capitulo_04.ipynb

{
 "cells": [
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.1 Ferramentas de Programação Matemática"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 1,
   "metadata": {},
   "outputs": [],
   "source": [
    "def minha_funcao(var_1, var_2): \n",
    "    resultado = var_1 + var_2 + 3\n",
    "    return resultado"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6"
      ]
     },
     "execution_count": 2,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "minha_funcao(1, 2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 3,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import log, sqrt, exp\n",
    "from scipy import stats\n",
    "def black_scholes(S0, K, T, r, sigma):\n",
    "    d1 = (log(S0 / K) + (r + (sigma ** 2)/2) * T) / (sigma * sqrt(T))\n",
    "    d2 = d1 - sigma * sqrt(T)\n",
    "    return (S0 * stats.norm.cdf(d1, 0.0, 1.0) - K * exp(-r * T) * stats.norm.cdf(d2, 0.0, 1.0))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "10.450583572185565"
      ]
     },
     "execution_count": 4,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "black_scholes(100, 100, 1, 0.05, 0.20)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.2 Árvore binomial"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[2, 4, 6, 8, 10]"
      ]
     },
     "execution_count": 5,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "[x*2 for x in [1, 2, 3, 4, 5]]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 6,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "[100.76, 86.0, 94.63999999999999, 111.2]"
      ]
     },
     "execution_count": 6,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "celsius = [38.2, 30, 34.8, 44]\n",
    "fahrenheit = [ 9/5*x + 32 for x in celsius ]\n",
    "fahrenheit"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 7,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import exp, sqrt \n",
    "def arvore_binomial_simplificada(S0, K, T, r, sigma, N=300): \n",
    "    # Define: delta t, u, d, a, p e um_menos_p. \n",
    "    delta_t = T / N\n",
    "    u = exp(sigma * sqrt(delta_t))\n",
    "    d = 1.0 / u\n",
    "    a = exp(r * delta_t)\n",
    "    p = (a - d) / (u - d)\n",
    "    um_menos_p = 1.0 - p\n",
    "    \n",
    "    # Cria a estrutura da árvore com todos os valores iguais a zero. \n",
    "    arv_b = [[0.0 for j in range(i + 1)] for i in range(N + 1)]\n",
    "    \n",
    "    # Cálcula o valor dos últimos nós da árvore binomial. \n",
    "    for j in range(N + 1):\n",
    "        arv_b[N][j] = max(S0 * u**j * d**(N - j) - K, 0.0)\n",
    "    \n",
    "    # Calcula os nós intermediários, dos últimos para o nó raiz.\n",
    "    for i in reversed(range(N)): \n",
    "        for j in range(i+1): \n",
    "            arv_b[i][j] = exp(-r * delta_t) * (p * arv_b[i+1][j + 1] +  um_menos_p * arv_b[i+1][j])\n",
    "    \n",
    "    # O valor do nó inicial da árvore é o valor da opção.\n",
    "    return arv_b[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.9628409345029771"
      ]
     },
     "execution_count": 8,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arvore_binomial_simplificada(S0=8.50, K=10, T=1.0, r=0.10, sigma=0.35)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 9,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "1.0208463755398038"
      ]
     },
     "execution_count": 9,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arvore_binomial_simplificada(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, N=4)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.3 Árvore completa / Convergência com Black-Scholes"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 10,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import exp, sqrt\n",
    "def arvore_binomial_completa(S0, K, T, r, sigma, q, call_put_flag='c', N=300): \n",
    "    # Define: delta_t, u, d, a, p e um_menos_p.\n",
    "    delta_t = T / N\n",
    "    u = exp(sigma * sqrt(delta_t))\n",
    "    d = 1.0 / u\n",
    "    a = exp((r - q) * delta_t)\n",
    "    p = (a - d) / (u - d)\n",
    "    um_menos_p = 1.0 - p\n",
    "    \n",
    "    # Cria a estrutura da árvore com todos os valores iguais a zero.\n",
    "    arv_b = [[0.0 for j in range(i + 1)] for i in range(N + 1)]\n",
    "    \n",
    "    # Cálcula o valor dos últimos nós da árvore binomial.\n",
    "    for j in range(N + 1):\n",
    "        if call_put_flag == 'c': \n",
    "            arv_b[N][j] = max(S0 * u**j * d**(N - j) - K, 0.0)\n",
    "        else:\n",
    "            arv_b[N][j] = max(K - S0 * u**j * d**(N - j), 0.0)\n",
    "    \n",
    "    # Calcula os nós intermediários, dos últimos para o nó raiz.\n",
    "    for i in reversed(range(N)):\n",
    "        for j in range(i + 1):\n",
    "            valor_acao = S0 * d**i * u**(2*j)\n",
    "            if call_put_flag == 'c':\n",
    "                valor_imediato = max(valor_acao - K, 0) \n",
    "            else:\n",
    "                valor_imediato = max(K - valor_acao, 0) \n",
    "            valor_esperado = exp(-r * delta_t)*(p*arv_b[i + 1][j + 1] + um_menos_p * arv_b[i + 1][j])\n",
    "            arv_b[i][j] = max(valor_imediato, valor_esperado)\n",
    "    \n",
    "    # O valor do nó inicial da árvore é o valor da opção.\n",
    "    return arv_b[0][0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 11,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "6.08772261436826"
      ]
     },
     "execution_count": 11,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "arvore_binomial_completa(100, 100, 1, 0.05, 0.20, 0, call_put_flag='p')"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.4 Entendendo o método de simulação de Monte Carlo"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 12,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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rpT6olDqplDrp8/k2sQx4eWiaI2012G0qlb8shYgY4Ip/eVTssNtorXUXfUQM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\ngg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xa981c50>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "%matplotlib inline \n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "f = lambda x: 12 * np.sin(12 * x) + 20 * np.cos(4 * x) + 3 * np.exp(x/3) + 30\n",
    "x = np.linspace(0, 10, 1000)\n",
    "_ = plt.plot(x,f(x))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [],
   "source": [
    "largura = 10\n",
    "altura = 140\n",
    "numero_simulacao = 50000\n",
    "\n",
    "x_v = np.random.uniform(0, largura, numero_simulacao) \n",
    "y_v = np.random.uniform(0, altura, numero_simulacao)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 14,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "array([ 4.78447031,  0.97171625,  7.64658805, ...,  0.46628852,\n",
       "        5.88992171,  1.16843071])"
      ]
