ipynb/ChoiWu2021-JEDC-SABR-CEV.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "# ChoiWu2021-JEDC-SABR-CEV"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "### Title: \n",
    "__The equivalent constant-elasticity-of-variance (CEV) volatility of the stochastic-alpha-beta-rho (SABR) model__\n",
    "\n",
    "### Authors:\n",
    "* Jaehyuk Choi ([@jaehyukchoi](https://github.com/jaehyukchoi))\n",
    "* Lixin Wu\n",
    "\n",
    "### Abstract:\n",
    "This study presents new analytic approximations of the stochastic-alpha-beta-rho (SABR) model. Unlike existing studies that focus on the equivalent Black–Scholes (BS) volatility, we instead derive the equivalent constant-elasticity-of-variance (CEV) volatility. Our approach effectively reduces the approximation error in a way similar to the control variate method because the CEV model is the zero vol-of-vol limit of the SABR model. Moreover, the CEV volatility approximation yields a finite value at a zero strike and thus conveniently leads to a small-time asymptotics for the mass at zero. The numerical results compare favorably with the BS volatility approximations in terms of the approximation accuracy, small-strike volatility asymptotics, and no-arbitrage region."
   ]
  },
  {
   "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",
    "#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": [],
   "source": [
    "# uncomment and run to see the all available parameter sets\n",
    "#pf.SabrHagan2002.init_benchmark()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table 2/3/4 and Figure 3 (a-c) (Set 1/2/3) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [],
   "source": [
    "# 1 (Table 2, Figure 3a), 2 (Table 3, Figure 3b), 3 (Table 4, Figure 3c)\n",
    "param_set = 1\n",
    "\n",
    "assert param_set in [1,2,3]\n",
    "set_no = {1:20, 2:19, 3:17}[param_set]\n",
    "\n",
    "m_bsA, df, ref = pf.SabrHagan2002.init_benchmark(set_no)\n",
    "m_cevA, *_ = pf.SabrChoiWu2021H.init_benchmark(set_no)\n",
    "m_cevB, *_ = pf.SabrChoiWu2021P.init_benchmark(set_no)\n",
    "m_bsC, *_ = pf.SabrLorig2017.init_benchmark(set_no)\n",
    "\n",
    "fwd = ref['args_pricing']['spot']\n",
    "texp = ref['args_pricing']['texp']\n",
    "strike_exact = ref['args_pricing']['strike']\n",
    "alpha = m_bsA.sigma/np.power(ref['args_pricing']['spot'],1.0-m_bsA.beta)\n",
    "\n",
    "if ref['is_iv']:\n",
    "    vol_exact = ref['val']\n",
    "    p_exact = pf.Bsm(ref['val']).price(**ref['args_pricing'])\n",
    "else:\n",
    "    p_exact = ref['val']\n",
    "    vol_exact = pf.Bsm(None).impvol(ref['val'], **ref['args_pricing'])\n",
    "\n",
    "m0_exact = {20: 0.1634, 19: 0.7758, 17: 0.2220}[set_no]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [],
   "source": [
    "vol_bsA = m_bsA.vol_for_price(**ref['args_pricing'])\n",
    "vol_bsC = m_bsC.vol_for_price(**ref['args_pricing'])\n",
    "vol_cevA = m_cevA.vol_smile(**ref['args_pricing'])\n",
    "\n",
    "m_cevB._base_beta = None\n",
    "vol_cevB = m_cevB.vol_smile(**ref['args_pricing'])\n",
    "\n",
    "m_cevB._base_beta = 1.0\n",
    "vol_bsB = m_cevB.vol_smile(**ref['args_pricing'])\n",
    "\n",
    "vol_err = (np.array([vol_bsA, vol_bsB, vol_bsC, vol_cevA, vol_cevB]) - vol_exact)/alpha\n",
    "exact = np.array([vol_exact*100, p_exact])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
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       "        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>BS-A</th>\n",
       "      <th>BS-B</th>\n",
       "      <th>BS-C</th>\n",
       "      <th>CEV-A</th>\n",
       "      <th>CEV-A</th>\n",
       "      <th>Exact $\\sigma_{BS}$</th>\n",
       "      <th>Exact P</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>0.868123</th>\n",
       "      <td>0.026870</td>\n",
       "      <td>0.026817</td>\n",
       "      <td>0.004192</td>\n",
       "      <td>0.024417</td>\n",
       "      <td>0.024344</td>\n",
       "      <td>74.187422</td>\n",
       "      <td>0.221383</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.000000</th>\n",
       "      <td>0.023573</td>\n",
       "      <td>0.023573</td>\n",
       "      <td>0.002721</td>\n",
       "      <td>0.021659</td>\n",
       "      <td>0.021659</td>\n",
       "      <td>71.666002</td>\n",
       "      <td>0.193837</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>1.151910</th>\n",
       "      <td>0.020901</td>\n",
       "      <td>0.020843</td>\n",
       "      <td>0.001598</td>\n",
       "      <td>0.019423</td>\n",
       "      <td>0.019345</td>\n",
       "      <td>69.325033</td>\n",
       "      <td>0.166241</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "              BS-A      BS-B      BS-C     CEV-A     CEV-A  \\\n",
       "0.868123  0.026870  0.026817  0.004192  0.024417  0.024344   \n",
       "1.000000  0.023573  0.023573  0.002721  0.021659  0.021659   \n",
       "1.151910  0.020901  0.020843  0.001598  0.019423  0.019345   \n",
       "\n",
       "          Exact $\\sigma_{BS}$   Exact P  \n",
       "0.868123            74.187422  0.221383  \n",
       "1.000000            71.666002  0.193837  \n",
       "1.151910            69.325033  0.166241  "
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(\n",
    "    np.hstack([vol_err.T, exact.T]), index=strike_exact/fwd,\n",
    "    columns=['BS-A', 'BS-B', 'BS-C', 'CEV-A', 'CEV-A', 'Exact $\\sigma_{BS}$', 'Exact P']\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "strike = np.power(10, np.arange(-2.5,1,0.025))*fwd\n",
    "strike_low = np.power(10, np.concatenate((np.arange(-2.5,0,0.05), np.arange(-0.05,-0.005,0.005))))*fwd\n",
    "\n",
