",
       "      <td>2.170</td>\n",
       "      <td>2.170</td>\n",
       "      <td>3.451</td>\n",
       "      <td>5.022</td>\n",
       "      <td>6.676</td>\n",
       "      <td>2.213</td>\n",
       "      <td>3.499</td>\n",
       "      <td>5.060</td>\n",
       "      <td>6.707</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>110</td>\n",
       "      <td>0.645</td>\n",
       "      <td>0.645</td>\n",
       "      <td>1.679</td>\n",
       "      <td>3.124</td>\n",
       "      <td>4.727</td>\n",
       "      <td>0.654</td>\n",
       "      <td>1.708</td>\n",
       "      <td>3.155</td>\n",
       "      <td>4.755</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>115</td>\n",
       "      <td>0.150</td>\n",
       "      <td>0.150</td>\n",
       "      <td>0.731</td>\n",
       "      <td>1.845</td>\n",
       "      <td>3.259</td>\n",
       "      <td>0.132</td>\n",
       "      <td>0.728</td>\n",
       "      <td>1.859</td>\n",
       "      <td>3.278</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.292</td>\n",
       "      <td>1.040</td>\n",
       "      <td>2.192</td>\n",
       "      <td>0.018</td>\n",
       "      <td>0.272</td>\n",
       "      <td>1.037</td>\n",
       "      <td>2.200</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Strike   Price       0     0.1     0.2     0.3  AVBS-0  AVBS-0.1  AVBS-0.2  \\\n",
       "0      90  14.200  14.200  14.351  14.871  15.754  14.194    14.333    14.864   \n",
       "1      95   9.527   9.527   9.997  10.952  12.198   9.510     9.990    10.962   \n",
       "2     100   5.269   5.269   6.254   7.632   9.161   5.277     6.282     7.662   \n",
       "3     105   2.170   2.170   3.451   5.022   6.676   2.213     3.499     5.060   \n",
       "4     110   0.645   0.645   1.679   3.124   4.727   0.654     1.708     3.155   \n",
       "5     115   0.150   0.150   0.731   1.845   3.259   0.132     0.728     1.859   \n",
       "6     120   0.030   0.030   0.292   1.040   2.192   0.018     0.272     1.037   \n",
       "\n",
       "   AVBS-0.3  \n",
       "0    15.757  \n",
       "1    12.213  \n",
       "2     9.187  \n",
       "3     6.707  \n",
       "4     4.755  \n",
       "5     3.278  \n",
       "6     2.200  "
      ]
     },
     "execution_count": 13,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_no = 9\n",
    "m, p, rv = pf.OusvUncorrBallRoma1994.init_benchmark(sheet_no)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "id": "79c53a5b",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "thetas = [0, 0.1, 0.2, 0.3]\n",
    "\n",
    "for theta in thetas:\n",
    "    m.theta = theta\n",
    "    print(np.round(m.price(**rv['args_pricing']), 3) - p[f'AVBS-{theta}'].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "6475a40c",
   "metadata": {},
   "source": [
    "## Table 2E"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "id": "6b260af5",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "<style scoped>\n",
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       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Price</th>\n",
       "      <th>0</th>\n",
       "      <th>0.1</th>\n",
       "      <th>0.2</th>\n",
       "      <th>0.3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>14.189</td>\n",
       "      <td>14.189</td>\n",
       "      <td>14.262</td>\n",
       "      <td>14.723</td>\n",
       "      <td>15.608</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>9.459</td>\n",
       "      <td>9.459</td>\n",
       "      <td>9.842</td>\n",
       "      <td>10.804</td>\n",
       "      <td>12.082</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>5.141</td>\n",
       "      <td>5.141</td>\n",
       "      <td>6.132</td>\n",
       "      <td>7.551</td>\n",
       "      <td>9.109</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>105</td>\n",
       "      <td>2.173</td>\n",
       "      <td>2.173</td>\n",
       "      <td>3.466</td>\n",
       "      <td>5.044</td>\n",
       "      <td>6.703</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>110</td>\n",
       "      <td>0.763</td>\n",
       "      <td>0.763</td>\n",
       "      <td>1.812</td>\n",
       "      <td>3.239</td>\n",
       "      <td>4.828</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>115</td>\n",
       "      <td>0.244</td>\n",
       "      <td>0.244</td>\n",
       "      <td>0.895</td>\n",
       "      <td>2.014</td>\n",
       "      <td>3.414</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>0.075</td>\n",
       "      <td>0.075</td>\n",
       "      <td>0.425</td>\n",
       "      <td>1.220</td>\n",
       "      <td>2.376</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Strike   Price       0     0.1     0.2     0.3\n",
       "0      90  14.189  14.189  14.262  14.723  15.608\n",
       "1      95   9.459   9.459   9.842  10.804  12.082\n",
       "2     100   5.141   5.141   6.132   7.551   9.109\n",
       "3     105   2.173   2.173   3.466   5.044   6.703\n",
       "4     110   0.763   0.763   1.812   3.239   4.828\n",
       "5     115   0.244   0.244   0.895   2.014   3.414\n",
       "6     120   0.075   0.075   0.425   1.220   2.376"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_no = 8\n",
    "m, p, rv = pf.OusvFft.init_benchmark(sheet_no)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "id": "371da4ff",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "thetas = [0, 0.1, 0.2, 0.3]\n",
    "\n",
    "for theta in thetas:\n",
    "    m.theta = theta\n",
    "    print(np.round(m.price(**rv['args_pricing']), 3) - p[theta].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "98c30142",
   "metadata": {},
   "source": [
    "## Table 2F"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "id": "5d8442d7",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
       "        vertical-align: middle;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Price</th>\n",
       "      <th>0</th>\n",
       "      <th>0.1</th>\n",
       "      <th>0.2</th>\n",