     },
     "execution_count": 14,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "x_v"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 15,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39062000000000002"
      ]
     },
     "execution_count": 15,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "pontos_abaixo_curva = y_v < f(x_v)\n",
    "proporcao_area_abaixo_fx = np.sum(pontos_abaixo_curva) / numero_simulacao\n",
    "proporcao_area_abaixo_fx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 16,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "546.86800000000005"
      ]
     },
     "execution_count": 16,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "area_total = largura * altura\n",
    "area_abaixo_fx = area_total * proporcao_area_abaixo_fx\n",
    "area_abaixo_fx"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 17,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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C1El9YXMvmx0HjiF/292u9un03ezfjJCKCm6Jnm3oO3jXxlK1VAK4/bpdro+r\nA5OcNholV4mijjOWRKTLk08+iT179vBiC2lnNhOSK5awe+gU8rfd7UkFM5VyxRKMvje7OoZc2bJE\nXgg2A42iQ4cO8aRLRETkodHRUUxOTuoOgwjdb/2llj9rVDCDsDd0nj1/xm1Yls1dOIfazPddHUOu\nLm2KeaUm2Qw0aiqVCk6fPs0r3EREMcALWkS08MJX2/48Vywhf+tHr5jRaVcFVWUxgE5emxhTcpyt\nMbMZaMQcP34c1WpVdxgUUJlMBkNDQygUCrpDISIFeEGLiOoLr3e8TWNGJ7l9J4QQKBQK+PznPw+j\nRclpVcUArLASvxVbYw5rdbWk7gCCqFKpYHp6WncYFGDVahWjo6O6wyAiIiKfNTblz/33L2BychJH\njx41LdG/tUpZGGyNuSdlhLa6GpMcE8PDw7pDICIiIiIfWS33PHfhHGYevQ9ydQkATBMcY/tO9O4/\n4ksj0AbRvQ1y0d1sTuYdA5ti/t9/cVd0q6sJIT4vhPiREOLbTd/rE0L8tRDiu+v/vWr9+0II8R+E\nEC8KIf5eCPELXgbvFZaOJiIiijfu04obYbnc8+z5MxsJjhlj+07sHjrlW4KTWH+pqihXvfi9v9v0\n73PfueT6mLpY2ZPznwAc3PK9TwCYkFL+LICJ9X8DwC0Afnb9axBAKNfzsHQ0ERG1kkhwO2schP15\nDnq540BJdiF/28csJyWdign4WWwAAOoSSBkCuWIJiRZ7g6yKStEBwEKSI6U8D2Bmy7d/DcDp9f8/\nDeD2pu+fkWu+DqBXCPEmVcH65dAh9x1uiYgovFoNcIUQqNfrPkdDOpgtQQoNkUDfwbssL7+Ku0Qq\nbWvWpVMxAT+LDTSs1NaKp2xtaGpXVIoOAM6rq/2UlPIH6///jwB+av3/dwFoLtD98vr3QuXs2bO6\nQyAiIo1KpRIymcwV32cVNgo6kexC/taPrlUBu3kQEIY/9ysEBgYGTN83QVdfeB1zF85Zvn3v/iMt\nZ8p0Fxtwk2BFqegAoKCEtFw749s+6wshBoUQTwkhnrp0KVjr/diUjIgo3v7mb/4G1WqV+zIoVET3\nNvQdvGtjVmKtr8tHfLnvbDaLJ554Aj09Pcjn877cp0p2mnY2ykgb23eufWO9Qaixfeemx1+Hdg1N\n29kauxDhLjoAOK+u9kMhxJuklD9YX472o/XvXwTw5qbb7V7/3hWklGMAxgDg+uuvD9SlMcMwwj1N\nTURErjQ2ynyvAAAgAElEQVQ+AzhzQ2Eia8tXDLBzxRKmH/mM5/c9N7e2TGp6ehqZTAbZbBbz8/Oe\n368qtcv2LrjniiWtyUwrWwsHWLW1EpyUwJ998yKuL/SFNtFxOpPzZQBH1///KIA/b/r+kfUqa+8C\n8OOmZW2hwQSHiIhIvb179+oOIdpWlvDqYyd1R4FqtRqqBAfAxmxM2DktemA2k7WwUsO9j73gNiRt\nrJSQ/iKArwG4RgjxshDigwD+EMAvCyG+C+Dm9X8DwFkA3wPwIoD/COCYJ1F7zDD8Wb9KREQUJ889\n95zuECJv/tlHdYcQTjIaBUWc7slplRyFubpax+VqUsr3t/jRgMltJYDfdhuUbpzJITLHpZxERAEX\nkcG63zb214Rc7/4jmxqVWtUqOYpjdbVIKxQKukMgCpx0Os0Eh4go6CKy7MpXwtBaEU2lK4oiWNTq\n79+TZ5ITKSMjI6EsgUjklXw+j9XVVd1hEBFFksoqftlrt/Zvp44S0aqimCuWsHvoFAoff8TW75j5\n23+YwcNPm9YQCzwmOSbK5TLGxsZ0h0EUKGyASETkDVVV/NL912LHgSu3Q0dlKZZnaqu2SkiHSaLH\nXUNYCYS2+ACTnBbK5bLuEIgCY3p6WncIRESRpWompzb7iun32zWvpDVOq5IF3VUDgx1v0ykRCmvx\nASY5LVQqFd0hEBERUQyomslpNVDfvE9DrH9RM6dVyYIuVyxBdLdJYoxkx0QorMUHmOS0MDw8rDsE\naoNdyInCI5/PI51O6w6DKPLaDdQb+zTyt30Ma4uQqEEkuyJTeMBM382DpjN5iZ5tyN9yvG1T056U\ngXsOXONleJ7pWEI6rqampnSHQG1IKZHP57mMiijgGsnN8vKy5kiIos/KQH3mce45bmZs34ne/Ufa\nDvTDrvG3zZ4/g9rlV2Fs32HpbxYA/uDX34nbr9vlQ5TqMclpoa+vjwPogJuensbQ0BBGR0d1h0JE\nLSwvL/NcSuSDdP+1HQetcxfOQS6+7lNEwSe6t2H30CndYfgiVyzZSuRSCYF7/9W1oU1wAC5Xo5C7\n//77dYdAREQxZhiG7hAAAMsXL2Duwrm2t4lqBTGnmPCZ29XbE/oEB2CS09LMzIzuEMgCVZs1iYiI\nnAhMk2QLZZCjWkGM1LrnwDWhT3AAJjkt9ff36w6BiIiIyLJOSUxUK4g55baHTFSFtS/OVkxyWhgZ\nGWEFLyIiIgqNTklM7/4jgAjG8jrtLJROjquw9sXZiklOC+VyGXfeeScTHSIiIgqFTtXVcsUSstce\n8CmaYOtUOjnOEkLg4acv6g7DNSY5bdx4443o6+vTHQYRERFRR1YG7Yvf+zsfIgk4XsBuqyYlPvml\nb4U+0WEJ6RYqlQoGBwdRrVZ1h0KKCSFYsICIiGKJxQcASImZR+8DYC0xjKOFlRrufuhZAAhtEQLO\n5LQwPDzMBCeimOAQEVHUGNt3Wrwdiw8AgFxdYkntDsI+o8Mkp4WpqSndIRAREfmK+1DDSSS7Ou7H\naeh+6y8puc+BgQHk83klx9KldvmS7hACb2GlFtpqa0xyWmAJaSIiihvOdIeP6N6GvoN3WV52pWJP\njhACTzzxBHK5HIaGhlAoFFwfUwvBYbAVYa22xme3hZGREd0hEBERkQa5XC40sxRC2NtXomJPjpQS\nUkpMTk5idHQUc3NzoXm8NpF13RGEwtW9PbpDcIRJTgvlchm5XE53GBQghsHeAkREcTA/P4/p6Wnd\nYVhSX3gdcxfOWb69F3typqenQ/N4NbO6jynu7jlwje4QHGGS08b999+PdDqtOwwKiFqtpjsEIgqw\noaEhjI+P6w6DFAjbsj07G+hV7cmJAqv7mOKstycV2upqLCHdRrlcBgAcPXqUA1wiImqpMdM7PDys\nORKKIztL0Ngn5yfaLfMTAMKV6nrj079a1B2CY5zJ6aBcLjPBISIKIT+XmNZqNdx///2YnJz07T6J\nGuwsQWOfnDXZfYfa/pwJDpBNG6GdxQGY5FjCvRgUFV1dXbpDIPJNb2+vr/cXtiVOFA3N5aOz6c7j\nldj3yREJZPcdwo4Dx3RHEnjV5XBf5GeSYwFnciiMtva7MAwDy8vLmqIh8l8YN0IT2ZV5xwByxRKy\nacNSot27/whgxHS3ghDI3/pRJjgWhbWqWgOTnBYqlQpyuRwbo1EoZTIZ3HTTTZtmIWu1Gq80hwiL\nnhCRFY09NvPLNVRXOpdEzhVLEKlwD14dk9JWkYY4SxkitFXVGmKayrdXqVRw5MgR1Ousn07hVK1W\nMTExoTsMcoGzbkSdZbNZzM/P6w5DKyd7bOTinAeRhEPt8iXdIYRDBK6JcibHxPDwMBMcohDgTCtR\nfOXzeTzwwAPhbEKpkJM9NrHfl0MdrdQl7n3sBd1huMIkx8TU1JTuEIjIAiY5RPE1PT2Nw4cPx37v\nlZO+N737jwAivkWV7DRPjbOLswu6Q3CFSY6J/v5+3SEQkQWccSWiuHPS9yZXLCF77QEPonHHr2q2\nM4+P+XI/UfBvH/6W7hAcY5Jj4tCh9rXTiYiIiLyUz+ctFSBx2vfGj6agdmfb/apmKxdf9+V+oqDy\n9Sk8/PRF3WE4wiTHxEMPPaQ7BCIiIoqx973vfZYG/U731/jRFJQVPcNPAqHdm8Mkx0Tc1/cSERGR\nXmfOnOmY5DQ3ArUr7sUHrOzLEetfcfdKSPfmMMkhsiCdTse+gg9RJ3yPEKnTqTR2omcb+g7ehVyx\n5Oj4TpOjoEqlUrZu36lfjgDw2d/Y5yKi6AhrU1AmOSb4Qb3Z+Pg4hoaGdIehlRCCM3xEHfA9QuQf\nkep2nOAAcPW7QbSysmLr9p2W60kAdz/0bBTaxbhW+rmdukNwhEmOiRMnTti+IhBViUQC5XIZY2Px\nqETSqrLL0tKSz5EQERG1pmJPjbE9nINXFaws16txTxEA4Nx3wtlAlUmOiXK5jFOnTiGR4MOTyWSQ\nSCR8q3iiW1z+TiIiCjcVe2rW+uXEcNeJMCK3XM9L3JMTMeVyGR/+8Id1h6Hd3Nwcq6MQEREFjIpB\neq5YgujKKYgmPET3NuRv/Ujklut5Kax7cpK6AwiqSqWCBx98UHcYREShkkgk2KSVyAeqBulycU7J\ncRoMwwj0qoj+41/UHUKo9KQM3HPgGt1hOMKZnBaOHz+O5eVl3WEQEYVKT08Pl/oGnBACmUxGdxjk\ngsq9NKpKSWcyGYyPj+P06dNKjucVK6Wj4y6bNiAA7OrtwR/8+jtx+3W7dIfkCD+JWmCVIKJwyefz\nLBgSAPPz85zJCTgpJXp6wrn8hNz1xjGzti/H/XDw6NGjKJfLGB4eVhCVd16biEchJTfml2u4urcH\n9xy4JrQJDsAkh+gKwuImTF6tDo58Po/p6WnbJUSJ4sryhTyDq9qDxk1vHDO5YglIur9AdPr0aVQq\nFUxNTSmIyjv1hdd1hxAKF2cX8MkvfQsPP31RdyiOcZRmolKp6A6BNLJaaCGZTLYsOU3+4swrkTfy\ntxyPdZnhIPJkw/yK+zYJ1WoVhw8fZrGiCFlYqeHex17QHYZjTHJMBH2qlYJheXkZUkpks9mN73F2\nh6izvXv36g6BrBAJ5Iol9O4/ApHs0h0NreOeEndE9zbdIYTKxZCWjwaY5JianJzUHQKFRL1ex/z8\nPIC1BOenf/qnNUdEFGxCCPze7/2e5WWhpJFc21uVK5bQd/AuzugExOz5M7pDCC8h0HfzoO4oQiUR\n4lM1kxwTXIJETtTrdbzyyiu6wyAKNCklDh8+rDsMsqD5ineuWMLuoVNAKlozOuPj48jn87rDsKV2\n+VWlx4vTzFD6zT/P/jg21SVCuy+HSY6JINd3JyKKAq7bDz7TybaVaLVWGB4exokTJ1AoFHSHYpmq\nks8NcZoZWp56NlZJnSph3ZfjKskRQnxUCHFBCPFtIcQXhRDdQoi3CCG+IYR4UQjxJ0KItKpg/RK2\nqzpERESq1ReubBKpeoCt2+TkJO644w68+qra2REvqSwfDaifGQq6OCV1qoR1X47jJEcIsQvA7wC4\nXkr5DgAGgN8E8H8D+KyU8m0AXgPwQRWB+mlxcVF3CERERFqZJTS9+49Erqz08vLyxt7KMFC93Cpq\niWsntcuXdIcQOkZI91C6Xa6WBNAjhEgCyAD4AYCbAPzp+s9PA7jd5X34LkwnOyIKJu7to3ATrWcM\n6lxqGCWxq56noPGpU2FNFmohXV7s+JmWUl4E8P8AmMJacvNjAN8EMCulXF2/2csAwtsqlagJB61k\nB/f2UZglenKmMwaz588Akq9tbTxIRhrV87w4thueVWBcrxqoQ1iThV29PbpDcMTNcrWrAPwagLcA\nuBpAFsBBG78/KIR4Sgjx1KVLwZo65J4cMsNBKxHFhdl+HCB++zcCR9Y82TifK5aAWjCKSgghMD4+\nji984QsoFAoQQii9yMhS6PaVfi6cj5mbObubAfwvKeUlKeUKgC8BuBFA7/ryNQDYDcC07pyUckxK\neb2U8vqdO4P14J04cUJ3CERkEfutEKmX6MmZfj8u+ze6u7t1h2CuturJxvm5C+eAgMwySClx9OhR\nAMBLL72Eer2Oel3d7Ivqwg1xcO47wZqMsMpNkjMF4F1CiIxYG2UMAHgOwDkA/3L9NkcB/Lm7EP1X\nLpfR1RWsaVvSI5vN6g6BOmApYgqCdDp0hUTbavW2issAcWlpSclxRPc2JHq2db6hDV7MpqlMnFR8\nbtZqNRw+fBjFYhF79uxRdp5P9GxjnxwHXolbdTUp5TewVmDgfwL41vqxxgB8HMDHhBAvAsgDeFBB\nnL5bWVnRHQJplkql+DogIkuWl4Ox1EcVuWi+XC0sA8R8Po+BgQHHv69iUC2SXei7eRBv/p0vIn/b\n3a6P1+DFbFpQlyE+99xzmJycVHIskezCVQODSo4VN1eHdE+OqzqQUspPAfjUlm9/D8A/cXPcIFA5\nNUrhxASHiOIq7MvSfvzjH+OZZ57Rdv/J7Tvxhv1HNpLCXLGE2fNnlJQv9mI2zdi+Q1lp5SBWqN35\npl1I/tN/jfQ1/1x3KKEU1j050Sp2r5BhGNxoTkREsSOSXaFflra6uorp6Wlf7zORSOB3/t0JPLr4\nNiysXDl+6N1/BNOP/BEA57NEotub5Va9+49g+iufi2zlvJn5ZfSu1hGtRaX+ieOenEgbHPRnSrOr\nq4sbp10QQrAaHhGRMgJ9B+8KzbK0IKnXJb4891bTBGeDmyphwkDfzd6MTXLFEhLdGU+OHQS1y5cw\n8+h9nlSmi4PY7cmJupMnT2Lv3r2e38/S0hI3TrsgpcSJEycwNDSkOxQiogiQnROcFAvzmDG272jb\nB2X2/Bmgttry550kujOeJp+tyoZHhVxd8qQyXQKAkYj2xeqw7slhktNCpVLBCy+8oDsMsuDDH/4w\nzp49C4DlhIMsatWniCLJQjf4/IG7fAgkfOTKYsuZgqsyKdRed7e53+skpFXZ8CjxosBCHUCtHt2L\n1QLAPQeu0R2GI0xyTFQqFQwODnJPTkjMz89vVF+RUiptGkZqGIaBD37wgygUCrpDIaJ2LHSDzxVL\nSquFRUV94fWWS6Jeq67A2OaumIPXxSDisKgk7AU1/CYAlN/Vj9uv26U7FEeY5JgYHh5GtVrVHQY5\nxOQ0eGq1Gk6fPo1Dhw5xRofIQ7mcu6vxVrvBc8+OuXZLonr3H4FIOl/q53UxiFZlw8Oiq6urbY+e\nKBTU8Ntnf2Mf/q/b36k7DMeY5JiYmprSHUJkFQoFFgqIqWq1ioceeoh70IjWCSEwNDSkdJnt0tKS\n8wsJRpKDQAVaLYnKFUvoO3jXeiIpYGzfaXlGzI8mlmGe5RBC4MEHH8QDDzyweYyx/t4ytu9kQQ0H\nwjqD08AS0ib6+/uVNZ+inxBC4NChQzhzRv3GPwoHv0u6EgWZlBJnz55VmvivrKwgm82iVquhVqsh\nkUhY7vuWfed7LQ8CWaWqtXbJQq5YuuIxXvjbcVRnftj2mH40sVwrcf0Zz+/HC1JKHDlyBIZhbOpx\nJ4w0kxsX9v3+X+HTv1oMbbLDmRwTIyMjyGSiW0pRFyklTp8+HchGYUREOkxOTirfRzg/P7+xbNdO\nY+vF7/2d5dtOP3af7bjiovutv2Tr9pkbD7cdc2T3HfJlkB72RKBer1/RxFuuLmH6K59lUu7Q7MIK\nPvmlb+Hhpy/qDsURJjkmyuUyxsbGuEnahmTS2qQg9zoREW0WlH2Etjreryx5F0jI2UkWgbUN/4ZJ\nWe5Ezzbkb7sbOw4cUxVaZ1GsUCrrvvfI6UlFZ3i9sFLDvY+Fs9pwdJ4FxcrlMl566SXdYYRGUD6k\nicKApc4pqHjF2z07ZYrnLpzDzKP34fUfv3bFz+TKssqwrPF6z6QQgPC/AqpXPXLM9PaksFaXLDrY\nDDRiKpUKtm3bpjuM0OBmciLr+H6hoPJrIBhldjbwz54/A7lqPivm58B8g4U+SW7kb/0Y8rd+xHIV\nP5W86JGzVU/KgBBrsx9RwmagEdLokzM3F+5yikRERHb4MRCMOjsV6jo93r4/Hxb6JLnRKLywe+gU\nsvsOeXpfW3ldPW5Xbw/+4NffideqK51vHCI9KYPNQKOEfXKIiBRLdSHRw9nxoLM6ENRxJT4s7Gzg\n7/R4+13W2cvndev7f/7ZRz27LzNel0ffk+/BR//kGU/vw2+NxI3V1SKEfXKIiNQSRhpXDQy6aoZI\nHrPRJ4f9dMzZTRLaNQjV0bzSbcPSdq5YpevxrNEmyS7Pq8c9+Q8ziNpC5PmlVd0huMIkx0R/f7/u\nEIiIIkUuvo5csYTMOwZ0h0ImRKob+VuOWx4I5ool35cbBZ2TpGRzg1Bs7InR1byyEQ88SHTkosYt\nAC32PVF7swsr+NifPBPaEtJsBmpiZGQEg4ODXLJGRKRY9Ttf1R0CmUj0bLM9oN5x4Bi6d799rWcO\nS0oj844BR0mJWYNQnXLFEmbPn7FXUtwCv5febeJxQYUoqwP49JcvhHLJGp91E+VyGUePHtUdBlHg\nsPQxOdVYjy8XX9ccCZlxusF98eXnmeCss9sfJ8i8KHiwdZbL131dfi6Ni6DZhXAWU2CS08LZs2d1\nh0AUOFzKSY6IBK4aGNQdBbXh5Cr73IVzmH+Gn5UNUapMJ7pzSo+X3XfoitkqL/f/bMVCGfHE5Wot\nsPgARZlhGI4auE5OTjr+XYqv7LUHNwY4iZ5tqC9wNidonGxwZ0+dzbQux1Jo7sI5yBV1zR/zt91t\nuhyv8T0vlsZt1f3WX/L0+BRMnMlpgVes4y2fz8Mw/O/K7IdMJoP3vOc9jn5XCMEEh2xrXsbDGZ3g\nEd329+MA0Zq5cM1GZbqgmz1/BqipqarVaa9Xrljy5XGL0lJCHXp7UrpDcIRJTgsjIyNIpcL5pJI7\niUQCMzMzkRzMG4aBo0eP4mtf+5rt3xVCQF5RAzR8kklOYPuteTCcK5YgutkvJ0j6bnaWeEZl5sI9\ngdw734vd179XdyBKKEtejaSlixp+zAgyIXfn079a1B2CI0xyWiiXy/jQhz7EjdYxVK/XIzGYN1Or\n1fDQQw/ZrhxYKBRcPyapVCoQCcbqarjr/ofR1sGw00E1BUtUZi7ck1i88NeoPvc3ugNRQknyKhKW\nS5L7kYAwIXcnjJXVACY5LVUqFTz44IORHexalclkmOhFzPT0tK3b53I5zM2572+wsrLCBCOGzHqH\n5IolbLuOPVaCwumVdM7K/cTqygq+9+gf6w5DCRUFAfK3ftTyEkjVRQ6uOL6GpqpBc/hdzrdghHkE\nyCSnhePHj2N5eVl3GFql0+nILFEi5+bm5mwnRmGVSPCUqJRItGxo2PfeY3jDL96qISjays2mb60N\nHgMmKkuirmhQ6sDiy89bvq2X11FF9zYtTVWD5tx3LuGqjLMtGGEeAfITvYW4DOraWV5exvz8vO4w\niHxTr7OXgioi2dXxau7cd/+HjxFRSy4aJXIZ0E9E6bFoFARwOqMz/8xZzF04Z+m29QXvEuVEujv2\nCQ4AXJxdwI9D2uvGDSY5RESknJWrp16XjSWLXDRKjPsyoA0iEbnHYvb8GchV541erS6DtJIc5nI5\n5PN52zFEZXZNhXqYp2QcYpLTQjab1R0CKcIlSEQ+szoz4GIGgdRxsywpVywhu4/7q0RXNnIzBm4T\nBKu/byU5rFarjlbYRGl2TReny9yCgJ8wLXR3d+sOgRThEiQin8k6Zh69r/NyFRczCKSO2xmIHQeO\nrSU6MU5ao7g3yW2CYPX3rSSHTj/Hoza75jcjIfCpXwln+WiASU5L3JNDROScXF3quFwl0cPKXEHg\ndgZi7sI5VL89EeukNYozBm4SBLsVzdzMJraS7r82crNrftvWlQxt+WiASU5LUe12T0Tkl07LVVi4\nUT8Vg0u3ezdCTxiRnDHIFUtAwn5vM2P7TtsVzVSUrW6W3XcIb3r/iLLjxVXYixUwyWkhit3uiYj8\n1OnqdhSX+ISNisF53Dd3i2QqsjMG2Z9/r63bG9t3YvfQKduPR65YQuYdA7Z+p10MOw4cU3KsuLu6\nt0d3CK4wyWmhUCjoDsF3bPpJQWds3+nJsgZSz8pylUSPt00AqTMVg3MVz6OTyllBIVcWdYfgmcXv\n/Z3l23Z197hKmqvf+arj320W96RbpXsOXKM7BFeY5LQwMjKCTCajOwxfseknNQti0tu7/4jyZQ2k\nntXlKvXVeDdc1k5RoYBWHx12ziEzMzNKYiG1rCYMxvad2P7Lv+0qaZaLrzv+3U2EsNyjh1o7/K7+\nUO/HAQD7iy1jolwuAwAOHz6sORIiPYKY9DZ/gE5/5bOx3ujcSSKR0FNZUCSwe+iUtduuxHgfRxAo\nev+0WnZo5xwSxPONVaI7ugU0jO07OvazEqlu9O4/gsze9/gTVCeyjulHPoPFl5/nsjUHrsqk8Klf\nKYY+wQE4k9PWk08+qTsEIseCOBPjRvMytVyxxF3rHSST9q9hKXnNMPEMDVVLP6NYWcyOvpsHdYfg\nGSsz53JlEdN/ecL17Inqaovzz5zljI4Dr1VX8Pt/cQEPP31RdyiuMclpY2xsTHcIRI69/e1v1x2C\nMmb7O+I+sOpkedneUrChoSH09LjfZGpnoBLlK+Bh0P3WX1JynDgvIU30bIts0QFg7YJS38G7Or9X\na6sdS8Z3ctWA+mTRbUzNenvC2xTTrteqK7jnT58NfaLDJKcNVlijMHvuued0h6CE6N5mur9D1QCN\ngGw2i7Nnz6Jarbo+Vn3FenLVd/MgIFiuXxc7m8rbaQyEY1cURAhPBuZBkyuWLM1Wud3wnyuW1prK\nKqSqCEEqIRCxxREdrdQk7n3sBd1huMIkpw32yokOIQSGhobWP4QFjO0710+mMTtrhVDfzYOmV0pV\nDdAImJ+fx+TkpJqD2eiXkiuWkL/1IxvvS/KXyipUuWJpbbZVUTGDUJBqqtOFgZUZERWz6zsOHEP+\ntruVvY5UVP5LAIBYm92Im1dmF3SH4EqMzkb2vec979EdAil04403YvfQKRQ+/hfo3X9krUM3uK8j\n6Fp9uHbaDEvBYrTIYXLF0sb7EkZ8loPYVfj4I8jfdrfSfQsql3zOXTiHmUfvi9merPh8flhJiN2U\nj956ekh0Zx0fq5mKrZt1rM1qxFFCiFAvWWOS00KlUsG5c9ywFhVSSnzwQ/8H5p9be0797tAdtSIA\nfmr54RqnK8YR0GmM8OpjJ4Fa/K6U2pErlvDm3/ni2pVuBVQ0Am3w+5waFHHZ2N4pIRbd7vYmNU4P\njWS5vqCmnDQbDrtTkxKf/NK3QpvocJRgolKp4Ld+67f0lF8lzywtLuC1/7Y2K+BnszAhBL7whS+s\nLZdbXwLJpZDWie4Wyw1idcU4PJwWE5h/9lHFkUSH6n0KgPoN83FtwKhyY3uQtSsuIZJdyirMqU6W\ndRWoMSJ0YXNhpRbavTlMckwMDw9jZYVXFKOoscTJzxOflBLDw8MAgN27d6/FwaIWlsma+Ub22G1y\nDgNhOBrszF04x6S1hey+Q1f0+nA9sDaSyjfMx7XaYVySuyuKS6zPpFtt/GuV0sfTSCqdrbSqtyeF\n9//TN0dql2FY9+awGaiJqakp3SGQV9ZPzL37j2Dm0ft8W14xOTmJ0dFRX+4rclo0jOzdfwTTf3kC\nqK36HBCZEgnkb/2I7cHOxl4OTYQQgW1EaWzfadrM0PVAsK7+7+3dfwTTj3xG+XGDLk7JXa5Y8rzQ\ngpXmo1blbzmupTDE7MIKxr++eRwpAPyzn+nD335vJpQt3q7udd9eQAfO5Jjo7+/XHQJ5Zf1qceOq\nVFT2dcRxz0+uWEL+luOIXV3PgMrf+lFHAwrdezmCmuCY9YZqcD2wljXly6xyxVL8+h5pminwi44z\nq7KeSwkjUJXvJIAn/yGcCQ4A3HPgGt0hOBKNEZ5iIyMjSKXaVPlhX4fQal7ilCuW1JReCYCgDtRU\naFdNaq0E8cdi24gwSJwOKOKy3MeuzDsGWj6mKgbWXjzucet7JFI9tl/3YbkmYwiBt71RTYUzOxoX\nIF1XEazXIl8UImUI2w1Knbz8rsqkcPt1uxz8pn5MckyUy2WcOnWq9Q2SSfZbCamtDSTjtNQgjETC\n6Lh3ILaNCAPm5dHfcjSo4HvQ3MILX235s1yx5HoQ6MXj3uh7FJcZHblorwJYT8rAZ9+3D7tCsPSn\nJiW++6N5LfedK5YgUt2ujxP1ohArNYlsVxKf+419lkegTi6HfupXig5+KxiY5LRQLpdb/3BlaaOv\nw+6hU9hx4Biy+24BEvF5OMO6PGprA8koLzWIguP/7nPY/o7OV0pj2YgwYGqXL2Hm0ftsJzpbLzwE\nQaLFudzP816nErpXDQwChvNttV6d+3LFEvqPf9GTinCBY/N8kxDAf3lqCj/4cTg3cftJxUxjHGaJ\nL84u4KN/8oxnHZvCOdL7CVcjAiFErxDiT4UQ3xFCPC+EuEEI0SeE+GshxHfX/3uVqmCDau7CubXG\nklnePSkAACAASURBVDEqOR3W5VFbT3q5YikeH8YhlHrDG/FfX3+LpT3S8WxEGDxydcn21dOtFx6C\noFX7gJtuugn5fN7naMytXe12NiPgtqeJFUF8XpWzeb6ZX67hyX+Y8aLuQ+SomGmMyyyxly8nCYS2\nfDTgfibnBIBHpZQ/B+BaAM8D+