    "m_cevB._base_beta = 1.0\n",
    "vol_bsB = m_cevB.vol_smile(strike, fwd, texp)\n",
    "\n",
    "m_cevB._base_beta = None\n",
    "vol_cevB = m_cevB.vol_smile(strike, fwd, texp)\n",
    "\n",
    "vol_dem = m_cevB.vol_from_mass_zero(strike_low, fwd, texp)\n",
    "vol_dem2 = m_cevB.vol_from_mass_zero(strike_low, fwd, texp, mass=m0_exact)\n",
    "m0_cevB = m_cevB.mass_zero(fwd, texp)\n",
    "\n",
    "m_cevB._base_beta = 1.0\n",
    "vol_bsB = m_cevB.vol_smile(strike*fwd, fwd, texp)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {
    "scrolled": true
   },
   "outputs": [
    {
     "data": {
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AiRMnBrprmSanRiDtgH7AhSKy1LN0BV4WkT9FZDnQGStoj6quBCYAq4AfgSHOAytzxMTE0K5dOwAOHDjAjz/+6CLXHY5s8vrrr3PfffcxdOhQdu7cyaZNm7jzzjv59ttvAbjuuuuIj49PWrwzAAMGDGD06LMrKY8ZM4YBAwakeq3kbb355pv07duXnTt3BqxvWSGnvLDmqqqoalNVbe5ZflDVfqraxLO9h6puT3bOC6paS1XrqerUnJAzr7J+/XqWLVvGoUOHgi2KwxGyHDx4kCeffJL33nuPq6++mqioKCIiIujevTuvvPJKuuf269ePuXPnEhd3JvHt6tWrWb58Oddff32G17700kspWrQo69aty3Y//Eloueo4skTLli2pX79+km99fHw80dHRQZbK4ciY++6DpUsDe43mzeHNNzM+bt68eRw/fpyrrroq09eoXLkynTt3ZsyYMTzxxBMAjB49mq5du1K6dOl0z1VVfvjhB06ePEnDhg0zfe1A4pIp5RO8ymPlypW8/fbbbN26NcgSORyhxd69eyldunS6LvITJkygePHiSUvnzp2T9g0YMIAxY8YAFh0+duzYNKevkrcVFRVFjx49GDp0aK6zaboRSD6jWrVqtGzZkvLlywdbFIcjQ3wZGeQUpUqVYs+ePZw+fTpNJdK7d28+//zzVPddffXV3HnnncyfP5+jR49y9OhRrrjiCoB/zQisWrXqrLY2btxIt27diImJ4fbbb/dnt7KFG4HkM6Kjo7nssssIDw/n5MmTzJgxg5MnTwZbLIcj13PeeecRGRnJN998k6XzixQpQq9evRg9ejRjxoyhT58+SW73yQ3vVatWPevc6tWrc/nllzNlypTsdMHvuBFIPmbDhg389ttv1KpVK8+WynU4/EVMTAzPPvssQ4YMoUCBAlxyySVERETw888/Exsb61P+rgEDBnD11Vdz6tQpZsyY4fO1t2zZwo8//kjXrl2z0wW/40Yg+Zh69epx9913JymPI0eOBFcghyOX88ADD/D666/z/PPPU6ZMGapUqcK7775Lz549ARg/fvy/4kCio6PZtWtX0vkdOnQgJiaGSpUq0bp163Svlbyt1q1b065dO5566qlAdi/TuBFIPsdrlNu+fTufffYZPXv2zHWeHg5HbuLGG2/kxhtvPGv7+eefz9NPP53uuSLC+vXrM7zG008/nWFbuQE3AnEAULJkSZo3b061atWCLYrD4QgRnAJxAFCoUCG6du1KVFQUqsqMGTNcHi2Hw5EuToE4zmLfvn0sXLiQNWvWBFsUh8ORi3E2EMdZlCpViiFDhiT5ph8+fJjo6OhcUV7U4XDkHtwIxJEqRYsWRUQ4evQoH330UaZcDh0OR/7AjUAc6VK4cGFat25NnTp1gi2Kw+HIZbgRiCNdRIT27dsnpT6ZN28eGzduDK5QDocjV+AUiMNnTp06xeLFi1m2bFmwRXE4HLkAN4Xl8JmIiAhuueUWwsLsf0d8fDwFCxZMyufjcDjyF24E4sgUhQoVIiIiAlVlwoQJfP7556hqsMVyOHKE6tWrU7hwYaKjoylRogRXXHEFmzdvBmDu3Lmcf/75xMTEULJkSdq1a8fChQtTbWfkyJGEh4cnpSqpWbMmw4cPz8mu+AWnQBxZQkTo2LEj559/vnPvdeQrpkyZQnx8PNu3b6dcuXLcfffdHDp0iG7dunH33Xezb98+tm7dylNPPUWhQoXSbOe8885LysD71Vdf8cgjj7BkyZIc7En2cQrEkWVq1apF/fr1AathMH36dBITE4MslcORM0RGRtKrVy9WrVrF33//DcD1119PeHg4hQsX5pJLLqFp06Y+tdWyZUsaNGjA6tWrAymy33EKxOEXtmzZQlxcnFMgDr8zcuRIlnrq2iYkJDBy5EiWL18OmGPHyJEjWbFiBQDHjx9n5MiRST/ER48eZeTIkUlZFeLj4xk5ciRr164FrM55Vjl69Cjjx4+nbdu21K1bl/DwcAYMGMDUqVPZv39/ptpauHAhf//9N61atcqyPMHAKRCHX7jkkksYMGAABQoU4NSpU2zbti3YIjkcAaFnz54UL16cYsWKMX36dB5++GGKFSvG3LlzERFuvfVWypQpQ48ePdi5c2ea7cyfP5/ixYsTHR1NmzZt6NevX+jFW6lqnljq1q2reZnY2Nhgi+Az06dP1+eee04PHDjg8zmh1L+s4PrnG6tWrfJLO/7k0KFDSevVqlXT6dOnq6rq6dOndeLEiVqiRAndvn37v85ZvXq1nnPOOdqnTx9VVW3YsKFGRUVpVFSUzp49Wz/77DNt165d0vE7duzQzp0762OPPRawfqR1b4FFmsXfXTcCcfidCy64gCuvvJKYmBgA56XlyJOEh4dz9dVXEx4ezty5c/+1r379+gwcODBpam3lypVJBvP27duf1Va5cuW45pprcl3J2ozwSYGISBUR6SYifT2vVQItmCN0iYyMpEmTJgDs3LmTjz/+mH379gVZKofDv6gq3377Lfv376dBgwa89tprbNmyBYDNmzfzf//3f7Rt29antvbu3cukSZNo1KhRIEX2O2kGEopIBHC7Z6kJrAUOA0WB2iKyAfgAGKGqJ3NA1nQptHs39O0LvXvDpZdCOu5zjpzj+PHjJCQkuGBDR56he/fuhIeHIyJUq1aNUaNGUbx4cRYsWMDrr7/OgQMHKF68ON26deOVV15Js5158+YlZbwuUqQIXbp04a233sqpbviF9CLRlwEzMQWyQFUTvDtEJBxoA9wILAGCrzZFYOpUGDsWihWDnj2hf3/o0iXYkuVrqlWrxu23346IoKr8+eefNGrUiPDw8GCL5nBkmvTywE2YMMHndgYOHMjAgQOzL1CQSU+BdFLVXant8CiTecA8ESkTEMkyyRatxNKf/qDZnhnIlxNg0iQoXNgUiCrMmAEdO0JERLBFzXd4Aw03btzIpEmTUFWaNWsWZKkcDkd2SVOBpKU8AESkNLDXY8TfHRDJMsn+/QVp0SaChg0vo2/fy7jh9w+oVvKw7fz9d7j4YihVCq6+Gq67zpRJAZcKLCepUaMG/fv3p3r16gCcPHnSTW05HCFMprywRKSDiMQBy4HdInJtYMTKPLVqxTN8OJQoAUOHQvW6BelwVSk+/BD2VWkG33wDl1wCX3wBF10ElSqBJxjJkXPUqFEjqVDV+++/z7x584ItksPhyCLpKhARiUqx6Smgg6pWBDoCbwZIrkwTHq4MHgxz58L69fD887B7NwweDOWrR9Lzsyv56uovOL55N3z5pY1I6ta1k999Fx580EYqzuU0R4iIiKB27dpUq1Yt2KI4HI4sktEIZLaIXJPs/SmgvIgUACoDQfe+So0aNeA//4FVq+CPP+Duu2HBArj2WihXvTA3T+1F7M2fk1gw0k5YuxbeeQfOPRdq17aTV64MbifyOBEREXTr1o2KFSsClgrFm17C4XCEBhkpkAuBLiLyg4jUAh4G3gYOAa8BNwdYvmwhAi1bwmuvwZYtMH06XHUVTJgAF14IVavCI4/AskFvojt2wiefQK1a8NJLpkS8eHy7HYEhISGBHTt2JOU3cjgcoUG6CkRVD6rqncDTwGigFzaFVURVG6vqzByQ0S+Eh5vpY+RI2LkTxo2DFi3gjTegeXNo2rEEL+26iU0fT4Nt28Drv71xI1SpAm3a2MEux5PfCQ8Pp0WLFnTr1g2Aw4cPc/jw4SBL5XA4MiJDI7qYD+Z6zOaxB3PdvTwzF/FEsseKyGoRWSki93q2lxSR6SLyj+e1RLJzHheRtSKyRkQuzVy30qdIEXPEmjIFtm+H996z0JHHH4dq1aBj73J8/EsdDh4EihaFl1+G06fhgQegcmXo3Nnmxxx+Izw8PMkja8qUKXz66ackJCRkcJbD4QgmGRnRe2NK409gI7AC6Ar0F5GvRaSyj9c5DTyoqg2AtsAQEWkIPAbMUNU6wAzPezz7+mABipcB73uCF/1O6dJw553w66+wbh089xzs2AG33grly8MNd5fip6YPk7BwMfz1Fzz5JOzaBWU84S/TpsH48XD0aCDEy5dcfPHFXHbZZUnBhi6XlsORO8loBPIG0FlVKwBXAP9V1R2qej0wHJjsy0VUdbuqLvasHwZWA5WAK4FRnsNGAT0961cC41T1hKpuwNKotPG5V1mkZk144gnTE/Pnw6BB8OOPcNllNov1yCf1WHnt02Zg9yqQESOgTx8oWxb69bNo+FOnAi1qnqZMmTLUq1cPgDVr1jB69GiOOgXtyAV4S9oWLVqU4sWLc/755/PBBx8k1cEZOHAgIsLkyf/+abzvvvsQEUaOHAlYjZMLLrgg1fZ//vlnAGbNmkXlyr7+Rw8OGSmQE5jnFYACx707VHU6NprIFCJSHWgBLADKqep2T3vbgbKewyoBm5OdtsWzLUcQMYes99+3Ka6vvoJWreD116FxY1t/5x3YswcbfcTGwg03wPffQ9eu0L17Toma5zl58iSJiYku4NCRa5gyZQqHDx8mLi6Oxx57jP/973/cfPMZf6K6desyatSopPenT5/myy+/pFatWsEQN6BkFIp9KzBeRIoAu4DByXdmNomiiEQDE4H7VPVQOrW0U9tx1jyGiNwG3AZQJaYKS95awsHGB8HPk12lSpn5Y9CgCGbMKMdPP5XjnnuK8sADibRtu49LLy3NudfeSMFevSj5++9oRAT7Zs0iPD6elnfdxe4OHdh10UUcrVo1yzLEx8cza9Ys/3Uql5Fe/6pXr87cuXNJTExk69atVKpUibCw0KpEkJ+fX2aIiYnJdQ4UCQkJSTKpKkePHuXw4cOEhYXRuXNnPv30U7p06cLgwYM5deoUl156KePHj2fTpk2UKFGCqVOn0rBhQ+Lj4zl+/DiHDx9OSjKasq/J2z969Ciq6rf7cfz4cb9/BtNVIKo6A/CtqG8GeLL7TgTGqurXns07RaSCqm4XkQqYkgIbcSRPGV8ZOMv9SVVHACMAWhRpoS3uawHlgWuAa4EL8Lsyueoqe12+HEaPDuPzz8swd24ZSpeG66+HAQMuoWVLG8Wwdi