       "      <th>0.3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>14.200</td>\n",
       "      <td>14.200</td>\n",
       "      <td>14.351</td>\n",
       "      <td>14.871</td>\n",
       "      <td>15.754</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>9.527</td>\n",
       "      <td>9.527</td>\n",
       "      <td>9.997</td>\n",
       "      <td>10.952</td>\n",
       "      <td>12.198</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>5.269</td>\n",
       "      <td>5.269</td>\n",
       "      <td>6.254</td>\n",
       "      <td>7.632</td>\n",
       "      <td>9.161</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>105</td>\n",
       "      <td>2.170</td>\n",
       "      <td>2.170</td>\n",
       "      <td>3.451</td>\n",
       "      <td>5.022</td>\n",
       "      <td>6.676</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>110</td>\n",
       "      <td>0.645</td>\n",
       "      <td>0.645</td>\n",
       "      <td>1.679</td>\n",
       "      <td>3.124</td>\n",
       "      <td>4.727</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>115</td>\n",
       "      <td>0.150</td>\n",
       "      <td>0.150</td>\n",
       "      <td>0.731</td>\n",
       "      <td>1.845</td>\n",
       "      <td>3.259</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.030</td>\n",
       "      <td>0.292</td>\n",
       "      <td>1.040</td>\n",
       "      <td>2.192</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Strike   Price       0     0.1     0.2     0.3\n",
       "0      90  14.200  14.200  14.351  14.871  15.754\n",
       "1      95   9.527   9.527   9.997  10.952  12.198\n",
       "2     100   5.269   5.269   6.254   7.632   9.161\n",
       "3     105   2.170   2.170   3.451   5.022   6.676\n",
       "4     110   0.645   0.645   1.679   3.124   4.727\n",
       "5     115   0.150   0.150   0.731   1.845   3.259\n",
       "6     120   0.030   0.030   0.292   1.040   2.192"
      ]
     },
     "execution_count": 17,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_no = 9\n",
    "m, p, rv = pf.OusvFft.init_benchmark(sheet_no)\n",
    "p.iloc[:,:6]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "id": "3533e4ba",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "thetas = [0, 0.1, 0.2, 0.3]\n",
    "\n",
    "for theta in thetas:\n",
    "    m.theta = theta\n",
    "    print(np.round(m.price(**rv['args_pricing']), 3) - p[theta].values)"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bf365a4a",
   "metadata": {},
   "source": [
    "## Table 2G"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "id": "d884f391",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style scoped>\n",
       "    .dataframe tbody tr th:only-of-type {\n",
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       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: right;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Strike</th>\n",
       "      <th>Price</th>\n",
       "      <th>0</th>\n",
       "      <th>0.1</th>\n",
       "      <th>0.2</th>\n",
       "      <th>0.3</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0</th>\n",
       "      <td>90</td>\n",
       "      <td>14.225</td>\n",
       "      <td>14.225</td>\n",
       "      <td>14.441</td>\n",
       "      <td>15.003</td>\n",
       "      <td>15.887</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1</th>\n",
       "      <td>95</td>\n",
       "      <td>9.600</td>\n",
       "      <td>9.600</td>\n",
       "      <td>10.130</td>\n",
       "      <td>11.084</td>\n",
       "      <td>12.306</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2</th>\n",
       "      <td>100</td>\n",
       "      <td>5.372</td>\n",
       "      <td>5.372</td>\n",
       "      <td>6.361</td>\n",
       "      <td>7.710</td>\n",
       "      <td>9.213</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>3</th>\n",
       "      <td>105</td>\n",
       "      <td>2.152</td>\n",
       "      <td>2.152</td>\n",
       "      <td>3.435</td>\n",
       "      <td>5.003</td>\n",
       "      <td>6.652</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>4</th>\n",
       "      <td>110</td>\n",
       "      <td>0.504</td>\n",
       "      <td>0.504</td>\n",
       "      <td>1.529</td>\n",
       "      <td>3.004</td>\n",
       "      <td>4.626</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>5</th>\n",
       "      <td>115</td>\n",
       "      <td>0.061</td>\n",
       "      <td>0.061</td>\n",
       "      <td>0.545</td>\n",
       "      <td>1.660</td>\n",
       "      <td>3.097</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>6</th>\n",
       "      <td>120</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.004</td>\n",
       "      <td>0.155</td>\n",
       "      <td>0.842</td>\n",
       "      <td>1.995</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "   Strike   Price       0     0.1     0.2     0.3\n",
       "0      90  14.225  14.225  14.441  15.003  15.887\n",
       "1      95   9.600   9.600  10.130  11.084  12.306\n",
       "2     100   5.372   5.372   6.361   7.710   9.213\n",
       "3     105   2.152   2.152   3.435   5.003   6.652\n",
       "4     110   0.504   0.504   1.529   3.004   4.626\n",
       "5     115   0.061   0.061   0.545   1.660   3.097\n",
       "6     120   0.004   0.004   0.155   0.842   1.995"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "sheet_no = 10\n",
    "m, p, rv = pf.OusvFft.init_benchmark(sheet_no)\n",
    "p"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "id": "b5a5b7c9",
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n",
      "[0. 0. 0. 0. 0. 0. 0.]\n"
     ]
    }
   ],
   "source": [
    "thetas = [0, 0.1, 0.2, 0.3]\n",
    "\n",
    "for theta in thetas:\n",
    "    m.theta = theta\n",
    "    print(np.round(m.price(**rv['args_pricing']), 3) - p[theta].values)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "id": "a46e86da",
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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