ASACSnlzwKYWP93KLX6MNu6TED3xlmyLi4nvShIv+V6y7edeXyM\n78GAsHv1NExXW1988UW8733v8+W+rCz5srtcqkFVT5N2wvS8OsUlst5RMcPLlRpqhLV8NOAiyRFC\nvAHAfgAPAoCUcllKOQvg1wCcXr/ZaQC3uw1SlxMnTiCdTm/+pkl/gTiczKNi64lz7sI5zD9zVlM0\n1E71O633JDSbu3DO8WCP1LN7ISFMFx4mJyfxwAMP+HJflhIRh8szvZ7FmbtwLjw77F0weq/WHUJk\nqZgJDFJ1tTDrzdgrbhAkbmZy3gLgEoBTQoinhRB/LITIAvgpKeUP1m/zjwB+yuyXhRCDQoinhBBP\nXbqkpia6F7Zt+8nVtETPNtO662H6kI67rSfOqG9MDDOriQufw+BoV/a4FWUlY30ghGi5lE01SwM0\nB8szvZ59iNPS0eXvf0t3CL5KJfxLXN1ePOYsmzoh3Z0AwF2SkwTwCwBGpZTXAZjHlqVpcm3jhunD\nI6Uck1JeL6W8fufO4L0YK5UKBgcHMT09vfE9uWLeeT1MH9Jxt/XEyVm48ONzGAxOO5+HqTpe0PYi\n2n3MnCShdsVq+XYMErmGXb09uPdfXYuUT7Vd3F485lI1dX68sKI7BMfcvFxfBvCylPIb6//+U6wl\nPT8UQrwJANb/+yN3Iepx/PhxVKvVTd+Tq0uYeXzsittGrbFklG09cXIWLsAsLnfhc6hfdt8h7B46\n5Xh5SK5Ywu6hU4EuPZzN+t8zpBM7F9icJqF2xeqiQ4w+8+eXVvH/nvsuVnzK69xePOZSNXWuDkHJ\n81Ycv0OllP8I4PtCiEYb1AEAzwH4MoCj6987CuDPXUWoQaVS2TSD00wuvm5aInWtP8BHOaMTcFuv\n7vBqT4BZvGrO51C/6rcnlDTek4tzCqLxxvz8fMvS0qpZ7YGzcYGtE5FwlYTaWaYUp4sO2WsP6g7B\nM1uvMc0urPjaN4cXj/3T6e19z4Fr2t8gwNy+ev5PABUhxN8D2Afg3wP4QwC/LIT4LoCb1/8dKsPD\nw21/3nYPQDLd+mekVbr/2is+5Hm1J7isLsVx+hwODQ0FphxwK2HpR+WkdLQZ0Z1TEI13/NqP03PN\nuy3fNlcsdX6vuFxWtWKj5nFsLjoIge7db9cdhXcCsDIzVyw52hDitlFu3LR7e4fjE6g1V0mOlPKZ\n9X01Py+lvF1K+ZqUclpKOSCl/Fkp5c1SyhlVwfplamqq7c/NpuMbmy1Z5Sm43vT+EdPvh2EvQBzZ\nGSw5WeZ044034vLly7Z/z09B2wPSjoplSiHJ6Txnt7JUp/cKz3EekDLSRU+CcuZxMjO4tQIuORf3\nPjmR1NfX1/bnZm+6WG22DKF2g2AWjgggI2Vrhsbu4Difz+Po0aNYWQnvhsqgUbFMqb4Q3OVqfrKb\nMLZtamwkfZ1difLAf6tY7T/SxG6/nOy+Q1yhodjFEPfJSeoOIIzMPjB4sgu2zM+1Xv7ROCFOf+Wz\nsaqWE2i1VVs3tzM4TqfTuHz5Mmq1mt2oqA0VA2lj+w7ULge3pYBfnCSMOw4cQ/fut681xl1fUZDo\n2YarBgZ9HfTF6bMwTvuPdLE6q2ls34ne/UeY4HjACPEUO5McEzMz7VfYmb2JRHeOS9UCrNOJciPR\n+csTtgfYpJ6ThpJWB8erq6sd91ak02ksL5uXjCdzKgYXvfuPYPqRzyiIJtycJoy5Ykn7IC8uiaof\n5bjJWtLceC50v/ajqhaiZdNbcbmaif7+/pY/a7W2OcSJbixYOVHmiiUgYfgQDXXipKGkVVY2jzPB\nsUfVno9csQSkuHQ0zIO1uCz/9aMcN1m74KWq8AmZ6+1J6Q7BMSY5JkZGRpBKmTypbdY2cy15sFme\nGVjhvqow4mDDP8nk5gUAqq9o5w9YKIkcYWGvDNUo/Rvknkcq8JzjD6tJc5yWSfotzBfxmeSYKJfL\nOHXqFLq3vWHje4mebcjfcrzliY1rc4OLywrCx9FVOfZTMCeE0ivrq6uryOVyAIQnDSZzxVLoB/pu\nRKEyVK5YQv/xL7YuhkBkgYD1XlB+jsFSMfuoea0a3gI9MXuqrMvufQ/2HP/PKHz8ERQ+/gje/Dtf\nbPtBzkF0MNkdhEX96qMKprOcijm5Kpd+8zs9iCQCpFTeVG9+fh4/+75PuGow2c5VA4OxWPJkJkoz\nBHZLYRM1a+wE6dQLyvcLmWGe2nBAAHj46Yu6w3CESU4L9z72AhZWrFdfCuta8nQ62s1L7W5GbFeF\njdacOnXK8/twclWuNvuKB5FEQ65YQv7WjypLHKSU+N6jf6zkWFvNXTgXiZL8V199te4QtItqAYI4\nzzTq0mrZWqJnm+/7o1Zq4d2I70SYe+UwyWnhFQd1wfMH7gpdhh/1DdZ2lz1Vv/NVjyKJhkKhgHK5\njGw2692dOOzrwTXZ7aneK+HF491oqhyFwfErr8Q76Z67cE53CJ7xeklho2RvuEYT3mqcv9ZmdNaW\nyuZvu7vjKhtSw8mYOAhYQrqFq3t7bDdAyhVLeG1iDPUFlpIOCjsDsbkL51gGvI1MJoORkRFUKhXv\nmmgmjLZ739qJS+laNxrnKBXXIRM9OQVH2SwKMzhuiFS37hCUCVK1K9Ul4b0aVGfTBkb+xTtx+3W7\ncOMfPhHqJoxeCEKJ9Li6urdHdwiOcCanhdLPOSuJyiprwWJn2VOQPpSDRgiBo0ePolwuY3h42LsZ\nwHoNiy8/7+hXdZeuFQGdxd06cFZ1Eaa+OK/8an3cZ+NkhKo7enrBweZ7Ten5yvBuT+L8cg2f/NK3\n8G8f/hYTHAoUp2Ni3ZjkmHj46Yv4s28622TlxdVNcs7Osqe4D7DakVLi9OnTqFQqmJqa8vS+5p99\n1NHvbVTh0VRlTQa0YZpUMm9jduC68gsDca9SGfe/36rstbfou6BRW8Grj5307PALKzWMf93bcyyR\nXY88+wPdITjCJMeE3aIDzQI6zoml7L5Dtqa2OcBor1qt4gMf+ID3g3nZuVlnW8nwNi7zxJbZAZUV\nBFVfGNA9G6cbq3Ras+PAMa29eJxeiCEKq9mFcJaRZpJjws0GK7nI5WpBkOjZhh0Hjtn6Hb8HGGGs\nbOfLbIXDmZjGpnWVDV3D+Bx10nfzICAMJcdSfWFg6+Zi1bLZLDKZjPLjqmD3okzgeTyjmiuWkEhr\n2sPk9kJMxKSNYC7VJWKSY8LNBivOBgSDk30Hfg8wol7ZzqnstQcd/Z4Xm9aj+BytlZP+iPsDOayC\n10muWMLuoVMofPwvlA6UM5kMHnjgARw9ehSGoSbJU8nuRZmgc/o+tkPbEmM2Ht5kOWYllePoqkw4\nV0jwnWringPXoCfl7EOQyw0CwuGHULuGY+SDVJfjwR73VLVgskm7U3M9K5xWwbNF4RXzarWKO+64\nA6Ojo6jVnC1H9koUzzs7DhxDdt8hTxMCXRcV/UjgiILkU79S1B2CI0xyTNx+3S78wa+/E7099jPX\nSC03CDOHgyMmqXpliwOOf5ezqOay195i+n03+198W1qleIAc1Jm5qJ53dhw4hsLvfhn52+5WtkSy\nq/eNG/+vZQ9XsvWFmJQhOKiiSLr9ul26Q3CE78cWbr9uF5751HsdrTWN4lW5sHH6HDBJ1Wvxe3/n\n+Hd79x/hMpItsvsOtRyQNfa/2OreLhJtj6lcQPY+eFkePJ/PR/q8M3fhHKa/8jlAKpg9Ewb63/vB\njX9uVFT0iUh2Id/m/lZqEsF4xYaHEdDS+xQNHBG08PDTF3Hdv/srR2tNo3pVLkzcPAdMUvVxs+Qs\nVywFZlCsnZFE/ra7OyYjdgfXxrY8une/3U1klqnuweOGVwU3EqkuiBv+TaQHerPnz6hJcAAkujNY\nfsuNm0pSqFh6afn+t78x0gmpDjWWpA28sO7HAZjkmHr46Yu450+fxWtVZyXzeBLUTBiungMmqfpw\nyZkadvbL2CnSUbt8CdNf+ZwvCUjkm/OKBK46cBeyxVKkB3oqm4I2mm1vfbT8OmfXZr7vaY8coqBJ\nGSK0+3EAJjmmfv8vLmDFZbUQzgbo5O5qPpNUfVwPVrhcDcb2nd6+hmUNM4+PeXf8dSoHx4G03kw1\nSDNWqqn+21pdBMkVS2tFDnzAHjkUF7t6e3Dvv7w2tPtxACCpO4AgcjqD06x3/xHMPHqf8pK2ZIHL\nq6JRHnS4ZqSAmjdNwUT3NteD8+y1BzH/zFlFEYWPSHbZThRF9zbIRXsl1+3e3q64vAdrly+t9XZC\nNC+uqJyN6/TabizN9Pz9zyWxFHG7envw5Cdu0h2GErzs6ZHGhkhdHZljzeXV/NcmvL9KHVoeJTgw\nkmtNKl3aKFsbU30H77I9WFbZHFSVyC9VayJXlyL796os627lte2mcAkRrbk4u4Cf+eRZ7PnEV3Dj\nHz6Bh5++qDskx5jkmHBSOtrM63//uOdXPOlKbnsYOGkkaiaZjOZEqa1qXBaJVE/bAUzCxr5svzbG\nB44QmH7kj/Dy6G/ZmglpNAe1s8RW9WsgtaWKZdx6HkX171W1x87qEsyoPo5EfmvsE7w4u4B7/suz\noU10mOSY+PSvut9k9epjJ7E89ayCaMgOX8vbdrC6uopcLqc7DLVEAlcNuJ9x2UouzrX9uZ3qU1G9\nKt6RlADkxhIou4nO7qFT1m5sJJW/BlJbsti4FaCI6t+rqiCA1eP48TiGcb+tg04Y5LMgP0UrdYlP\nf/mC7jAcYZJj4qnJGdfHmH/mLxVEQnYY23cqSXBULjGsVqvI5/PKjqdb9tqDyBVLSPdfq/S4nQYn\nK3Xr+6xUXc3t6urC0NCQkmN1oroPi9MlUC1naIQAIGBs32mrcptV1ZXN+xziVuGw+62/pDsET+SK\nJYhUt5LjWOH960aE8rXpso4S+aD8rn7s6u3RHUZLswseLVX3GJMcE1/8xvcVHMXeWSVyV/z9JtR9\n+KztUVAz6KzX65ienlZyLN2aZ8l2/+t/v7b3RUU1M2EoHTioupq7tLSEhx56SMmxOvGiD4uTZO+q\ngUHA2LLM0kgif+vHUPj4X2D30ClfNshHcRN+O1HeS9J34LfdHcDGOcbrKmuJnlzsXpvkj/GvT2FP\nvifQMzphxCTHhI6eBfPz877fZ6QoLB2cK5Yguph0biY2EhyBtffIjgPHUPjdL7s7bMJA/taPKB04\nqEyYwpygOkn2csUS8rccX1+S493MjRVhXBbkVJT3kqiomGjHjgPH0P/rH3d1n600+vQQeeHJf5ix\neXmcOonmzmiXDCHcJzqpLmDFWvnoRCKBnp4eJjpu1Gv48Ve/oGww1mmPSNw0D5iVnoTrajqhN8sV\nS5h+5DPKjxs2TpO9XLEUiKvVcSrDH9U9OQ3G9p2O+h452WM5d+Ec5v77F2zflxWJHl78onhSVZDL\nb5zJMfGut17l+hj5A3dZvm29XmeCo8Dqj9U1D4z6oMMuL/cMeFIoIOZNQVX0HNKtUYY/6jM6Tnob\nhU3v/iMQyS5bv5O/7W5HCc7Mo/dhafZHtn7PKg2LPIgCQUVBLh3iPRJo4aXpBdfHyBVLyN92t4Jo\nIkok0FgOo6yuSDKt5jiI38bnTqrf+WrrH7pMKDxZqhPjhn0i2aWk5xB5z9i+01Fvo7BxkrA6ufgx\ne/6MpzN/nOGnODIEcPt1u3SH4QiTHBOvzLpPcoD4bZ61SiS7kL/1oxsbmZUtgFpdik2ndL+17ffk\nMqHwYtbMi14+oSASvgyahQB6Ut5+fDSuyjtZ5hR8Avnb7vatkEMQNMqUJy0mOk4ufni9t4kz/P4R\n0Ff6mpv/NwtzdT4mOSauVljGL+pLLWwzGYSpHJCqWvoU214rDrh9jXsxaxbbZSVS+jJolhJYrcsr\n+tuo5PVVeb2k7V5GUbFqMRFxklB4nYRwht8fu3p7UH5Xv5bBdcoQ+Gc/0+f/HQccm4FGyD0Hrrmi\nA7dTPCluYTIIUzkgVXUlL8rVjpxol4i6eY1n9x3yZFAe12Ulfl5pXqlJrNroX2RX1N+DTnsZhZ3V\n16iT84qTvT8ULJ/7jX148hM34St//wMt979Sk/jbf3DfKzFq7n3sBd0hOMIkpxVFn925YgkQhpqD\nRYDZB1zbpVA2iW411W9UDBZVN3jUqV2He8dJSqpLSfNWM3FcVqJjA7uXF1rjUMkqmkvx2rNaxMTJ\necXrYhVxTEr9lE0buP26XXj46Yt4raqv+WRcFwK0c1HRNg6/Mckxce9jL9jqsN7O3IVzgFRfJjeU\nWjV9VFgJS1VeoWKw6EWDR106DTgcDSosllh3Im4zqFHcwB6ht09rAa0C6OX1GSuNT90kKbliybMZ\nnajPLuo2v1zDjX/4BD795Qu6Q6EtjJBetA3mGVYzVYUHAF752aTV+n2FlbBUNWvzunN2mFgZcPTu\nP+JgxtK7k2auWIJIdXt2/GARuOqfH4lUggPEZMlhQKsAeplgdkoUVMxIerWfK44zxH67OLuA2QV9\nszhkznXvSE2Y5Jh4g8KmR7zy06S2apr0qVxaoPJDaMeBY0x0YG1WJFcsIX/rR2we2eOTphHO5mX2\nSbz236J3MSUOA8o4Fqbp9LyqmJH05HPXSNpKvsJ53ZvI3C6FBbn8xCTHhMpZuaB9UOdyORiGvj1C\nZh8+vfuPAEZSyfFVL1OysrQiyuwUBtjoDRWQae1YzASsq12+hJdHfytS1brisIk8bssqgfZ/s7F9\np5IZSS8+d0Wqx