3Uq0fU2LFUHzMGzjnHMgb37w8lS2bqurNmzaJTp07+7Uwuwpf+rVy5kjlz5nDBBRdQo0aNnBHMT7jn5xurV6+maNGi/96YWru9e5vx8uhRG/WnZOBAW/bsgV69zt5/xx3mSbN5s81Pp8Phw4eTZBIRihQp8i8ZO3fuTOXKlVm8eDEREREUK1aMK6+8ku+//5477riDr776iptuuon33nuPyMhIihYtSmRkJOHh4Wf1NXn7RYoUQUTOvh9ZJDIykhYtWvilLS9p/o0TEZ+y3flynMeT6xNgtaq+nmzXZGCAZ30A8G2y7X1EpJCI1ADqAL+nd41jlY7B/wHtgE+BTtik1xDgF8DPDj1Nm8Krr1qIyPffW1zJiBE2vdWkiTlubStSG376CbZuNRdggPvvNz9isJNz2b+t3EyjRo0YPHhwkvI4cOBAcAVyODxUrFjxXzVv+vfvz+jRozl48CC//PILPXv2POscb0nb5MumTZtyUOrsk94I5D0ROQSMAX5R1aQRgGe00BHoD0QDHTK4TjugH/CniCz1bBsKvARMEJGbgU3YuAFVXSkiE4BVmAfXkOTp5FNDw9T8tvoA8cAPwJfAZ8D72MjkBeCmDCTNJAUK2B+grl1h/34LUhw1Ch591NyCL74YBgwoT8/b76PwffdZnpWaNe3khx+GyZMt9Xy/fhao4hI8pku5cuUA2L9/P8OHD6dTp06cf/75QZbKEVDSm3YpUiT9/aVLp78/g9GHr2zdupWSyWYVLrjgAnbv3s3zzz9Pt27dKFy48FnntG3b9qxKht5Eo6FCmiMQVb0A++m9EVgrIodFZJuIHAb+wX6q31XVjJQHqjpXVUVVm6pqc8/yg6ruVdUuqlrH87ov2TkvqGotVa2nqlMz1atooDemQHYD47HprFKe/euAuzGV5UdKlIDbb4fffoM1ayyp4+rVZl+vWBGGDIE/9tc8k27r3nttOmvqVLj8cosxefFF/wqVR4mJiaF9+/Y0btwYcK6+juCxcOFCtm7depZXVd++fXnttdfo379/kCQLPBlFon+nqt2AGOBcLBK9DVBcVXuq6g85IGP2iOKMMrnSs20pNqHmNdUvBH4DEv132bp1LaZkwwb4+We44gr49FOb4mrRAt5+G/bWaQvDh5ur16RJ0K4dHPc4up0+bW5fmzenf6F8SlhYGO3bt6dYsWKoKpMnT2b+/PnBFsuRjzh06BDfffcdffr0oW/fvkllnL3cc889TJ8+nQ4dMvyPHbL45MqiqqdUdZWq/qaqq1X1dKAFCyjXAHs5Y6b/LzbJVh14ELO2+OkPbViY1bT6/HPTE++/bzWt7r3XRiW9e8OPsYVI6N4TJk6EZ56xExcssAzB1apBly6U+/FHZy9Jg4SEBI4fP86JEyeCLYojH9C9e3eKFi1KlSpVeOGFF3jggQf47LPPzjquZMmSdOnShXS8TTMkO+fmCKqaJ5a6detqljmoqmNUtZuqRnharKGqj6rqYlVNzHrTabFsmep996mWKqUKqpUrq/7nP6pr1yY7aO1a1aefVq1Z0w4qUkR1xQr/C5MLiI2Nzdb5iYmJmphoD2rr1q269l83Mvhkt3+5HX/1b9WqVX5px58cOnQoKNf99ttvtVmzZn5rL617CyzSLP7uhpYzfaAoBvQFpgA7MS+uusCrQEugPjDSv5ds2tQcs7ZutfIkTZqY+aN2bUu1NWYMHK1QC556CtauZfE775jbYv361sBLL8Fjj7mcXB5EJOnf2i+//MKUKVM4fTq0B8qO/Mvp06eZOHEirVq1CrYo6eIUSEpKAIOAH4EdwIdYFIo3k8Y+bMpru38uV6iQuan/8APExcELL5jZo39/qFDBjPILfhcONmpsGYI9+aH45x/zI27UyDIFv/ce7N3rH6FCnF69enHjjTdSoEABVNW5+zpCioMHD1KyZEk2bdrEU089FWxx0sUnBSIiPTxFpPIXpbE49xnAnZ5tc4D/AFs97+OSrWeTypXNc+uff8zzsGdPG4m0bQs33dSat96CJFfzTz6x1PJvvAEnT8Jdd5nNxEs+/vcdERFBGU+ust9//53333+fPXv2BFkqh8M3YmJiOHToELGxsVTxk5txoPB1BPIcsF1E3hWRcwMpUK7nSsz99xzP++cxY3xH4AMsd3E2EYGOHS2eZMcO+PBDiIxM4L77zPDety/Mng1apizcdx8sXWrLY49ZA0uXWs33Bx+EP//MvkAhTIMGDWjXrh2lSpkPtzp3X4fDb/jqhdUMuAg4Bkz01Oh4wpMYMf9RhTMuwA9j5bZ2AXcAFbCE92MAPzhNFSsGt90Gw4cvZskSuPlmq2PSsSM0aGDVFvfsAZo1O2MfCQ+HCy6wjI9Nm1oKlXfegSNHsi9QiFGsWDE6duyIiHDkyBE+/PBDNm7cGGyxHI48gc82EFVdpqoPYz+fQ7Co8XUiMltEbhSR/GlPqQs8icXML8XcgFdiMfplsRiUn/1zqebNzdSxbRt89pkleXzoIRts9OkDM2ZAYiJmkZ840Q586y1QtbB477/vuLh8OcV1/PhxwsPDU40KdjgcmSdTP/qeuuhPYrVAIj3rHwF3AV/5XbpQQoBmWHKWDcBcrGL8LM8Clhh/BtnOyxUVZXnifv0VVqywvHDTplkmlLp1zUFrxw4sjcM998DixRYaHx1tSqR7dysI/9hjtj2fUKpUKW655ZakdCjz589n+3Y/eUM4HPkQX43oQ0RkPp4aHkA/tRQjL6jqGKALcEkA5QwtwrDAxHexHMIe0wTTsInAHz3vT5DtgMVGjeDNN22w8fnnZoh//HFL8XPNNZbLMTERG6Z4eeYZm9Z69VWb9rrgAquclQ/wuvqeOHGCefPmsXjx4iBL5HCELr6OQC4HXgMqquqdqvqvnBGqehS42t/C5QkKYLm5AC4EJgAXe94/j8WYPIPVXMwGkZFw443mvfXXX2Zbnz3bqinWrAnPP29KBhHLST9livkL/+9/ZkTZvdsa2rPHhjZ53NhcqFAhBg8ezMUX28M4cOCAc/d1ODKJrwpklqp+qSkKSInIA951VZ3mV8nyIoUxy5G3uF5zoCKmQOpg2cbexoIZs0G9ehYysmWLFUysXRuGDbNZq169zFaiigWaPPLImYyPYK5fF1xgFvqXX/bMheVNChcunFTp8LvvvmPkyJEkJPg5778jT5GbSto+9NBD1KlTh6JFi1K/fn1Gjx7tp176jq8K5Mk0tj/hL0HyJdcAsZhb8CvASeBerI7J5cBYIBuOU4UKWa6tn3+22lYPPGAjlIsuspmr11/3xJWInAlQvP12y/pYpozlpK9cGa6+Os8b3a+44gq6d+9OuOc+nHJ17R1pkFtK2kZFRTFlyhQOHjzIqFGjuPfee/ntt9/8eo2MSFeBiMiFInIhUEBEOnvfe5Zb8IujqoPKwEPAEsyD61HMq6svcL/nGMUqo2SRWrVsQLFliwUnli5tYSKVKplBfsECz6gkOhoGDYI5c2xk8sADZrX31ikZNcpqmuQxSpQokfQFX7FiBe++++6/CgQ5HCmJiYmhR48ejB8/nlGjRrFixQrAki3++uuv7N+/H4Aff/yRpk2bUr58eb9e/5lnnqF+/fqEhYVx7rnn0r59e+bNm+fXa2RERiOQTzxLISxDlPf9x1hpprsDKl1+pCFW+GoDMBu4zzZH/x1tiiabn4/ISAtE/PVXWLbMlMfEiRbtfs458NFHycJF6tc3rTNmjL3ftw9uvdW00UUXwbhxZ9LP5yFKlixJtWrVKF68eLBFcYBVF81oeTXF8SM963t8ODebtGnThsqVKzNnzhzASsf26NGDcePGATB69OiA1wQ5duwYCxcupFGjRgG9TkoyqgdSQ1VrYHXMayRbaqrq+ao6Ob3zHdkgDGiPKRRAw9WKYtXz7P8KeBHIRrmQpk2tHMm2bZZm/vRpC1qsWBHuvjuVPI0lS9ro47nnYN06KwJfqRJMn551IXIhFStW5OqrryYsLIxTp04xduxYNru6LI50CHZJ28GDB9OsWTMuvfTSrHYhS/gaiZ53S2qFCEdqHzGl4a2aGYsVBa6GeXeNJMsTikWLWizJsmUwd66FiYwYYS7CHTvaQOOk132icmV44glTIN7gE++/npkzbYrr6NE0rxVqHDx4kL1797rMvsFklg/LQymOH+hZL+3DuX4gqyVtvd5/3qVq1aqptj948GCio6OJjo7mv//977/2Pfzww6xYsYIJEybkeP2QNBWIiKxOtr5ZRDaltuSMmI6zeA8rzfs0ZoQfhEXo3IjFmWTBmUjEiiJ+/rnZSv73P3u9/nqLKxk61ILYAauUdfHF5uZVsaJtGzPG5sQqVrTkjsuXZ7OTwad06dIMGTKEGjVqALB8+XK2bdsWZKkcuYmcKGn7wQcfEB8fT3x8PEOHDk3a/tRTTzF16lSmTZtGsWLFsn2dzJLeCOTWZOt9gX5pLI5gURPzj/sHK8k7EJiKeXBVwaxWWaRMGfPw/ecfK9l+3nmmUGrWtDCSmTNTCRX59FNz87riCvj4Y8vP1S/0PyJez6yEhAR++eWXpLluR/4m2CVtX3zxRb744gumT5+elCw0p0kzRbuqzk22/kvOiOPIEgKc51neAL4HRnMmgHEbFsA4AKt3kgnCwiwY8bLLYNMm+OADm9765hto2NAGGv36mfNWUhrhjh2t6LvX3QtsWmvYMPPwatw4+30OAuHh4dxyyy1JPv9HjhzhyJEjlC1bNsiSOXKS7t27U6BAAcLCwmjYsCEPPPAAgwcPPus4b0nb7JDelNTQoUMpWLAgderU+de25COUQJOmAhGRZ31pQFXTihFxBINCWE6A5HkBfsLcgbthCmQ7ZksplLmmq1aF//4XnnzSZq68RRIfe8z0wpAhkPRZLlXKwuG9LFpkmSBffx3OPx8GD7aoxhBLbJh8LnvGjBmsXLmS+++/n8jIyCBK5cgpMsrk7A0UTI25c5P+kzNw4EAGDhyYbvuHDh1Kd2SRG0oTpDeFVcXHxZHbGYTZS2p73t+FRcDfBSwi0/m4IiNhwABYuBDmzYNu3cyLq25duPxyq67o+ZN+hg4drH6vN/98//5mkN/qp2pcQaBLly5cddVVScrj2LFjQZbIkVcIlZK26U1hDcpJQRwBpmay9cFYOpWPMWN8I8x+0hfIRKyTiMWPtG1remHECJviuuIKCxUZMsRGJknhFKVKWWDi/febrWTq1CQDfKWvvjLFcuWVEBGRzc7mDFFRUdT31GCJi4tj7NixXH/99UkGd4cjKxw8eJAqVapwzjnnBCU9SWZIzwurerL1mmktOSKlw79cDPwfVvP9A6AoVhirMtAdmIilVckE5cvb1FZcnLn9VqhguqJSJZut+ldhRBHo3NmCFEUgIYGK330H114L1apZQ1u2+KOnOUaJEiVo3LgxlTxZj3PD9IIjNMkrJW2Tf+XXYr4+a1Ms/wRONEfAKQ7cjkW3r8aUyGKgF5aKHjI9vRURAdddZ5lQFi82F+BRoyxosXNni3o/K6QiPJyFn3xiGYJbtLDUwdWrW1h8iFCsWDF69OhBwYIFSUxMZMyYMSxcuDDYYjkcASVNBaKqRZOth6lquOc1+RKeM2I6Ak59LLJ9E/ADNp0F8AXQAjO8Z5IWLcybd8sWG2xs3Gh289q1bcrrX9nTw8PNmPL99xak+PDDFpQC8PvvVvTEk1sot3Pq1CkKFixIoUKZ9FJwOEIMXwtKvZ3G9jf9Ko0j+IRjcSRez9SiWLR7Oc/70ZhXVyYCFUuVMn2wdi1MmmSDi4ceMhv63XdbrMm/qFEDXnzR/IQBvvvO7CaVKlkuriVLstq7HKFQoUJcd911SXEBq1atIi4uzqWKd+Q5fE3nPjCN7aEfJeZInx7AN9gnRYH/ApcB1YFhQCYS84aHQ8+eZj9fvNhGIyNGWP2SoUMbn6lTkpJnnzWl0bcvfPEFtGxpDeViRCTJh3/jxo3s3bs3x9NMOByBJqN07jeJyE1YOvebUizPY7kuHfkFAZYBXwJNMGVSC8vFNRbIhBdrixYwcqQZ3Z98Ev76qxgXXWS2kk8+gbM8Yps3N22zdatNZ3kDtBISzuRcyaV07dqVZs2aJSVn/PXXX11uLUeeIKMRiDddSUH+nb6kL/bTMSCg0jlyH4UwI/sPQBzwnOe1L2diSzb43lz58vD00zBu3Hw++8xGKbfcYkGLw4bB9pS2l+LF4d57be4L4I8/rAh89ermxTV7dq4sx+tNh7JmzRp+/vlnl0/LkSfIKJ17Z1XtDLzkXfcsF6rq9SlrozvyGZWxmpT/ADOArlhsyUHP/q3J1jOgYMFEBg60marYWLOfv/CCefX262d6IlXatDGj+wMPWK3ejh1teJPFtNiBpnHjxtx5551JWVc3btzoqh+GEN6Stt7MuNHR0dx1110BuVZGJW1zA76mc08qXStGmHcJnGiOkCGMM9NYO7Fa72Dp5uuTqUqKItCpk+Xa+ucfS5XyzTfQqhW0b5+GG3CNGmfKLY4YYdZ5TzwG06fnOmVSpkwZwHJpjR07lmnTpgVZotDn5ZdfJjY29l/bYmNjefnll/1+rSlTpiRlxo2Pj+fdd9/N+KQ8iq9eWBVFZJKI7MV+Dk4lWxyOM8QkW78HeA3Ld6DAVZ73PlrOatUyc8eWLfDGG2b+8LoBv/UWHE5Z/6RIEfPS+u47mwtLSLD08jVq2Ilz5uSq6a2oqChuuOGGpGytR48e5XgerPCYE7Ru3ZrevXsnKZHY2Fh69+5N69atc+T6d9xxB7169Up6/+ijj9KlSxdUlf3799OtWzfKlClDiRIl6NatG1uS2ez27dvHoEGDqFixIiVKlKBnz54cOXKEyy+/nG3btiWNdHLltKeqZrgAU4Dx2H/Lg0AzYBJwq4/nfwrsAlYk2/Y0Nsmx1LN0TbbvcSxQcQ1wqS/XqFu3ruZlYmNjgy1C9tirVsMSVS2oqn1UdaaqJtpuX/p3+rTq11+rXnCBKqjGxKg++qjqli3pnBQXZweVKGEntWihOmNG9vqSBXzp35dffqlvvvmmnjp1KvAC+Rl/fT5XrVqV5XNnzpyppUuX1mHDhmnp0qV15syZfpHp0KFDSevVqlXT6dOnn3XMkSNHtE6dOvrZZ5/p7NmztVSpUrp582ZVVd2zZ49+9dVXeuTIET106JD26tVLr7zyyqRzu3btqr1799Z9+/bpyZMnddasWapq97RSpUp+6YNq2vcWWKQ+/MamtviqQPYCUZ71A57XksBfPp7fAWiZigJ5KJVjG2K+PoWAGlgawPCMruEUSIiwQlXvVdUSak+utqr+T3Xu13Mz1cz8+arXXqsaFqZaoIBq//6qy5alc8KRI6ojRqg2bqzq+YLq9u225AC+PL9t27bpkiVLkt4fO3YscAL5mdygQFRVhw0bpoAOGzbML/Konq1AoqKiNCYmJmkZMWKEqqouWLBAS5QooVWrVtUvvvgizfaWLFmixYsXV1V75iKi+/btO+u4UFAgvtowEjgzk31ARMoAR4BKvpysqrOBfRkeaFwJjFPVE6q6ARuJtPHxXEdupxHwJjb2/Bzz3HoUzut9HlyHz9Nb554LEyZYcOKdd5ptpFkzuOQS+OmnVGaqvNNby5dbZmAwK33VqpZaePFi//QvG1SoUIHmzZsDsGnTJt58803ikkpAOjIiNjaW4cOHM2zYMIYPH36WTcRffPPNN/8qQ3vrrVZ7r02bNtSsWRNVpXfv3knHHz16lNtvv51q1apRrFgxOnTowIEDB0hISGDz5s2ULFmSEiUyWagnl+CrAlmA+diAxSGPB77GkoFnh7tEZLmIfCoi3jtYCdic7Jgt+KioHCFEYaz87i/Aatjac6vl4yru2f8rNumZATVqmD1k82YLXl+xwopfNW1qcSYnTqQ4QcQWgHvugdtvN+1zzjmmWL77zi/dyy7FihWjQYMGVKhQASCpiJUjdbw2jwkTJvDss88yYcKEf9lEcoL33nuPEydOULFixX8Z71977TXWrFnDggULOHToELNnzwZs9qdKlSrs27ePA//K62OEQuBpmuncU9CPM8rmPqyEfTT2XzKrDMeiCNTz+hpwExaulpJULZ8ichtwG5hny6xZs7IhTu4mPj4+b/dvQDzrotbBXCABzutzHvG14/nzxT8zPNdL27ZwzjnCjBll+fLLKgwaFM1DD53gqqu20r37NooVS8Ud7JprKHDppZT/4Qcqf/01+4cPZ020lXIMO36cRD8VisrK84uJieG3335DVVm2bBklS5ZMcv/Nbfjr8xkTE8Phs7wjMmbu3LmMHDmSVq1acfjwYVq1asXIkSOZO3dutmtqJCQkJMmkqhw9evQsGf/55x+eeOIJvv/+ewoXLsyFF15Ihw4daNq0KXv37iUiIoLw8HDi4uIYNmwYAIcPHyY6OpqLL76YW2+9lddee43o6Gh+//132rVrR3R0NHv37mXLli3ExMScJVdmOX78uP9/Q7I695XZBUt+sSKjfZgB/fFk+34CzsuofWcDCW3O6t9KVV3qWY9T1Uaq+qaqnj1VnCqJiao//aR6ySVm6StSRPXuu1XXrUvnpFOnVPfvt/UFC8xK//DDqps2+dyPtMjO8ztx4oROmjRJl6Vr5AkuucUGEghS2kAiIyM1KioqaenZs6e2bt1aX3zxxaTj3n//fW3cuLEeP35ct27dqh07dtSoqCitU6eOfvDBBwokOUvs3btX+/fvr2XLltXixYvrVVddldTOoEGDtGTJkhoTE6Nbt27NVj9y1IgOPOvL4vOFUigQoEKy9fsxuwfYLHlyI/p6nBE9/ymQ5PyhqueqPelIVR2oqr/73vayZaoDBqhGRJjRvVcv0w/psmqVau/equHhZqW/4QbVRYt8v2gK/Pn8li9frl9//bWeOHHCb21ml/yiQEKZnDai+62krYj8H1Z1op6IbBGRm4GXReRPEVkOdPYoEVR1JTABWAX8CAxRVZfGND/TEpiP1Srpj+XiagO0Aj4BjqZ/utcesnEjPPII/PyzGeE7dbKiiGcZ3AEaNLDC7+vWma1kyhS46KJUknTlPIcPH2b//v0UKODrDLTDESCyqnly2+JGIKFNpvp3UFXfVZvWQlVjVPUR308/dEj19ddVK1e2MXjTpqqff6568mQ6Jx04oPrLL7aekKDas6e5Bfvoauvv55eQkKCqNr01YcIE3blzp1/bzyxuBJL7CaYbLyJSR0SeFJEPPa91AqjXHI60KQYMwWpmzsb8A5M7ic8k3fQpRYtaeZF162xkcvq0ZYqvUwfefhuOHEnlpJiYM+6/u3ZZGuHbbrMkji+8APt89VL3D2Fh9tXds2cPcXFxHMsFIyNH/sPXVCbdgT+wzEb7gHrAIhHpEUDZHI70EaA9VjVxhGfbMqAL8GHGpxcsaCEgf/4JkydbCq1777UEjk8/DXvSikkpX96yO86YYYkbn3jC4knSzPgYOCpWrMi9995LtWrVAFi0aBGrVq3KcTkc+RNfRyD/Ba5U1RtU9XFVvREL+Ptv4ERzODKB1/m7MVYA6wbP+7Ge9d9Is757WBh07w5z59rSrh0884zphHvuMdvJ2dcTuPBCM6IsX2456Js2tX3ffQdLl/qpYxkTEREB2HT0smXLWLlyZY5dOxC4mBf/o6ka+rKPrwqkMjAnxba5nu0OR+4hHPtr4w1L3YvVLmkHnEOGRvd27eDbb2HlSujTBz74wJI33ngjLFuWxklNmljWx4gIs8g/+KCNTC69lLTLLPofEWHQoEF0794dMGP73LlzQ6p4VVRUFFu3buXkyZMB+9HLb6gqe/fuJdJPMU3J8dWNYynwIPC/ZNse8Gx3OHIv92DhqWOBd4FbgIeBm4E7MUfxVGjYED791KrpvvkmfPihVdO97DJ49FErO5JqoLAILFhgmufNN81zq2VLYvr1M7evABMWFpb0Q7Fy5UpmzZpFo0aNQiZVRuXKlZPsOrlF8R0/fjwgP745SWRkZGBqi/hiaQcaYGWDtmFpTbZ53jfIqvXe34vzwgptcqR/iao6S1V7qWq4qoqq9lDVjGJCVHXfPtUXXlAtW9Y8t1q3Vv3qK8sQnCbHjql+9JFq3bq65NVXbduBA6rHj2ezI76TPEnfwoULdb83UNLP5OXPZ17um2oOeGGp6mqPErkOSznSG2jo2e5whAYCdMTiSDZgOQ9+w/4KAcRjKUJToUQJGDrU7CEffGBOV7162Ujlo49SybkFEBlptpFVqzjQsqVte/ppS+D16qtw6JAfO5eW3DbyOHLkCNOnT2fRouymr3M4zuCrF9Z9QClVnaOqE1R1rqq6YlKO0KUK8AKWttObOPV9zKq3O+3TChe2/Itr1lg24KJFzZu3Zk14/XWIj0/lpPDwM/NdPXqY1nn4YXP3GjYsHXcv/xEVFcWdd95J+/btAdixYwd///13wK/ryNv4akTvBGwQkZ9FZJCIFAugTA5HzhEJRHjWvfkQynjevwXMIlXvrfBwuPZaWLjQqubWr2+282rVzIMrzbCQzp0tFH7BAlt//nlTJjlATEwMhQoVAmDevHl8++23nDx5Mkeu7cib+DqF1ROr3DAOy8y7XUQmisjVAZTN4chZWgNPetaPYy4jnYEWwEjPthSImJ18xgyYP9/qtj/9tLkAP/QQpFmFtE0b+Pprc/fyZGdl2TIbzqxb589epUqPHj3o378/BQsWRFVZvHgxp065SQVH5vA5El1VD6jqx6p6IWYPKYrNJjsceY9IrBbmR1g5tUFANayO5o7UTzn3XPjmGwtM7NnTnLBq1LApr61b0/DiadjQ5r/AilqNHg1161pofAADAsPDwylXrhwAW7ZsYcqUKaxYsSJg13PkTXxWIAAicoGIvAcsxIo8PRUQqRyO3EBhzO13OfAzlsDxGUyRDCBNJ/bGjeHzz+Hvv+Gmm2DUKOjf/1xuvNGUS5oMGgQbNsADD5gmatzYtgWYKlWqcNNNN9GsWTMA4uLi2LlzZ8Cv6wh9fDWivyIicVgR0njgUrVUds8HVDqHIzcgWHqUKcAarITZRGzKKx2De82aMHy46YRrr93M5MkWrN6jh013pUqFCvDKK+bu9Z//QK1atl01oNHtVapUISwsDFVl2rRpTJo0yQXyOTLE1xFINNBXVaur6qOqujSAMjkcuZe6wDuY99bXnDG4347l5EqFChVg8OD1xMWZgf3XX+G888yGPn16GoHqpUvDc89Zni2wQu/e6PZff/Vzp84gIvTt25drrrkGEeH06dP88ccfJCS4igqOs/HViH6HqqZMZeJw5F9KAN0960eBJcAmz/tTpGonKVkSnnzSEvm+/jr88w9ccgm0bm329HRTQLVrB//7HyxZAhdcAF26wC+/+LFDZyhcuDBlyphm/Ouvv/juu+/YtGlTBmc58iOZsoE4HI5UKILlZ3jI8/5LzE5yE5CKXTo6+kw6+Y8+goMH4ZprzOQxahSk6gxVtKhVw9qwwbTPqlWWoCvAbriNGjXi5ptvpkYNy/ny119/sScH4lYcoYFTIA6HPxDOZJZrixnfxwFNgMugxKISZ8WTFCpkgep//QXjxlkuxoEDLXnju++mUfwwKsq0z/r18MMPlpP+5EnL/Dhzpt8TN4pIUg6lhIQEpk6dyvTp0/16DUfo4hSIw+FvagLvYXaS54Gl0OzhZlaadyw2xZWM8HC47jqzkX//PVSpAnffbbWqXnrJRihnUbjwmfTxa9fCnDk2rdWxY0AUickZzm233UbXrl0BS4/y+++/O/tIPibTCkRE6onIVSJSPQDyOBx5h1LAf4A4+OuhvywQsS9Qm1QN7iLQtavVJJk9G1q2hMcft6DE//zHCiGmSsOGNh/27rs2MunSxTL/7t3r9y5FRUURExMDwIoVK/jxxx/Zv3+/36/jCA3SVSAi8pqI9E32vj+wEqv/tlpELg+wfA5H6FMIdlyxw745kzH7iDf54hFSNbi3b2+1qv74wwztL75oI5J77oFU7dmRkTBkiI1G3nnHbCYlS9q+NMPhs0ebNm244447KF26NAALFixg69atAbmWI3eS0QikJ1Z12st/gXtUtQwwGBdI6HD4ThjmuTUbGOjZNgKozhkPrhS0bAlffgmrV5uZY/hwCw0ZNMhsJ2cRGQl33WVVEUUsKVeDBub+m2bwSdYQkSRvrYSEBH799VeWpVl1y5EXyUiBlFHVTQAi0hgblH/i2fc55hXvcDgyi7cYVXcsK3BVz/sPgd/PPrxePStwtW4d3HknjB9vM1fXXmsZUNKkcGHzHV682IJPunUzV2A/Ex4ezpAhQ7jwwgsB2L17Nz///DMnUs1z78grZKRADopIOc96e6zwiPcTEcGZr4HD4cgKtbFan2A2kqeAc7HI9+mc5blVtSq89ZbFkgwdaoGI55xjlRJnz07Fdl64sKUJ3rAB/vtf+O03O2HtWr93pVChQkmV+9atW+cCEPMBGSmQCcA4EbkHeIx/m/7OxdLNORwOfxAJ/A28AqwGLgFaYXElKX6Hy5SxTPBxcWYfWbLEHLAuuMA8uc5SJNHRZpHfsAHGjDFfYYCPPw6IMmnbti333HMPRYoUAeC7775jzZo1fr+OI7hkpEAewyoiXIzN1n6QbF9zzzaHw+EvimEBiRuwTMCHsYJXDbDJ4xRxgzEx8Nhjljrr3XdhyxabpWre3GJLzhoAxMRYACLAgQM2Oqlf31IGb9ni164ULlwYsJrimzZtYm8AvMIcwSVdBaKqp1T1GVXtrqovaLLsaqr6lqo6BeJwBIJCWDDiauArrHjCLZjV8ejZhxcufMYJa9Qoiy28/nrTDR9/nEbJ3eLFrbTinXfCZ5/ZqOTBB/3u/hsZGcngwYM599xzAVi7di1jxowhPtXyjY5QIsM4EBFpJiJ9RKSW5/0LIrJcRL4QkdKBF9HhyMeEA9cAi4AfsUzARTz7xgEpQjAiIqB/f6tT9fXXpiNuvdUyA7/xRiold8uXh7ffttzz119vbl5H0igMnw3CwsIIDw8H4NixY5w4cSJphOLsJKFLRnEgg4E5WKHPhSLyFpao4QMsD+lbAZfQ4XCYu8qlwFDP+43ADcC7qR8eFgZXXQW//w7TppkX1wMPWMndZ59NpeRu9eo2Ctm82Sz1YArl9dfheCqlGLNBkyZNuPnmmwkPDycxMZGPPvqIuXPn+vUajpwhoxHIQ0BHVT0X+/jeBfRR1feBPpiviMPhyGmqA4uxbyRYgOL9QIqYQRG4+GLLbvLbb5bU96mnTJE8/DBs356i3VKl7PXIEZvKevBBq5D42Wdw+rTfxBcxB87Tp09TpUoVSnmum5CQ4Fx/Q4iMFEhZVV0CoKoLgaOqutvzfi9nBtMOhyOnaY6llQermvgOUAO4AxuhpOC882DyZFi+3Ipavf66DTzuuMMyoPyLqCgbuvz8s01z3XST5d5audKvXShYsCBXXHEFDRo0AGDJkiW89dZbHDhwwK/XcQSGzObCSi3RtMPhCDZPYC7Ag4BPgTqY0T0VR/smTWDsWDN7DBpkAYreMuxnlUXv0gUWLICJE8132Du9lWqGx+xTqVIlmjdvnpRva/v27Zz248jH4V8yUiBFRGS2dwGKJns/B6sa7XA4cgM1MevkOmwUMhaoh9VvTyUEo1Yt+OADCw25/34rw96kCVx5ZYqsJyJw9dVWwKpoUZvKOu88G8acpXGyR4UKFbjkkksQEU6dOsXnn3/Ot99+69drOPxHRgrkZsz73Lvckmz9Y897h8ORm6gMvA2sB+7FAhEbAtNSP7xiRSvDvmkTPP20ZQM+7zy48EKbwTorKDEhwVy9Zs+GZs3gppsolGaq4KwTERFBr169aNeuHWDeW0uWLCEx3dKNjpwkoziQURktOSWow+HIJBWA1zB7yJNAB8/2n4FVZx9esqQZ2OPi4LXXLFnjxRfDuefCpEnJSu4WKmTRi+vW2dDliy9o06+fpQ72MzVq1KB8+fIALF++nMmTJ7uKiLmIHCkoJSKfisguEVmRbFtJEZkuIv94Xksk2/e4iKwVkTUicmlOyOhw5FnKYjm2IrHcWvdi8SRpEB1tLr8bNsCIEebye/XVNr3lDVIEzGPr1VdhzRq2XnONhb+DVcYKQKndNm3acOutt1K2bFkAfvvtN1atSkUTOnKMnKpIOBK4LMW2x4AZqloHmOF5j4g0xFyEG3nOeV9EwnNITocjbyPAL9gENMAuoD8W8Z6CQoUsCPGvv+CLL6xy4sCBFpT46qtw6JDnwGrVWH/bbXZAfDxcdJGlkB8/3q+VEUWEihUrApCYmMiff/7J2mR5vDQAVRgd6ZMjCkRVZwMpQ5euBLxTYKOw2iPe7eNU9YSqbgDWAm1yQk6HI19QGqjvWf8DmIT9XbuRVI3tBQpYTOGyZVbkqm5diyGpUgUefTRFvaqoKHPxio62AibnnWdGFT8TFhbGrbfeyqWX2gTF3r17ef/9911BqxxGckpre0rgfqeqjT3vD6hq8WT796tqCRF5F5ivqp97tn8CTFXVr1Jp8zY8g/EyZcqcM2HChMB3JEjEx8cTHR0dbDEChutf8Ig4GEGV8VWoNKkSYSfD2NllJ3H94zhW+Via56xZU5Rx46owe3YZwsKUTp22cOONO6he3ZOoKyGB8tOnU+OTTyi0Zw8LP/6YI7VqBawPhw4dYt26dTRq1IiCBQty8uRJChQoQFhY9v8j5+Zn5w86d+78h6q2ysq5aSoQEXnWlwZU9UmfLuS7AnkPmJdCgfygqhPTa79evXqal9NFz5o1i06dOgVbjIDh+pcL2IWlkn8Py/rbHxiGBSemwfr1FpD48ccJnDgRTrduNjpp3968fzl61PyDb7jBTpg0yXLOeyoZBorx48ezf/9+br/99qSo96wSEs8uG4hIlhVIeuq5SrKlDmaj6IKVwLnQ875OVi7qYaeIVADwvHr9ALd4rumlMmclaHA4HH6nLKZANgB3Y9V/6vLvIg4pqFnT0siPHz+fZ56x+JGOHW3mauJESChU5Izy2L/fohVr14aXX/Z7jq3knHPOObRt2zZJeaxYsYJTp1wctL9JU4Go6iDvgpnerlfVdqp6g6pegBm6s8NkLMQJz+u3ybb3EZFCIlIDU1KpFPl0OBwBoRzwBhaQeBtWOg7sb9yO1E+JiTnFk0+aC/D778Pu3dCrl6WT/+ADOHYMKFECFi2y4cmjj9rOceP8amj3Urt2bZp7vMJ27NjBxIkTWRKAUr75HV8nCC8Hvkmx7Vugqy8ni8j/AfOAeiKyRURuBl4CLhaRf7CCVS8BqOpKrBLiKiyB9RBVdfmeHY6cphI2ndXC834o0BhI2zRCkSKWW+vvv+HLL01n3HGHZUAZNgy2F28A331nEYrFi0O/fuYvHEDKly/PwIEDadHCOvLPP//w008/cTIArsb5DV8VyFpgSIptd+JjSVtVvV5VK6hqhKpWVtVPVHWvqnZR1Tqe133Jjn9BVWupaj1VneqjjA6HI5A8gaWPL4zFk3yKVUxMhfBwG4EsWACzZlkW4BdesCzA/fvDkpJdLPBwzhybBwMrWBIgZVKtWjUiIiIAG5H8/fffFChQAMApkmzgqwK5BXjAM3pYICJbgAdxqUwcjvxDbc5MXC/BEh3VBF6DsBOp/5SImE3km29sVDJ4sBW6atkSOl4Yzjc72lrZ3S1b4IknbFrr0UcDlqwRoH379txxxx2EhYWRmJjIiBEjmDYtjTwvjnTxSYF4UrrXAa4HXsdK2dRR1cUBlM3hcORWWgILsOmth+DcvudacGI6iXNr17bih1u2WCDixo1W9KpePXj768rEL/7bDO6vvGIHDx/u1xokyfGOPhITE2nSpAnVqlUDrD7JmjVrXFCij2TJSdoTGFhQRKL8LI/D4QgV2mAJGmPheNnjcCsWkPglkE6+w+LFrU7VunUwYQKULQv33guV2lTiwZKfsW3yImjUCIYODehIBEyRdOzYkXr16gHmrTVu3Dg2b94c0OvmFXxSICLSBKs28BGWiRegIzYL6nA48jOdYMm7S8zNpgDQG1MuM9M/rUABuPZaq5Q4fz507QpvvQWVe7SkR9FY5ry1mMQSpSyL4z33+D11fGo0bdqUG264gSpVLJJg/vz5rF+/3o1I0sDXEchw4ElVrc+ZolK/ABcERCqHwxFaCJaEaDmWmGgPsND30889F/7v/8yGPnQozF8gdBhQg/r1YdR/1pA4eoyljh88GAKQOt5LWFgYderUSYof2bt3L0eOHEl6fzDAI6JQw1cF0gj43LOuAKp6BFdQyuFwJCcci2Bfg2X9BRgHXAf48NtbpQo8/zxs3gyffw6lS8PAlxpQ7eRaZjQYgn78MdSpY4GIOeA9dcUVV9C4cWPA6pG8++67zJ49O+DXDRV8VSAbgXOSbxCRNph7r8PhcPybQlj6eIC9wFagqOe9DwHhhQrBjTfa9NbixXDpDaXovv5tGiSs4Nfw9hx64+Oc0B8ASaOPAgUKcPHFFyfVb9+3bx+zZs3i2LF0AmPyOL4qkGHA9yLyDGY8fxwzlT0RMMkcDkfeYAgwB/u12Q/UAp4G4n07vUUL+Phj89669dX6DCj5HdV3zKdq7YI8++gRjnS7DnIgyjwiIoI2bdpQxpPHa/369cydO5eEBItzPnHiRL6zlfjqxvsdFo1eBrN9VAOuVlXnPO1wODLGm8/wGJYa5RksruQDfBqRgFVMfPBBiycZ+0NJWrWC715exdHvZ5LY8hw2dLmZk1sCZx9JSatWrbj//vuTMvVOnjyZzz77LF8pEZ/deFV1sareqapXqOpgVfV//UqHw5G3qYjNXczDIsvuAJpgHlw+/u6GhcHll1tGlK/iWvPJo//wUfQDVJ45mmNV6/LtRe/wz5qcqZseFXUmkqFevXo0adIkacprzpw57NiRRvKwPEKaCkRE/pNs/dm0lpwR0+Fw5CnaArM5k2HvKqATsChzzVStCo+9VJxbDrzKb8OXs6F0a2JmfE3d+kKnTlbbKqdMFE2bNqV169aA1SeZM2cOGzduBCxg8ejRozkjSA6S3gikcrL1KuksDofDkXm8rr8rsECB1UBr4MXMNxUeDh0HN6D5zmnUX/MtL7wgnFi/lRN9b6Jh2T3ceqsVRsyp2aVixYrx4IMP0rJlS8ASOL722mt5rmJigbR2qOodydYH5Yw4Docj31EAGIwlSHoJqzYEVgS7AFAsE22JUL5uMYYOhcdqz4O+Y+mZOI3en4+n/cftqFnTkjn263cmh2OgKFSoUNJ6mTJlOP/88ylfvjwAy5cvZ+/evXTs2NEvVRODRXpTWDV9WXJSWIfDkYcpBvyXM/VHHsMi0LI4BRXWuxdhC+ZTskIk0091ZNF1r1CjWiLPPAO1akGHDubdlROxgSVLlqRLly6Eh4cDsHXrVtauXZukPOLi4jhy5EjgBfEzaY5AsBgP5Yz/RGooFjrkcDgc/uVWLFmjN1x5NdAgk220aAF//IHcfDPnjH+En/+nbBr5CJ9/Dm+88TK33tqaIUM6c/nl0KcPFCsWy4oVC3nkkUf82pWUXH755Zz2JIpMTExkwoQJ1KhRg169egGQkJCQpGxyM+lVJAxT1XDPa1pL7u+hw+EITVpjXloAs4CGWD7wTZlsJybGqlt9/DHcfjtVq1q6lPHjW1O8eG+6dYvl99/h+utjueKK3kyd2pqvvw688d2bETgsLIwBAwbQoUMHAI4cOcKrr77KihzI/ZVdMjX5JiKVRKS1iFQMlEAOh8NxFq2xcOZvgPqYrSQzkegicPPNpkz+/hsGDeLCVufw9dcTmD27Nzfd9CQxMb3p0WMCK1Z05pprXqZkyVj69YN580px/DjExsby8ssvB6BzULZsWcqWLQtYSvkGDRokvd+2bRuTJk3KlXm4fM3GW1VE5gBxwPfAJhGZKyLVAiqdw+FwAEQBzwJ/AZcBj2PTW1lJS3XoEIwcCSNG0LlzZ+644w5eeOE57rnnDr79tjPbt8PLL7cGejNpUixDhzahRIlYLrusN/v3t2bfvowukD1iYmLo0aNHkgLZt28f69atSzLKx8XFsXLlShITcybWJT18HYGMAv4AYlS1LFAcy7U5KkByORwOx9lUA74GpgBHsKISN2HZf32lVSvo3BnefJPYadMYPnw4w4YNY/jw4cTGxlKgADz8cGd++GEChQv35sILbwd6Ex09gZde6kzp0i/TokUsb71lRbEgsKOTxo0b8+CDDxIZacnFFi9ezLRp05ICFrdu3crhw2nUFg40qprhAhwCIlJsKwgc9uX8nFjq1q2reZnY2NhgixBQXP9Cm6D0L15VH1PVAqpaUlXnZOLcH37QmaClixbVmTNnqqrqzJkztXTp0knvVVWHDRumgA4bNkwTElQXLFC94YaZGh5eWmGmgmqtWjO1cOHS+sYbM/XECT/2Lw0SEhJ07969Se/fe+89HTVqVNL73bt3a0JCgs/tAYs0i7+7vo5A5mMlYpLTCktI4HA4HDlPFBZ0uBTL1NcsE+dedhkLy5VjQqlSdO7UCYDOnTszYcIEFi60QiaxsbEMHz6cfv36MXz4cH75JZY2bWDs2M5Mnz6BEiV6c9FFTxIX15sTJyZw//2dKVUKevSA996Df/4JTOBiWFgYJUuWTHp/zTXX0KVLF8DsJylrvAfSPTg9N97krAN+EJHvgc1YBHpX4Ivk6UxU9Un/i+hwOBzpkLxa0THMU+sJ7C9uWojwyDvvwMKFcPw4FDZf4c6dO9O5c2diY2Pp3bs3EyZMQEQYNGhQ0nvvMXfddQfPPfccw4YN48EHOxMbCz/9ZMuUKXaZGjXgkkvgoougfXsoV87/3S+XotEePXpQqlQpAPbv38/bb79Nz549adasGadPn+bkyZMUKVLEL9f2dQQSic08ngDKel4nYR7a3pQmldM82+FwOHKCTdiIZK8Px157rRWmKnx2XbyFCxcmKQtIe3TitZ0sXhxLz54wfDisX2+jj/fegyZNLB/XtddC+fJQrx7ccguMGmXVF/09QilQoACNGzemQoUKgKWg79KlC1WrVgVgw4YNvPLKK0k1348fP569C2Z17iu3Lc4GEtq4/oU2uap/x5Ot/5+q7kvn2MRE1R9/VP3zzzQPSdm3lLaS1GwnyTl5UnXePNWXX1bt3l21eHFVUx2qlSqp9umj+u67qr//rnr8eKpN+I19+/bpL7/8oidPnlRV1Xnz5mXLBuLrFBYiUgTL4B+dQgH9lj0V5nA4HH7Em4JqD3AzFkMyDXP7ScmRI3DddXDxxRZs6APpjU6825ITEQFt29ry8MOQmAgrV8KcObbMng3jxp05tkkTcxTzLo0aQcHUZM8CJUqUSApYBKhRo0a22vNJgYhIf+BdLHQneXymAlWzJYHD4XAEgtLAR8CNwC1Y0EHKxEzR0XDnnfDSS7B2LdSunWGzqaU58dpFfCEszJREkyZ2aVWIi4M//oBFi2yZMAFGjLDjCxWCpk2hWTNTJg0b2mvFihYfmR1S2k8yi68jkJeBa1R1erau5nA4HDnJDcB6LIq9NpCam88998Brr8Hrr8P77+eoeGBKoHp1W665xrapmi3Fq1AWLYJJkywbi5eYmDPKpFEjqF/fkkRWq+a/EUtG+KpATmLZaBwOhyO0+A+WGvYpoCbQN8X+8uUtx/tnn8HTT4MnAjyYiJgyqFXLZti87Npl01+rVtnrypVnKxYRqFLF0tUnX2rUgMqVzRMsIsI/cvqqQIYBr4vIM6qamZhPh8PhCC4CjMA8tG7CJt07pDjmoYdg3jxz673iipyW0GfKlrUl5WzZrl2wZo15dq1ff2aZOhW2b//3sSLWRsWKtmQHXxXI31gmmjvlzKSbAKouI6/D4cjtFAQmAucDPbEQ6HrJ9terByGQ/TYtvIqlffuz9x09ailX1q+Hbdv+vWS3QKKvCmQMMBoYT5bLuzgcDkcQKYGlgm0LXAssD644OUWRImYradgw9f3ZMcT7qkBKAU+qBiIw3+FwOHKImsB3QCJnl8v7+GOzgWzY4D8jQR7H10j0z4B+gRTE4XA4coQ22Cgk5T/vAgVsTmdTZitW5V98VSBtgI9FZI2IzE6+BFI4h8PhCAg/YxPzyfEG1W3YkNPShCy+TmF95Fn8johsBA4DCcBpVW0lIiUxe0t1YCPQW1X3B+L6DocjH/IJVtEo+byKUyCZxicFoqqBLhzVOYV78GPADFV9SUQe87x/NMAyOByO/MKbWFm85FSqZNNYToH4TLoKREQuzKgBVZ3pP3GSuBLo5FkfhQUxOgXicDj8Q2oZPMLDYdAgn9KZOAxJz7FKRDJSxaqqNbMlgF1jP+YT8aGqjhCRA6paPNkx+1W1RCrn3gbcBlCmTJlzJkyYkB1RcjXx8fFER0dnfGCI4voX2oRi/6qMr0KBQwXYcGv6P3Oh2LfM0Llz5z9UNb3qKWmSrgLJCUSkoqpuE5GywHTgbmCyLwokOfXq1dM1a9YEVtggMmvWLDp5KqflRVz/QpuQ7N9AzKV3F/92J0pMtIyHHkKyb5lARLKsQHz1wgoYqrrN87oLK1LVBtgpIhUAPK+7giehw+HIk1yIFZ5KHoD+yCNmC3H4RFAViIhEiUhR7zpwCfY4JwMDPIcNAL4NjoQOhyPP4s0nldyKW6QI7NwJp04FQ6KQI9gjkHLAXBFZBvwOfK+qPwIvAReLyD/AxZ73DofD4T+qYCnekyuQ8uUtl/ru3UESKrTwuSJhIFDV9UCzVLbvBbrkvEQOhyNf0RmLODuN/Rp6U7nv2pX9VLX5gGCPQBwOhyN4XAgcApZ43pfw+OocOBAceUIMp0AcDkf+xWsHifW81qgBd91lVZccGeIUiMPhyL+UAxpyxg5SvTq88w40aBA8mUKIoNpAHA6HI+jcwL8DBU6ehIQEKFw4WBKFDG4E4nA48jf/Ad7yrCcmQmQkvOQcP33BKRCHw+FQYB8WgV6sGOx3yb99wU1hORwOx0WYEpmJeWI5LyyfcArE4XA4bsEUCEDx4m4E4iNOgTgcDsf1ydaLFoXDh4MmSijhFIjD4XCABRNGYzVBEhODLU1I4BSIw+FwgKVyvQb4YFCwJQkZnBeWw+FwAFQAtgPx8bB9e7ClCQmcAnE4HA44o0AefhianZXj1ZEKToE4HA4HnFEgUVFw5EiwpQkJnAJxOBwOMAWyAygcBUePOkO6DzgF4nA4HADlsbogUtLeHz8eTGlCAqdAHA6HA6BUihU3jZUhToE4HA4HnFEgtdrA66+7bLw+4OJAHA6HA84okFJ1YUDdoIoSKrgRiMPhcADUBcYC9Y/BX3+5KSwfcArE4XA4AIpjxaU2z7eKhAsXBlmg3I9TIA6Hw+FlLrDTM5d19GhQRQkFnA3E4XA4vFwNdKho6ydPBlWUUMApEIfD4fDyLXBoP0wETpwItjS5HjeF5XA4HF7OA2qJrbsRSIa4EYjD4XB4mQnsrggffght2wZbmlyPUyAOh8Ph5S0grggsvS3YkoQEbgrL4XA4vBQDDiksWgTbtgVbmlyPUyAOh8PhpRhwCGjdGsaMCbY0uR6nQBwOh8OLV4GAM6L7gFMgDofD4aUYcEpACjs3Xh8QVQ22DH5BRA4Da4ItRwApDewJthABxPUvtMnL/cvLfQOop6pFs3JiXvLCWqOqrYItRKAQkUWuf6GL61/okpf7Bta/rJ7rprAcDofDkSWcAnE4HA5HlshLCmREsAUIMK5/oY3rX+iSl/sG2ehfnjGiOxwOhyNnyUsjEIfD4XDkICGrQETkFRH5S0SWi8gkESmexnEbReRPEVmaHW+DnCYT/btMRNaIyFoReSyHxcwyInKtiKwUkUQRSdPDJYSfn6/9C7nnJyIlRWS6iPzjeS2RxnEh9ewyehZivO3Zv1xEWgZDzqziQ/86ichBz/NaKiJPZtioqobkAlwCFPCs/w/4XxrHbQRKB1veQPQPCAfWATWBgsAyoGGwZfexfw2AesAsoFU6x4Xq88uwf6H6/ICXgcc864/lhe+eL88C6ApMBQRoCywIttx+7l8n4LvMtBuyIxBVnaaqpz1v5wOVgymPv/Gxf22Ataq6XlVPAuOAK3NKxuygqqtVNc8GfvrYv1B9flcCozzro4CewRPFb/jyLK4ERqsxHyguIhVyWtAsEpDPWsgqkBTchP0zSA0FponIHyISqjma0+pfJWBzsvdbPNvyEnnh+aVFqD6/cqq6HcDzWjaN40Lp2fnyLEL1eYHvsp8nIstEZKqINMqo0VwdiS4iPwPlU9n1H1X91nPMf4DTwNg0mmmnqttEpCwwXUT+UtXZgZE4c/ihf5LKtlzjVudL/3wgpJ9fRk2ksi1XPL/0+paJZnLts0sFX55Frn1ePuCL7IuBaqoaLyJdgW+AOuk1mqsViKpelN5+ERkAdAO6qGcSL5U2tnled4nIJGwolys+xH7o3xagSrL3lYFcU8Qgo/752EbIPj8fyLXPL72+ichOEamgqts9Uzi70mgj1z67VPDlWeTa5+UDGcquqoeSrf8gIu+LSGlVTTMPWMhOYYnIZcCjQA9VPZrGMVEiUtS7jhmmV+SclFnHl/4BC4E6IlJDRAoCfYDJOSVjoAnl5+cjofr8JgMDPOsDgLNGWyH47Hx5FpOB/h5vrLbAQe9UXgiQYf9EpLyIiGe9DaYf9qbbarC9A7LhVbAWm9Nb6lk+8GyvCPzgWa+JeRssA1ZiUwtBl91f/fO87wr8jXlYhFL/rsL+FZ0AdgI/5bHnl2H/QvX5AaWAGcA/nteSeeHZpfYsgMHAYM+6AO959v9JOt6DuXHxoX93eZ7VMsxx5/yM2nSR6A6Hw+HIEiE7heVwOByO4OIUiMPhcDiyhFMgDofD4cgSToE4HA6HI0s4BeJwOByOLOEUiMPhcDiyhFMgDofD4cgSToE48j2euhXZTruSheu+KCL3pbHPZ5lE5HdfEt85HP7GKRCHIwiISBmgP/ChH5p7FXjWD+04HJnCKRCHIzgMxNJ+HPNDW5OBziFUm8KRR3AKxOFIhog0EJFZInLAU5K2R7J9LUVkiYgcFpEvRWS8iDyfxUtdDvzio0z1RWSDiPRJbb+qHgf+wBIWOhw5hlMgDocHEYkApgDTsCJJdwNjRaSeJ4PpJGAkUBL4PyxhYlZpAmRYkdFTd3sacLeqjkvn0NVAs2zI43BkGqdAHI4ztAWigZdU9aSqzgS+A6737CsAvK2qp1T1a+B374kiEuMxZseLSONk218QkTki8pWIFEl2reLA4QzkaY8ndbqqfpfBsYc9bTocOYZTIA7HGSoCm1U1Mdm2OKz0Z0Vgq/47fXXyEqFHgSuAr7wbPIqklqq2B37GShN72Q8UzUCewcBvqhrrg+xFgQM+HOdw+A2nQByOM2wDqohI8u9FVWArsB2o5C244yGpwptnVLI7RXvtOVPLfipwQbJ9y4G6GcgzGKgqIm/4IHsDrI6Dw5FjOAXicJxhAXAEeEREIkSkE9AdGAfMAxKAu0SkgIhciZVoTY8SwEHP+kHMduLlB6BjBucfBi4DOojIS2kdJCKFgHOA6Rm053D4FadAHA4PqnoS6IF5SO0B3gf6q+pfnn1XAzdjU0V9MfvIiXSa3A/EeNZjgH3J9o0GuopI4QxkOgBcDFwuIs+lcVgPYJZ6apA7HDlFgWAL4HAEG1Wtnmx9JWmMDFR1EdDc+15EFmBeW2kxF3gcGAVcCvyarK09IjIauB14MwOZ9pG+h9VDmGJzOHIUV9LW4fAREemIud7uAW4EPgBqqup2z/4fMAUTB3yoqiNF5EXM9rELG80cCYbsDkcgcArE4fAREbkNeA5z9V0HPK6q3wdXKocjeDgF4nA4HI4s4YzoDofD4cgSToE4HA6HI0s4BeJwOByOLOEUiMPhcDiyhFMgDofD4cgSToE4HA6HI0s4BeJwOByOLOEUiMPhcDiyxP8DLrxd7FgOEiUAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "vol_arr = [vol_cevB, vol_bsB, vol_dem, vol_dem2]\n",
    "K_arr = [strike, strike, strike_low, strike_low]\n",
    "\n",
    "labels = ['CEV-B', 'BS-B', 'DMHJ', 'DMHJ-2']\n",
    "\n",
    "ls = ['-', ':', '--', '-.']\n",
    "colors = ['b', 'gray', 'r', 'magenta']\n",
    "\n",
    "for k in np.arange(4):  # len(vol_arr)\n",
    "    plt.plot(np.log10(K_arr[k]/fwd), vol_arr[k]*100, label=labels[k], color=colors[k], linestyle=ls[k])\n",
    "\n",
    "plt.plot(np.log10(strike_exact/fwd), vol_exact*100, 'kx', label = 'Exact')\n",
    "\n",
    "plt.xlim([-2.5,0.5])\n",
    "plt.ylim([min(vol_cevB)*100-50, max(vol_cevB)*100+50])\n",
    "plt.ylabel('Implied BS volatility (%)', fontsize=12)\n",
    "plt.xlabel(r'$\\log_{10}$( k )', fontsize=12)\n",
    "plt.legend(fontsize=12, loc=1)\n",
    "\n",
    "abc = 'abc'[param_set-1]\n",
    "plt.title(f'({abc}) Set {param_set} ($M_T={m0_cevB:0.4f}$ / {m0_exact:0.4f})', fontsize=16)\n",
    "\n",
    "plt.grid()\n",
    "#plt.savefig('../Latex-Etc/images/Set3-DeMarco.pdf', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 1"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Select [0, 1, 2, 3, 4, 5]\n",
    "ind_exact = 0  # 0:base, 1:fwd, 2:sigma, 3:beta, 4:vov\n",
    "\n",
    "subfig_title = [\n",
    "    r'(a) Base parameter', \n",
    "    r'(b) $F_0 = 0.2$', \n",
    "    r'(c) $\\sigma_0 = 0.1$', \n",
    "    r'(d) $\\beta$ = 0.2', \n",
    "    r'(e) $\\nu$ = 0.4'\n",
    "][ind_exact]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = {\"sigma\": 0.2, \"vov\": 0.1, \"rho\": 0, \"beta\":0.1} # base\n",
    "\n",
    "texp_exact = np.arange(1,11)/10\n",
    "log_m_exact = np.array([\n",
    "    [-3.36585222, -1.96687272, -1.46047053, -1.1908933 , -1.02056457, -0.90185897, -0.81369244, -0.74521469, -0.69023839, -0.64496119],\n",
    "    [-9.40618218, -5.18722753, -3.71849273, -2.95858225, -2.4889435 , -2.16746276, -1.93224571, -1.75188663, -1.60869713, -1.49192629],\n",
    "    [-10.5886564, -5.80757216, -4.14740495, -3.29059218, -2.76218756, -2.40113409, -2.13737701, -1.93541265, -1.7752668, -1.64481175],\n",
    "    [-5.68807177, -3.15635005, -2.26897624, -1.80741883, -1.52102876, -1.3243837 , -1.18015626, -1.06935131, -0.98124325, -0.90929863],\n",
    "    [-3.14610095, -1.87742179, -1.41669492, -1.17103613, -1.01570233, -0.90742306, -0.82701231, -0.76458422, -0.71449569, -0.67327591]\n",
    "])\n",
    "\n",
    "params_all = [\n",
    "    {\"sigma\": 0.2, \"vov\": 0.1, \"rho\": -0.5, \"beta\":0.1, \"fwd\":0.1}, # base\n",
    "    {\"sigma\": 0.2, \"vov\": 0.1, \"rho\": -0.5, \"beta\":0.1, \"fwd\":0.2}, # fwd\n",
    "    {\"sigma\": 0.1, \"vov\": 0.1, \"rho\": -0.5, \"beta\":0.1, \"fwd\":0.1}, # sigma\n",
    "    {\"sigma\": 0.2, \"vov\": 0.1, \"rho\": -0.5, \"beta\":0.2, \"fwd\":0.1}, # beta\n",
    "    {\"sigma\": 0.2, \"vov\": 0.4, \"rho\": -0.5, \"beta\":0.1, \"fwd\":0.1}, # vov\n",
    "]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [],
   "source": [
    "params = copy.copy(params_all[ind_exact])\n",
    "fwd = params[\"fwd\"]\n",
    "del params[\"fwd\"]\n",
    "\n",
    "m_cevA = pf.SabrChoiWu2021H(**params)\n",
    "m_cevB = pf.SabrChoiWu2021P(**params)\n",
    "\n",
    "texp = np.arange(0.001, 1.01, 0.02)\n",
    "\n",
    "m0_A = np.array([m_cevA.mass_zero(fwd, t1, log=True) for t1 in texp])\n",
    "m0_B = np.array([m_cevB.mass_zero(fwd, t1, log=True) for t1 in texp])\n",
    "T0 = m_cevB.mass_zero_t0(fwd, 1) # texp is not important"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "m0_arr = -np.array([m0_A, m0_B])*texp/T0\n",
    "m0_exact = -log_m_exact[ind_exact]*texp_exact/T0\n",
    "\n",
    "labels = ['CEV-A', 'CEV-B']\n",
    "ls = ['--', '-']\n",
    "colors = ['r', 'b']\n",
    "\n",
    "for k in np.arange(2):\n",
    "    plt.plot(texp, m0_arr[k], label=labels[k], color=colors[k], linestyle=ls[k])\n",
    "\n",
    "plt.plot(texp_exact, m0_exact, 'kx', label = 'FDM')\n",
    "\n",
    "if ind_exact == 0:\n",
    "    plt.ylabel(r'$-T\\; \\log\\;M_T\\;\\; /\\;\\; T_0$', fontsize=16)\n",
    "    plt.xlabel(r'$T$ (time-to-expiry)', fontsize=16)\n",
    "\n",
    "title_T0 = '  ($T_0 = {val:0.4f}$)'.format(val=-T0)\n",
    "plt.title(subfig_title + title_T0, fontsize=16)\n",
    "\n",
    "plt.legend(fontsize=14)\n",
    "plt.grid()\n",
    "#plt.savefig('../Latex-Etc/images/m0_{num}.pdf'.format(num=ind_exact), bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Figure 2"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "# Set 1\n",
    "param = {\"sigma\": 0.5, \"vov\": 0.4, \"rho\": 0.0, \"beta\":0.5}\n",