1Zs4bzuTWTungPX6A7BESY5JmYVbnhztozHO0tLSxgcHNS2Kd7swydXLCF/y3Eg\n5W5Ak+hR3+U9qjNx+Xy+423S/dfaLgywNqPzMYjuzmXBve5lE7QLDF6rXb4UqbLEmzeRC6Te8MZI\nFfMA4tlLrdVSYJWFM7xIkFUWyCEKk96eFJuBRonKPjkAWu9F0WBlZQVnz57FTTfdpOX+W32I5Yol\nFD72Z8jfdrfjJRztKoA55cdAWQiBoaEhJBL+vR2np6fb/lykuvGm9484OnauWEL/8S+i8PFH0G7R\nhhfPV7M4XiWPWlniRgPJt/3eI3jo3P/EnXfeqTskUmDHgWNN53qhvHBGrlhC5h0DSo61IaBFIoi8\n1JMy8OlfLeoOwzE1a4Qi5p4D1+Ajf/KMkmPNnj8D1FaVHEuVyclJXLqkp3Rppw+xXLGEXLGEuQvn\nMP3IH8HOpL8XV0V79x/B9COfUX7cZnfeeSdOnjwJABgdHfX0vqySiiqfGdt3mJbJ9WLWbatcseT5\ncxdEUZt9zKYNvLfrRXzkXxzD5OSk7nCUieN+nGaNc71XlC81DmiRCCIvCKxd8L/nwDWhncUBOJNj\n6vbrdiGbVrPELKgDjmq1qjuEluYunMP0Vz4HOwmOVwMGP5aTnD59GpVKBQ899JDn92XV/9/e3UfH\nVd53Av/+ZnRljTQ2erHJARlDoFkoE0dW6wS33vXZwWxkbCfR0gSX4pLT7dbnQNkA8XGBwGlID1nc\n9ZKYcyg9h5OWxsAS8kLV8BKcBtR1lwYWE5k4CniTEGwQtBjbwpY1QqPRs3+MRsjynZn78jz3bb6f\nf2zLmjuPdO/c+/yel99PV70hu2Uj0rTA+CxOhZvrIilLoZK2TO+doR/hr+/8s0QFOGHUNPIiJdBW\nGDtoup+9jR6UUmP59fYNeO6WS2Md4AAMcqo6Oamnto2uzmISOH1IjO7Z5aq2kPEOg+FlCuPj4/j8\n5z9fdwlZkNTECS17O+bvqwi6novTwoNAMuoaxaXz7MaxPbvw/oTeQnSm94PV0/rRtbHYjzOtAMvj\ncuuwQyPdwX7SPldE1bRrzDAcNi5XszEwNAKBnuwoIsyyArjrfLkagZOU+U5zAMsUSqXoFYwtz6b5\nn80yvSyllkbLjpe0gqAAbJc7epZuQtflNyCby+Pd3ffh5L6n9B3bhZM//aHrpB5hGS9Oo6PVcl2B\nPuznns6lxm6yTBLFXZz34MzHmRwbO3Yf0HaD1lWcMs6stkWuOl+uZr+UMvrwGRsebNwNp6oU+03s\nWjvIMZDIjpjGz1+q+YOkMqHWwZqeilUWPLcBThRkc3ltM3ZxCUiJ6lnQVP9+uvfg0QBaEowG7b3V\n9taovqURSVsf78Wi/J+46ny52Rph8vc7NjyIo0/f29AbTqO6p8yxhOyzaWgaP3/ThROnpNmuZPkK\nYyAj7gMIcRDU3j+iOEinBNPT9YfwH37+UACtCYbvO7uIpEVkSESemPn3h0XkBRH5pYg8KiLN/psZ\nLJ0ppHUWuowrNw9zgfPZL9P7D0b37IKa0pNlLK5iH6QnYJ+Nc8kM6HRv+J6fZrtc2+mmwAuPxn4A\nIQayuTzg87wy4QAlxfS0QtFBkKMAnH/rkzjvliexevuzGBgaMd84Q3QMX90A4JU5//5LAF9XSv0G\ngGMA/ljDewRqW9+F2roL2VweYmmuu1NDc3P0YkqnD/O25jTOyFiOO9amN+82fCdE0txsGyPNyz4W\ndhOMMHENzv9sn5ogIxhuBhCslKDV4sILL7rWXe/5tUlM5EHxYGLIys2QXyUWGhkt4NbH9sc20PF1\n1xSRpQA2APjGzL8FwKUAvjvzLd8E0O/nPcLQ39uNq1ct03aRqYng9uVMTk4G9l5OpTLO9ticnCxh\ntFB0/FAxvak89rMYPnVtuDH+ezwCHp0PU2n0rbCbYISJa9Dus10pPHrR7QEkI3A5gFCcVqFv5I8r\nP9dPEhN5UDxE6fNeKJawY/eBsJvhid+hoZ0A/gxAZdF0F4BRpVSl+uWbAGyTbIvIFhHZKyJ7wypM\nWcud/cvxG2e2aTlWWJ3lqNT9cLtiyOmGUdMzLY281DCIYp1+COCollXKit7MpikNP/PoVLqpZoBx\neN8zSKX01EmzJ2jr6XP9+SoUG3dv4HyrL+iE6YmtqN8DiYKkc696kDzfJkRkI4B3lFIveXm9Uup+\npdRKpdTKJUuit+Z1YGgEv3jnpJZjhTXdHZW6H15msjrWbqm7Rt508Bj0UsMoiXpWQAVntayi8nO0\ntbUZH3RIck0uncvIxMpU7bxWko1MT5tM6a4w/rNnYpVdLWp+/vYJuIn5vGRZm56K3qoIorDo3Kse\nJD9jIasBfFpEXgfwLZSXqd0DoF1EKsPfSwHEciHfHd8f1nasRh8N8hKM1FsjH9Ra6SCXGkZJUpbq\nReXnGB8fx4MPPohzzz0XgJlZ1ohM3Bqh87Ne6zMdVLKR+ckPyB23Ka071m5xn0Gv+D4DUaIZ2/ou\nDLsJnngOcpRStyqlliqlzgPw+wCeVUpdDWAQwGdnvu3zAP7BdysDNjA0gtGC3roAYVfYDpPXDkpl\njfy5Nz+Bro1bZwIeQXrRksDWSkelkxyoOst5oqI9Y9XdN7fxv3wx8KxZdjo7O3H11Vfj9ddfh1IK\nDz74INJpvUuipgsntB4vSrK5PJqX9Wg5Vq3PdJB1lbi8MGAeUpEzECUCWq0U+nttd55EnolVrTcD\n+KKI/BLlPTp/Y+A9jDKxwapj7ZaG3d+hIxj5IOB5HEuvfSCw2bH2NdeE2klOp9Po6uoK9k0dpJiM\ngtFCsebmzPaMhcMf+gQ6110fegKCY8eOQUTQ1NQEEcFtt92GLVu26J3RSXjRWl2JFaoF8EGP2jtN\nyEL+zNY784CBKBEwHuP9gFp63UqpfwLwTzN/fw3AJ3QcNywmNlhVOuWje3ahdPxdiERnz4xJca8x\ncOp5Cz5BRqlUwpEjR4J9U1XC6J5dsV9mOVoozs7ICsLNVjM9XX5IlErlvR4HDx7EN77xDb33gIQX\nrdXV4ax2XQc9as89H8HwswSxIWfyieZJx3gtdLKH/jwytcEqm8vj3Ov+Drf9/cvo7Ow08h5R03L+\nx8Nugm+VWaQwii3qXtLkVBgBnSlRLepaLOpdEpv0mRwdHc5agy6Bj9oXo3dNJpGf8xqHZbtEppVi\nPCCf7KeiR9v6LoSVNtOhvfvKHtzZvxxHjx41cvyoSVYWoeA/6JWR/8AlqMPcMEtOEj6To2PpaK1O\nK0ftg7OgKbj7i9fz2rysJ/az2UQ6dMc0sxrAIMdWf283dny2x1EdDrcqlWMbZSYnClmEBMDmVcti\n/UENXII6zA3TeU1QYGonm8uj9aNrPb++Xt2ToPffSUvjJqN5fyq4+4vX81p85zUDrSGKl4yVjm1m\nNYBBTlX9vd0Y/ot12LxqmdZFSnGuHOtV2CPpCsBDzx8CUA52PLPCz9IVlLjvpZqrYZacJCgwtTM2\nPIjxnz3j+fUda7fU/P9K2vpgMmEKOi+r3R7Sw2twrCaSm62QyjJWyl+fIOHSIrjriuWxzawGMMip\n687+5fj6phVoz1jajvnWaCH4zeQhispI+shoAd97yXvZpq6+6zW2JrqCqkE0X2pmNEH3jFujLDlJ\nUmBqx8/eKmlxVr2+XAC4xdN7uGqPtaBhrssomHjtxbCbQBHzkTPbMDmlZgdA6XQlpWId4AAMchzp\n7+3GHZ/OaSu2d+SH9+k5UAyE1WGuplAs+ZuZk3ASAQTJOvuiUDpglczVIwayGyYpALBNOy3pSH3O\nTPA8I5xucjVrEkTSDVWcMP4e9IGwVxNQ9PzinZOx3lAfBEG5bmScNWbhFocGhkawY/cBrZ2useFB\nnBh6Stvxoiy9aAna11wTuRFLr7e10T27ABVSIoAATb6xP+wmaNe+5hoc+cE9QGkq7Kb4Zpd2uq2n\nL3KfM93SixZ7CkDEyrj73Ugq8Uv/Go3Xa4eokSmU60bGeTaHMzlV3D6wHzc9uk/7qHIQm/BbW1uD\nLyA5T3rRkkCLdgahYR6SCezglZchRTvxhGVZyGa9FYhshOU4Xmeq1MSYyxeYv/4bOelAGNrXUIek\nqQAAIABJREFUXNOwxbiJ/DBRNzJIDHJsDAyN4OHnDxlJGBzEtPn999+Pe+65x/j7VBO1JWo6JCcN\ntgMJzdLlurPrgjQt8L1hXSmFsbEP2tjc3Oz4tY2wHMfrgInrPYGmr39JM+lAwLK5PLouv8HVZzSY\nBBQUhjgXtwyaqbqRQeHQho0duw8Yq4gSxLT5bbfdhoMHDxp9j1rC2tNhUthpsIPU1rOu5v+LAHFc\nyqzzs5fKLIRS5cApvWgx2tdcg4k3X8HJfd6Xok5NnbqUbnJy0kV7vM0AxU160RJX59DTgIvhmZyu\nDTcm7v4YB9lcfvb3/uZf/1Ht6yjdVDcbH8VTSoDmJkGhGMOHWMCslMQ6fTTAmRxbJjY+VwQxwxFm\ngAMAk4dexru7k5VcoRFGyisW911X8//jGOAAepesnPOFR7Dshkdw7s2PY+m1DwCAr/TGfsX1nLjl\nquaJpNC57nrXAYXpJBUMcMJX8zksKXRdfgPPU0JNK6BQTN6SbBOK0wp7D8a7cD2DHBsmpzIb5cZ5\nct9TiVriFZU02OSdzn05869tP+mNdTC5FC9KKrVsnAQiXRtu8nS/NT0QlaT7Ylxlc3m0rVh/2tel\naYHn64YoiR56/lCsM6wxyLHBtIJ6BLXEK4jVtUFXQw9L0teh6woGjj597ymd1bBn+hopCM/m8uXZ\nszp7Z7x2VLO5vNHPwbFn7jd2bHJucd916Nq4dSZgFqQXLfE080eUdF95fDjsJnjGPTk2utszRpes\nNYqgOn5BhKSVB9/onl3JzbLWAOvQde3LUVPvY3TPrtnrIuwUtS3nfzy09w5Njb0zfpecdazdgiNP\n3O3rGNVMF04YOS65N3efDhHZOzZeDLsJnnEmx4bJjVaNtFQhaaPLlRHkJBWWnKtt+ScT/8DXGQzM\nDeLb11wTaqHYRkghPV+tz6HfJWdJ/xwQETUCBjk2+nu7sXnVMiPHPvqjxlmqkLQ00hVJrbnQCB3l\n8Vf/Wdux5gbx2VweqZZWbcd2K+zlcmGotoS0bcV630GKycEokzVyZN6fRBSeBU0pdMc8BTMAtGes\nsJvgGYOcKu7sX46dm1ZovUDHhgehJhpjqULzsp7EjoZmc3m0Lf9k2M3QrhE6yjo/f/OD+OlCeJv/\nkzZr6sSpSQjKeyq6Nm6tmx3QCWP7CQ3XyFEop8i9etUyWCmGOkRhen9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by/O8ECVcZV/2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\niIiIiChRGOQQEREREVGi/H/mcclKZtQ07gAAAABJRU5ErkJggg==\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa07d68>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "fig = plt.figure(figsize=(14,8))\n",
    "plt.scatter(x_v[pontos_abaixo_curva], y_v[pontos_abaixo_curva])\n",
    "plt.scatter(x_v[~pontos_abaixo_curva], y_v[~pontos_abaixo_curva], c='black');"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.5 Simulação de Monte Carlo – Precificação de opções europeias"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def monte_carlo_europeia(S0, K, T, r, sigma, q, N=1000000):\n",
    "    z = np.random.standard_normal(N) \n",
    "    ST = S0 * np.exp((r - q - 0.5 * sigma ** 2) * T + sigma * np.sqrt(T) * z) \n",
    "    pT = np.maximum(ST - K, 0) \n",
    "    return np.mean(pT) * np.exp(-r * T) "
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 19,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.84402692872105645"
      ]
     },
     "execution_count": 19,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_europeia(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.6 Simulação de Monte Carlo – Opções que dependem do caminho"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 20,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def monte_carlo_asiatica(S0, K, T, r, sigma, q, media_dias, dias_no_ano=252.0, N=10000): \n",