    "fwd = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [],
   "source": [
    "m_cev = pf.Cev(sigma=param['sigma'], beta=param['beta'])\n",
    "m_cevB = pf.SabrChoiWu2021P(**param)\n",
    "m_ln = pf.SabrUncorrChoiWu2021(**param)\n",
    "T0 = m_cevB.mass_zero_t0(spot=fwd, texp=1)\n",
    "\n",
    "m_mc = pf.SabrMcTimeDisc(**param)\n",
    "m_mc.set_num_params(n_path=10e4, dt=0.05, rn_seed=1234)\n",
    "\n",
    "tarr = np.arange(0, 3.001, 0.25) # Set1\n",
    "tarr[0] = 0.05\n",
    "mass0 = [m_ln.mass_zero(fwd, t, log=True) for t in tarr]\n",
    "mass1 = [m_cevB.mass_zero(fwd, t, log=True) for t in tarr]\n",
    "mass2 = [m_cev.mass_zero(fwd, t, log=True) for t in tarr]\n",
    "mass3 = [m_mc.mass_zero(fwd, t, log=True) for t in tarr]\n",
    "#print(mass0[0], mass1[0], mass2[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Figure 2(a)\n",
    "plt.plot(tarr, -tarr*(mass0)/T0, 'b--', label = 'GHJ-LN')\n",
    "plt.plot(tarr, -tarr*(mass2)/T0, 'r-.', label = 'YW')\n",
    "plt.plot(tarr, -tarr*(mass1)/T0, 'k-', label = 'CEV-B')\n",
    "plt.plot(tarr, -tarr*(mass3)/T0, 'kx', label = 'MC')\n",
    "\n",
    "plt.ylabel(r'$-T\\; \\log\\;M_T\\;\\; /\\;\\; T_0$', fontsize=16)\n",
    "plt.xlabel(r'$T$ (time-to-expiry)', fontsize=16)\n",
    "plt.grid()\n",
    "plt.legend(fontsize=12)\n",
    "\n",
    "#plt.savefig(f'../Latex-Etc/images/m0_Set1_log.pdf', bbox_inches='tight')\n",
    "#plt.savefig(f'../Latex-Etc/images/m0_Set1_log.png', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "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": [
    "# Figure 2(b)\n",
    "plt.plot(tarr, np.exp(mass0), 'b--', label = 'GHJ-LN')\n",
    "plt.plot(tarr, np.exp(mass2), 'r-.', label = 'YW')\n",
    "plt.plot(tarr, np.exp(mass1), 'k-', label = 'CEV-B')\n",
    "plt.plot(tarr, np.exp(mass3), 'kx', label = 'MC')\n",
    "\n",
    "plt.ylabel(r'$M_T$', fontsize=16)\n",
    "plt.xlabel(r'$T$ (time-to-expiry)', fontsize=16)\n",
    "plt.grid()\n",
    "plt.legend(fontsize=12)\n",
    "\n",
    "#plt.savefig(f'../Latex-Etc/images/m0_Set1_abs.pdf', bbox_inches='tight')\n",
    "#plt.savefig(f'../Latex-Etc/images/m0_Set1_abs.png', bbox_inches='tight')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## Table 5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [],
   "source": [
    "params0 = {\"sigma\": 0.1, \"vov\": 0.1, \"rho\": 0, \"beta\":0.1}\n",
    "fwd = 0.1\n",
    "texp = 0.5"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "-0.3 : 0.06219860721758867 -0.2 : 0.06048185906564118 -0.1 : 0.0587565151871829 "
     ]
    }
   ],
   "source": [
    "rho_arr = np.arange(-3, 0)/10\n",
    "params = params0.copy()\n",
    "mass_arr = list()\n",
    "for rho in rho_arr:\n",
    "    params['rho'] = rho\n",
    "    m = pf.SabrChoiWu2021P(**params)\n",
    "    mass = m.mass_zero(fwd, texp)\n",
    "    mass_arr.append(mass)\n",
    "    print(rho, ':', mass, end=' ')\n",
    "\n",
    "pd.Series(mass_arr, index=None).to_clipboard(excel=True)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [],
   "source": [
    "beta_arr = np.arange(1,5)/10\n",
    "mass_ln = []\n",
    "mass_mc = []\n",
    "mass_cevB = []\n",
    "mass_cev = []\n",
    "\n",
    "params = params0.copy()\n",
    "for beta in beta_arr:\n",
    "    params['beta'] = beta\n",
    "    m_ln = pf.SabrUncorrChoiWu2021(**params)\n",
    "    m_cev = pf.Cev(beta=beta, sigma=params['sigma'])\n",
    "    m_cevB = pf.SabrChoiWu2021P(**params)\n",
    "    m_mc = pf.SabrMcTimeDisc(**params)\n",
    "    m_mc.set_num_params(n_path=20e4, dt=0.05, rn_seed=1234)\n",
    "    \n",
    "    mass_ln.append(m_ln.mass_zero(fwd, texp))\n",
    "    mass_cev.append(m_cev.mass_zero(fwd, texp))\n",
    "    mass_cevB.append(m_cevB.mass_zero(fwd, texp))\n",
    "    mass_mc.append(m_mc.mass_zero(fwd, texp))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "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>0.1</th>\n",
       "      <th>0.2</th>\n",
       "      <th>0.3</th>\n",
       "      <th>0.4</th>\n",
       "    </tr>\n",
       "  </thead>\n",
       "  <tbody>\n",
       "    <tr>\n",
       "      <th>GHJ-LN</th>\n",
       "      <td>0.056572</td>\n",
       "      <td>0.007966</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>3.197258e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>MC</th>\n",
       "      <td>0.056567</td>\n",
       "      <td>0.007963</td>\n",
       "      <td>0.000150</td>\n",
       "      <td>3.223208e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>CEV-B</th>\n",
       "      <td>0.057023</td>\n",
       "      <td>0.008090</td>\n",
       "      <td>0.000155</td>\n",
       "      <td>3.477015e-08</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>YB (CEV)</th>\n",
       "      <td>0.056082</td>\n",
       "      <td>0.007636</td>\n",
       "      <td>0.000124</td>\n",
       "      <td>1.331990e-08</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "               0.1       0.2       0.3           0.4\n",
       "GHJ-LN    0.056572  0.007966  0.000150  3.197258e-08\n",
       "MC        0.056567  0.007963  0.000150  3.223208e-08\n",
       "CEV-B     0.057023  0.008090  0.000155  3.477015e-08\n",
       "YB (CEV)  0.056082  0.007636  0.000124  1.331990e-08"
      ]
     },
     "execution_count": 20,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pd.DataFrame(\n",
    "    [mass_ln, mass_mc, mass_cevB, mass_cev], index=['GHJ-LN', 'MC', 'CEV-B', 'YB (CEV)'],\n",
    "    columns=beta_arr\n",
    ")"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": null,
   "metadata": {},
   "outputs": [],
   "source": []
  }
 ],
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