    "    delta_t = 1.0 / dias_no_ano\n",
    "    S = np.zeros((media_dias, N)) \n",
    "    t_inicial = T - (media_dias - 1) * delta_t\n",
    "    sn = np.random.standard_normal((media_dias, N)) \n",
    "    \n",
    "    # Simula o valor do primeiro dia usado na média\n",
    "    S[0] = S0 * np.exp((r - q - 0.5 * sigma ** 2) * t_inicial + sigma * np.sqrt(t_inicial) * sn[0]) \n",
    "    \n",
    "    # Simula os outros dias\n",
    "    for j in range(1, media_dias):\n",
    "        S[j] = S[j - 1] * np.exp((r - q - 0.5 * sigma ** 2)*delta_t + sigma * np.sqrt(delta_t) * sn[j]) \n",
    "    \n",
    "    # Calcula o payoff\n",
    "    pT = np.maximum(np.average(S, axis=0) - K, 0)\n",
    "    return np.mean(pT) * np.exp(-r * T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 21,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.76767824935032736"
      ]
     },
     "execution_count": 21,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_asiatica(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03, media_dias=30)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 22,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.87356627096136186"
      ]
     },
     "execution_count": 22,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_asiatica(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03, media_dias=1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 23,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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SeqmTQF1pKvE4Tgc725IknamiDKRopffAE8f4TweeWXR8eaudbQO1pJXSSaD+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\nS5IkSUtgoJYkSZKWwEAtSZIkLcH/D3w6iANXZotMAAAAAElFTkSuQmCC\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa3fb38>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "asian_option = np.zeros(252)\n",
    "for i in range(1, 252):\n",
    "    asian_option[i] = monte_carlo_asiatica(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03, media_dias=i, N=100000)  \n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax = plt.subplots(figsize=(12,6))\n",
    "ax.set_ylabel('Valor da Opção')\n",
    "ax.set_xlabel('Parâmetro M (média_dias)')\n",
    "_ = plt.plot(asian_option[1:], '.')    "
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.7 Modelo Longstaff e Schwartz\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 24,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def monte_carlo_longstaff_schwartz(S0, K, T, r, sigma, q, N=500000, P=40): \n",
    "    delta_t = T / P\n",
    "    df = np.exp(-r * delta_t)\n",
    "    S = np.zeros((P + 1, N))\n",
    "    \n",
    "    # Simula o valor do ativo\n",
    "    S[0] = S0\n",
    "    sn = np.random.standard_normal((P + 1, N))\n",
    "    for t in range(1, P + 1):\n",
    "        S[t] = S[t - 1] * np.exp((r - q - 0.5 * sigma ** 2) *\n",
    "                    delta_t + sigma * np.sqrt(delta_t) * sn[t]) \n",
    "   \n",
    "    # Longstaff Schwartz\n",
    "    V = np.maximum(S - K, 0) \n",
    "    for t in reversed(range(P)): \n",
    "        mask = V[t] > 0 \n",
    "        if np.sum(mask) > 3: \n",
    "            reg = np.polyfit(S[t][mask], V[t + 1][mask] * df, deg=3) \n",
    "            v_esperado = np.polyval(reg, S[t][mask]) \n",
    "            V[t][mask] = np.where(V[t][mask] > v_esperado, V[t][mask],\n",
    "                    V[t + 1][mask] * df) \n",
    "            V[t][~mask] = V[t + 1][~mask] * df \n",
    "        else: \n",
    "            V[t] = V[t + 1] * df\n",
    "   \n",
    "    return np.mean(V[0])"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 25,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.83769983372212198"
      ]
     },
     "execution_count": 25,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "monte_carlo_longstaff_schwartz(S0=8.5, K=10, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.8 Gregas"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.8.1 Delta\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 26,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_formula(S0, K, T, r, sigma, q):\n",
    "    d1 = (log(S0 / K) + (r - q + (sigma ** 2)/2) * T) / (sigma * sqrt(T))\n",
    "    return exp(-q* T) * stats.norm.cdf(d1, 0.0, 1.0)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 27,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45068066334990481"
      ]
     },
     "execution_count": 27,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_formula(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 28,
   "metadata": {},
   "outputs": [],
   "source": [
    "from math import log, sqrt, exp\n",
    "from scipy import stats\n",
    "def black_scholes(S0, K, T, r, vol, q):\n",
    "    d1 = (log(S0 / K) + (r - q +  (vol ** 2)/2) * T) / (vol * sqrt(T))\n",
    "    d2 = d1 - vol * sqrt(T)\n",
    "    value = (S0 * exp(-q * T) * stats.norm.cdf(d1, 0.0, 1.0) - K * exp(-r * T) * stats.norm.cdf(d2, 0.0, 1.0))\n",
    "    return value"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 29,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_dif_black_scholes(S0, K, T, r, sigma, q, ds=0.001):\n",
    "    x1 = black_scholes(S0 - ds, K, T, r, sigma, q)\n",
    "    x2 = black_scholes(S0 + ds, K, T, r, sigma, q)\n",
    "    return (x2 - x1) / (2 * ds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 30,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45068066145725894"
      ]
     },
     "execution_count": 30,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_dif_black_scholes(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 31,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_dif_arvore_binomial(S0, K, T, r, sigma, q, ds=0.001):\n",
    "    x1 = arvore_binomial_completa(S0 - ds, K, T, r, sigma, q)\n",
    "    x2 = arvore_binomial_completa(S0 + ds, K, T, r, sigma, q)\n",
    "    return (x2 - x1) / (2 * ds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 32,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.4295720142865611"
      ]
     },
     "execution_count": 32,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_dif_arvore_binomial(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 33,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np\n",
    "def monte_carlo_europeia(S0, K, T, r, sigma, q, N=10000000, seed=0):\n",
    "    np.random.seed(seed)\n",
    "    z = np.random.standard_normal(N)\n",
    "    ST = S0 * np.exp((r - q - 0.5 * sigma ** 2) * T + sigma * np.sqrt(T) * z)\n",
    "    pT = np.maximum(ST - K, 0)\n",
    "    return np.mean(pT) * np.exp(-r * T)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 34,
   "metadata": {},
   "outputs": [],
   "source": [
    "def delta_dif_monte_carlo(S0, K, T, r, sigma, q, ds=0.001):\n",
    "    x1 = monte_carlo_europeia(S0 - ds, K, T, r, sigma, q, seed=0)\n",
    "    x2 = monte_carlo_europeia(S0 + ds, K, T, r, sigma, q, seed=0)\n",
    "    return (x2 - x1) / (2 * ds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 35,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.45078801367792742"
      ]
     },
     "execution_count": 35,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "delta_dif_monte_carlo(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.8.2 Gamma"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 36,
   "metadata": {},
   "outputs": [],
   "source": [
    "def gamma_dif_black_scholes(S0, K, T, r, sigma, q, ds=0.001):\n",
    "    x1 = black_scholes(S0 + ds , K, T, r, sigma, q)\n",
    "    x2 = -2 * black_scholes(S0, K, T, r, sigma, q)\n",
    "    x3 = black_scholes(S0 - ds , K, T, r, sigma, q)\n",
    "    return (x1 + x2 + x3) / (ds**2)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 37,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.1296167333464382"
      ]
     },
     "execution_count": 37,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "gamma_dif_black_scholes(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.8.3 Theta"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 38,
   "metadata": {},
   "outputs": [],
   "source": [
    "def theta_dif_black_scholes(S0, K, T, r, sigma, q, ds=0.01):\n",
    "    x1 = black_scholes(S0, K, T - ds, r, sigma, q)\n",
    "    x2 = black_scholes(S0, K, T + ds, r, sigma, q)\n",
    "    return -(x2 - x1) / (2*ds)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 39,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0075745901153336792"
      ]
     },
     "execution_count": 39,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_dif_black_scholes(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)/100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 40,
   "metadata": {},
   "outputs": [],
   "source": [
    "def theta_1dia_black_scholes(S0, K, T, r, sigma, q, base=252.0):\n",
    "    x1 = black_scholes(S0, K, (T * base - 1)/base, r, sigma, q)\n",
    "    x2 = black_scholes(S0, K, T, r, sigma, q)\n",
    "    return -(x2 - x1)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 41,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "-0.0030079030027372333"
      ]
     },
     "execution_count": 41,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "theta_1dia_black_scholes(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.8.4 Vega"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 42,
   "metadata": {},
   "outputs": [],
   "source": [
    "def vega_dif_black_scholes(S0, K, T, r, sigma, q, ds=0.01):\n",
    "    x1 = black_scholes(S0, K, T, r, sigma - ds, q)\n",
    "    x2 = black_scholes(S0, K, T, r, sigma + ds, q)\n",
    "    vega_1 = (x2 - x1) / (2 * ds)\n",
    "    return vega_1 / 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 43,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.032775766747360713"
      ]
     },
     "execution_count": 43,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "vega_dif_black_scholes(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 44,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.032794171262257255"
      ]
     },
     "execution_count": 44,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "bs_vol35 = black_scholes(8.5, 10.0, 1.0, 0.10, 0.35, 0.03)\n",
    "bs_vol36 = black_scholes(8.50, 10.0, 1.0, 0.10, 0.35 + 0.01, 0.03)\n",
    "bs_vol36 - bs_vol35"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.8.5 Rhô"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 45,
   "metadata": {},
   "outputs": [],
   "source": [
    "def rho_dif_black_scholes(S0, K, T, r, sigma, q, ds=0.01):\n",
    "    x1 = black_scholes(S0, K, T, r - ds, sigma, q)\n",
    "    x2 = black_scholes(S0, K, T, r + ds, sigma, q)\n",
    "    rho_1 = (x2 - x1) / (2 * ds)\n",
    "    return rho_1 / 100"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 46,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.029877761172990347"
      ]
     },
     "execution_count": 46,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "rho_dif_black_scholes(S0=8.50, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "#### 4.8.6 Análise das Gregas\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 47,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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UrsTVRgCkABDuRWsz0/6338zyPytn/TsiOxu6doX58+H33+HGG61OJK7ByeR0ftl4mJ83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\nSUVORK5CYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xaa0f7f0>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "delta_bs_v = np.vectorize(delta_dif_black_scholes)\n",
    "gamma_bs_v = np.vectorize(gamma_dif_black_scholes)\n",
    "vS0 = np.linspace(1, 20, 100)\n",
    "\n",
    "import matplotlib.pyplot as plt\n",
    "fig, ax1 = plt.subplots(figsize=(8,5))\n",
    "ax2 = ax1.twinx()\n",
    "ax1.plot(vS0, delta_bs_v(S0=vS0, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03), linewidth=2, label='delta') \n",
    "ax2.plot(vS0, gamma_bs_v(S0=vS0, K=10.0, T=1.0, r=0.10, sigma=0.35, q=0.03), 'r', label='gamma')\n",
    "ax1.legend(); ax2.legend();"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.9 Volatilidade\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 48,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": 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ZN3tYt6uSarvtLhHH+ERTOFepLUCfkOe97W3N7VMiIslALlbjMiLSG3gNuNIY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\nYII=\n",
      "text/plain": [
       "<matplotlib.figure.Figure at 0xd6a2e48>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "import numpy as np\n",
    "import pandas as pd\n",
    "import pandas_datareader.data as web\n",
    "petr = web.DataReader('PETR4.SA', data_source='yahoo', start='8/31/2006', end='8/31/2016').dropna()\n",
    "petr['Log Ret'] = np.log(petr['Adj Close'] / petr['Adj Close'].shift(1)) \n",
    "petr['vol_252'] = petr['Log Ret'].rolling(window=252, center=False).std()\n",
    "petr['vol_252'].plot();"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 49,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</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>2016-08-25</th>\n",
       "      <td>12.42</td>\n",
       "      <td>12.64</td>\n",
       "      <td>12.35</td>\n",
       "      <td>12.53</td>\n",
       "      <td>12.53</td>\n",
       "      <td>40290500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-26</th>\n",
       "      <td>12.69</td>\n",
       "      <td>12.90</td>\n",
       "      <td>12.45</td>\n",
       "      <td>12.55</td>\n",
       "      <td>12.55</td>\n",
       "      <td>50650500.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-29</th>\n",
       "      <td>12.50</td>\n",
       "      <td>12.96</td>\n",
       "      <td>12.45</td>\n",
       "      <td>12.87</td>\n",
       "      <td>12.87</td>\n",
       "      <td>36990100.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-30</th>\n",
       "      <td>13.04</td>\n",
       "      <td>13.23</td>\n",
       "      <td>12.97</td>\n",
       "      <td>13.09</td>\n",
       "      <td>13.09</td>\n",
       "      <td>51893700.0</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-31</th>\n",
       "      <td>13.13</td>\n",
       "      <td>13.22</td>\n",
       "      <td>12.71</td>\n",
       "      <td>12.85</td>\n",
       "      <td>12.85</td>\n",
       "      <td>61016100.0</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Open   High    Low  Close  Adj Close      Volume\n",
       "Date                                                         \n",
       "2016-08-25  12.42  12.64  12.35  12.53      12.53  40290500.0\n",
       "2016-08-26  12.69  12.90  12.45  12.55      12.55  50650500.0\n",
       "2016-08-29  12.50  12.96  12.45  12.87      12.87  36990100.0\n",
       "2016-08-30  13.04  13.23  12.97  13.09      13.09  51893700.0\n",
       "2016-08-31  13.13  13.22  12.71  12.85      12.85  61016100.0"
      ]
     },
     "execution_count": 49,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "petr = web.DataReader('PETR4.SA', data_source='yahoo', start='8/31/2006', end='8/31/2016')\n",
    "petr.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 50,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/html": [
       "<div>\n",
       "<style>\n",
       "    .dataframe thead tr:only-child th {\n",
       "        text-align: right;\n",
       "    }\n",
       "\n",
       "    .dataframe thead th {\n",
       "        text-align: left;\n",
       "    }\n",
       "\n",
       "    .dataframe tbody tr th {\n",
       "        vertical-align: top;\n",
       "    }\n",
       "</style>\n",
       "<table border=\"1\" class=\"dataframe\">\n",
       "  <thead>\n",
       "    <tr style=\"text-align: right;\">\n",
       "      <th></th>\n",
       "      <th>Open</th>\n",
       "      <th>High</th>\n",
       "      <th>Low</th>\n",
       "      <th>Close</th>\n",
       "      <th>Adj Close</th>\n",
       "      <th>Volume</th>\n",
       "      <th>Log Ret</th>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>Date</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>2016-08-25</th>\n",
       "      <td>12.42</td>\n",
       "      <td>12.64</td>\n",
       "      <td>12.35</td>\n",
       "      <td>12.53</td>\n",
       "      <td>12.53</td>\n",
       "      <td>40290500.0</td>\n",
       "      <td>0.010429</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-26</th>\n",
       "      <td>12.69</td>\n",
       "      <td>12.90</td>\n",
       "      <td>12.45</td>\n",
       "      <td>12.55</td>\n",
       "      <td>12.55</td>\n",
       "      <td>50650500.0</td>\n",
       "      <td>0.001595</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-29</th>\n",
       "      <td>12.50</td>\n",
       "      <td>12.96</td>\n",
       "      <td>12.45</td>\n",
       "      <td>12.87</td>\n",
       "      <td>12.87</td>\n",
       "      <td>36990100.0</td>\n",
       "      <td>0.025178</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-30</th>\n",
       "      <td>13.04</td>\n",
       "      <td>13.23</td>\n",
       "      <td>12.97</td>\n",
       "      <td>13.09</td>\n",
       "      <td>13.09</td>\n",
       "      <td>51893700.0</td>\n",
       "      <td>0.016950</td>\n",
       "    </tr>\n",
       "    <tr>\n",
       "      <th>2016-08-31</th>\n",
       "      <td>13.13</td>\n",
       "      <td>13.22</td>\n",
       "      <td>12.71</td>\n",
       "      <td>12.85</td>\n",
       "      <td>12.85</td>\n",
       "      <td>61016100.0</td>\n",
       "      <td>-0.018505</td>\n",
       "    </tr>\n",
       "  </tbody>\n",
       "</table>\n",
       "</div>"
      ],
      "text/plain": [
       "             Open   High    Low  Close  Adj Close      Volume   Log Ret\n",
       "Date                                                                   \n",
       "2016-08-25  12.42  12.64  12.35  12.53      12.53  40290500.0  0.010429\n",
       "2016-08-26  12.69  12.90  12.45  12.55      12.55  50650500.0  0.001595\n",
       "2016-08-29  12.50  12.96  12.45  12.87      12.87  36990100.0  0.025178\n",
       "2016-08-30  13.04  13.23  12.97  13.09      13.09  51893700.0  0.016950\n",
       "2016-08-31  13.13  13.22  12.71  12.85      12.85  61016100.0 -0.018505"
      ]
     },
     "execution_count": 50,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "petr['Log Ret'] = np.log(petr['Adj Close'] / petr['Adj Close'].shift(1))\n",
    "petr.tail()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 51,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import optimize\n",
    "def volatilidade_implicita_black_scholes(S0, K, T, r, q, price):\n",
    "    def vol_function(sigma): \n",
    "        return black_scholes(S0, K, T, r, sigma, q) - price \n",
    "    return optimize.fsolve(vol_function, 0.40)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 52,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.27540212470094033"
      ]
     },
     "execution_count": 52,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "volatilidade_implicita_black_scholes(S0=8.50, K=10.0, T=1.0, r=0.10, q=0.03, price=0.60)"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 53,
   "metadata": {},
   "outputs": [],
   "source": [
    "from scipy import optimize\n",
    "def volatilidade_implicita_arvore_binomial(S0, K, T, r, q, price):\n",
    "    def vol_function(sigma):\n",
    "        return arvore_binomial_completa(S0, K, T, r, sigma, q) -  price \n",
    "    return optimize.fsolve(vol_function, .40)[0]"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 54,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.39754137954395169"
      ]
     },
     "execution_count": 54,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "volatilidade_implicita_arvore_binomial(S0=8.50, K=10.0, T=1.0, r=0.10, q=0.03, price=1)"
   ]
  },
  {
   "cell_type": "markdown",
   "metadata": {},
   "source": [
    "## 4.10 Algumas questões práticas: pontos de atenção em relação aos parâmetros"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 55,
   "metadata": {},
   "outputs": [],
   "source": [
    "import numpy as np"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 56,
   "metadata": {},
   "outputs": [
    {
     "data": {
      "text/plain": [
       "0.095310179804324935"
      ]
     },
     "execution_count": 56,
     "metadata": {},
     "output_type": "execute_result"
    }
   ],
   "source": [
    "np.log(1 + 0.10)"
   ]
  }
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