dl_option_test.ipynb

{
  "nbformat": 4,
  "nbformat_minor": 0,
  "metadata": {
    "colab": {
      "provenance": [],
      "authorship_tag": "ABX9TyNfarrcf2LpsGCZbwpKiFBJ",
      "include_colab_link": true
    },
    "kernelspec": {
      "name": "python3",
      "display_name": "Python 3"
    },
    "language_info": {
      "name": "python"
    }
  },
  "cells": [
    {
      "cell_type": "markdown",
      "metadata": {
        "id": "view-in-github",
        "colab_type": "text"
      },
      "source": [
        "<a href=\"https://colab.research.google.com/github/ashish1610dhiman/pinn_option_pricing/blob/main/dl_option_test.ipynb\" target=\"_parent\"><img src=\"https://colab.research.google.com/assets/colab-badge.svg\" alt=\"Open In Colab\"/></a>"
      ]
    },
    {
      "cell_type": "code",
      "execution_count": null,
      "metadata": {
        "id": "JOg6L-bympvQ"
      },
      "outputs": [],
      "source": [
        "import torch\n",
        "import torch.autograd as tgrad"
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Analytical solution\n",
        "\n",
        "![image.png](data:image/png;base64,iVBORw0KGgoAAAANSUhEUgAAAZgAAACHCAYAAAArzE+vAAAKrGlDQ1BJQ0MgUHJvZmlsZQAASImVlwdQU+kWx79700NCSwhFSuhNkE4AKSG0AEqvohKSAKGEGAgqNkTEFVhRVESwoktVcFWKLCoiim1RVOy6IIuIsi4WREXlXWAIu/vmvTfvzJw5v5yc7/+d7879Zs4FgCzPEYlSYHkAUoUZ4mBvd3pkVDQdNwRwQBmQAQ0ocbjpImZgoD9AbDb+3T7eA9BUvGM2pfXv//9XU+Dx07kAQIEIx/HSuakIn0b8FVckzgAAdQjJ667MEE1xJ8JUMdIgwg+mOGGGR6Y4bprRYLomNJiFMBUAPInDEScAQKIjeXomNwHRIbkhbCHkCYQIixB2SU1N4yF8AmEjpAbJkab0GXF/0Un4m2acVJPDSZDyzFmmDe8hSBelcFb/n4/jf1tqimR2DwPESYlin2AkKiLP7EFymp+UhXGLA2ZZwJuun+ZEiU/YLHPTWdGzzON4+EnXpiz2n+V4gRdbqpPBDp1lfrpnyCyL04Kle8WLWcxZ5ojn9pUkh0nziXy2VD8rMTRiljMF4YtnOT05xG+uhiXNiyXB0v75Qm/3uX29pGdPTf/LeQVs6dqMxFAf6dk5c/3zhcw5zfRIaW88vofnXE2YtF6U4S7dS5QSKK3np3hL8+mZIdK1GcgLObc2UPoMkzi+gbMMWCANpCAuBnTgj/zyACCDvypj6iCsNNFqsSAhMYPORG4Yn84Wcs3n060srKwBmLqvM6/De9r0PYRo1+ZyOR8AcOZNTk62zeX89QA4vRkA4ou5nOE5AGSVAbhSwJWIM2dy03cJA4hADlCBKtAEusAImAErYAecgBvwBL4gAISCKLAMcEEiSEU6XwnWgo0gDxSA7WA3KAMHwRFQDY6Dk6AZtIEL4DK4Dm6BXvAY9IFB8BqMgo9gAoIgHESGKJAqpAXpQ6aQFcSAXCBPyB8KhqKgWCgBEkISaC20CSqAiqEy6DBUA/0MnYEuQFehHugh1A8NQ++gLzAKJsFUWAM2gBfADJgJ+8Gh8FI4AV4BZ8G58Da4FK6Aj8FN8AX4OtwL98Gv4TEUQMmgaChtlBmKgWKhAlDRqHiUGLUelY8qQVWg6lGtqC7UHVQfagT1GY1FU9B0tBnaCe2DDkNz0SvQ69GF6DJ0NboJ3Ym+g+5Hj6K/Y8gYdYwpxhHDxkRiEjArMXmYEkwlphFzCdOLGcR8xGKxNKwh1h7rg43CJmHXYAux+7EN2HZsD3YAO4bD4VRxpjhnXACOg8vA5eH24o7hzuNu4wZxn/AyeC28Fd4LH40X4nPwJfha/Dn8bfwQfoIgT9AnOBICCDzCakIR4SihlXCTMEiYICoQDYnOxFBiEnEjsZRYT7xEfEJ8LyMjoyPjIBMkI5DJlimVOSFzRaZf5jNJkWRCYpFiSBLSNlIVqZ30kPSeTCYbkN3I0eQM8jZyDfki+Rn5kyxF1lyWLcuT3SBbLtske1v2jRxBTl+OKbdMLkuuRO6U3E25EXmCvIE8S54jv16+XP6M/H35MQWKgqVCgEKqQqFCrcJVhZeKOEUDRU9FnmKu4hHFi4oDFBRFl8KicCmbKEcplyiDVCzVkMqmJlELqMep3dRRJUUlG6VwpVVK5UpnlfpoKJoBjU1LoRXRTtLu0b4oaygzlfnKW5XrlW8rj6vMU3FT4avkqzSo9Kp8UaWreqomq+5QbVZ9qoZWM1ELUlupdkDtktrIPOo8p3ncefnzTs57pA6rm6gHq69RP6J+Q31MQ1PDW0OksVfjosaIJk3TTTNJc5fmOc1hLYqWi5ZAa5fWea1XdCU6k55CL6V30ke11bV9tCXah7W7tSd0DHXCdHJ0GnSe6hJ1Gbrxurt0O3RH9bT0Fumt1avTe6RP0GfoJ+rv0e/SHzcwNIgw2GLQbPDSUMWQbZhlWGf4xIhs5Gq0wqjC6K4x1phhnGy83/iWCWxia5JoUm5y0xQ2tTMVmO437ZmPme8wXzi/Yv59M5IZ0yzTrM6s35xm7m+eY95s/maB3oLoBTsWdC34bmFrkWJx1OKxpaKlr2WOZavlOysTK65VudVda7K1l/UG6xbrtzamNnybAzYPbCm2i2y32HbYfrOztxPb1dsN2+vZx9rvs7/PoDICGYWMKw4YB3eHDQ5tDp8d7RwzHE86/ulk5pTsVOv0cqHhQv7CowsHnHWcOc6Hnftc6C6xLodc+ly1XTmuFa7P3XTdeG6VbkNMY2YS8xjzjbuFu9i90X2c5chax2r3QHl4e+R7dHsqeoZ5lnk+89LxSvCq8xr1tvVe493ug/Hx89nhc5+tweaya9ijvva+63w7/Uh+IX5lfs/9TfzF/q2L4EW+i3YuerJYf7FwcXMACGAH7Ax4GmgYuCLwlyBsUGBQedCLYMvgtcFdIZSQ5SG1IR9D3UOLQh+HGYVJwjrC5cJjwmvCxyM8Iooj+iIXRK6LvB6lFiWIaonGRYdHV0aPLfFcsnvJYIxtTF7MvaWGS1ctvbpMbVnKsrPL5ZZzlp+KxcRGxNbGfuUEcCo4Y3HsuH1xo1wWdw/3Nc+Nt4s3zHfmF/OH4p3ji+NfJjgn7EwYTnRNLEkcEbAEZYK3ST5JB5PGkwOSq5InUyJSGlLxqbGpZ4SKwmRhZ5pm2qq0HpGpKE/Ut8Jxxe4Vo2I/cWU6lL40vSWDigxGNyRGks2S/kyXzPLMTyvDV55apbBKuOrGapPVW1cPZXll/bQGvYa7pmOt9tqNa/vXMdcdXg+tj1vfsUF3Q+6GwWzv7OqNxI3JG3/NscgpzvmwKWJTa65GbnbuwGbvzXV5snnivPtbnLYc/AH9g+CH7q3WW/du/Z7Py79WYFFQUvC1kFt47UfLH0t/nNwWv627yK7owHbsduH2eztcd1QXKxRnFQ/sXLSzaRd9V/6uD7uX775aYlNycA9xj2RPX6l/actevb3b934tSyzrLXcvb9invm/rvvH9vP23D7gdqD+ocbDg4JdDgkMPDnsfbqowqCg5gj2SeeTF0fCjXT8xfqqpVKssqPxWJazqqw6u7qyxr6mpVa8tqoPrJHXDx2KO3Trucbyl3qz+cAOtoeAEOCE58ern2J/vnfQ72XGKcar+tP7pfY2UxvwmqGl102hzYnNfS1RLzxnfMx2tTq2Nv5j/UtWm3VZ+Vuls0Tniudxzk+ezzo+1i9pHLiRcGOhY3vH4YuTFu51Bnd2X/C5duex1+WIXs+v8FecrbVcdr565xrjWfN3uetMN2xuNv9r+2tht19100/5myy2HW609C3vO3Xa9feGOx53Ld9l3r/cu7u25F3bvwf2Y+30PeA9ePkx5+PZR5qOJx9lPME/yn8o/LXmm/qziN+PfGvrs+s72e/TfeB7y/PEAd+D17+m/fx3MfUF+UTKkNVTz0upl27DX8K1XS14Nvha9nhjJ+0Phj31vjN6c/tPtzxujkaODb8VvJ98Vvld9X/XB5kPHWODYs4+pHyfG8z+pfqr+zPjc9SXiy9DEyq+4r6XfjL+1fvf7/mQydXJSxBFzpkcBFOJwfDwA76oAIEcBQLmFzA9LZubpaYNmvgGmCfwnnpm5p80OgHokTI1FrHYATiBukI1ouwEwNRKFugHY2lrqs7Pv9Jw+ZVjki+WQyxT1qvCywT9sZob/S9//jGBK1Qb8M/4Ldr4GW4mA0AkAAAA4ZVhJZk1NACoAAAAIAAGHaQAEAAAAAQAAABoAAAAAAAKgAgAEAAAAAQAAAZigAwAEAAAAAQAAAIcAAAAAx3WaXwAANqVJREFUeAHtnQe8HkXZt0VIaNJCJ0AChCJFmnSUjgrSUemJILxAKKK+YgGBV18E6YKINOlgo8VGD9I7SJHqC5JELLTQEfi+6zrs6GTZp57nJM85575/vyszO21n/zs798zuyTkf+lBYKBAKhAKhQCgQCoQCoUAoEAqEAl2kwKfpy4nw4S7qU3QlFAgFQoFQoJ8rsAD9nwj/DxauupbwOlWqRFooEAqEAqFAIwXWoMBCcBe8UlU4HEyVKt2f5n1bqgu7OQN9+mgX9iu61HcKeL+H9F3zbbe8ZNs1o2KzCnyyKPgU4eRmK0W57lZgOrp3OfwVRnVZV3enP6/Cf3dZv6I7faPA/9CsE8vn+qb5tlvV6TkOLwGfl7DmFBhOsfVhWFHchaxpK8GMRZrhvLAY3AC+Htsf5odZodc2Gy0sA1vBV+ACOAi2BLdLZXPwOfEMJJuHi1FkSXHDoVDPvGFzw1wwO3wE1FPmgEY3yPrXgg/156Fds9++M3WQeC+XAwdIJ8yH2kH3xU40lrXhitSBfD4cC6PBfue2LQcH5AkDPD4n15ePvzQeTW9klk3j0LGYj0PHYiM7igLeZ8N2zXMuCCPBHfmy0Kmdh2PF/p0FvTH19ZlV04T6qJmhGvocV5n5qazPtuXEurNAN9n6dOYxmASPwKpwBriQdYdyN6jDD0Fdq/DZnwnaMgfkGLgKqho37XHYDaYDbTQ4GX7ZgwFin+I6HoD7Cu7NQp1tvdcFh5J/f4H1jduWoceXgwOylp1Ihjr/oFaBJtL9MOc57wHvTbqXPyeuA+ut+cDdAi/DF3rbGPU/BhdD3tfUZ8MTYHrQ4b4Ch8NgsBFc5IPguJF8HN7Kcb1xtAn5acxZ17hjIrXzR+KuXGvZfmSoveO13nivVd90J9prwHE4EdI99ZqcyDphTni2e0ybjalT0iXppFaJpNcVpJX7PCdpt0GqZzvWS8eXEZ8DusG8F46fPWBPULOX4EpYBm4G00bDmuAcfzKY9iewjgvKVaAtczWgMDYoejVv3lhYBz4Lx0LqyNHE3bW8DJZfGwaKfYcLSQ+zHj9pYuj1rgVVNgOJDnS1y+ukuCsHV+czQpWptWUdpHNVFWgybRvK+RB7vnRuwwOgU7YyDTlpPArG27XtqZg0dvw5DtV3OdgCnKDs+/XwchF3LA4G246LfAAci5LfS+MHQi1zLD0J5ToevwK3wDCostVJVGvHT2/urTto+/8E5P34GcedMid5nxf7u2sbjbqQq6XvZPJ0jnIeDIXcRnLgyj+/thRv9Kzn7UyN+Cc5ifOS9/xwsJ93wqyg40j9tlyy44mYflZKaCfUw9pAOoE7lAPAwVFls5H4O7C8N9XQAbQgDBQbwoW4m3Mn4ABM2qSwnuAOwuHwKXCQWedaWBdMr7W99FxpEunEBDof7TlJ+/ClfvveupN2Ao2l66vlNOudz4nMyc42LgJfVZRNp21eugY1XbRcaAAfp3G4baZB0kIn4fNbZe5UHVOrwh/AOvfBZ2AxqFVvKHmXguWPgd6aDsDX6mmnYbv79bbRUv2tObZdx0ateatU5d+H6Vm33ilgOwmfYec1Xy2rS5UtT+KTYB0n8KPASdoxWutZJ6sl814u0QaLZ2dx/OgwfE7Hgf09FDTfDpwEu3pQ2CyEN4DldEBtmSJcBTYi14CDspE5WaaJwXpXgjdqoJmTmzfjVbgZkk4O5BFQzxyYOmsn+KqJs1zXh9n2r4Zag7lcp9HxshRIfXZycbLqpH2cxtI4cOJqxXxok0O9lfhH6lT2PJMh6TNznbIDNevw4vqTs0j3tdFixOfy8qLuqoSNbEsK2LZjvFOLRhc7jr/U504vdIbRts+Z7R8G7ZgT7xWQ+uiiudFc6PP1W3BsngYjoC9sLxr1+tSwFXy+5gBNJ+V85r2YAF7nilDLvPb0zLXqtHva9AF/CpKg1xGfvSen8T92NL8ZyRM2rtm/SviAOdCcAL8OSSvD70A9c/dguZ/VK1TkjST0gbb8aOiUHURDtpn6MV2nGi7asT2vz/ZdoboSataOo2Dq26cbVHJcPlCUt95gs6FcsM+bznwbSA9+0t3Jo5blC525axUq0n074QLHds8o0joRuMpP99qJstMLHfuYxrqTaiPHYPmyuctyQZj6OY54vfH8GfIfK/gCYV+bi9RWqdLZ3ZXX+CeoNx4cZ5a7E+aElsyt27WQxHR1njxdsw3lE4Q7moFo63BRauTDlpxN0syVRL0b9OWi7gGEjexoCtiuzqydh6Oq/Xzyt+0Dqwp1IM3XCLb/MqzVZHvDKefDaT1fK7iTrmdOsJeC5beoV3CA5qmXY8OFjqt1F4NqkXRfingtW4cMyzWz0Nm8KGv51aFTliZ/23Uh0hemRpPAc7Qz1p3DrJuot2j+NuV08jrjFaA/2WF01mu8COo50BOKcmcSpgXMmsQdT1NYyswTj+RgoyLhFcKvgRNEK/ZMUfhJwqdaqdiPyiaNbqLPToSuapKtROQT6aAiXLtIu6YiL0+ag4NU9lHi/8gzexF3tZNPPNf2oq16VR8hU23cZWxfr2CW5zWnvln37SyvKprek1vWFfBgs8W54FHwELwAP4Rk6r53OqgIk6NwEdnIti4KqPHTjQo3me9CZ7Ws7G1ZvJNRdXEsai5CZu6JNf/PhqWil5WOPdS5/xy+B07Q28GD0F9sKB39eNHZuwjfrdHxWUlfscjz+t4Dn9nTID23RKstX6XoyU6vLtYwdR9KWP9yqHJiDRvo8gIz0L8r4RXw4dYU12OvW64Gb1rZnNzvAx9U4/VsaTJdDdleo9du9dqZkcy5sgLLEU/9tC++Eu0Lm4VGdaKeSyfWzIO9flE+9a/RrsTvM5fBWVBv1UX2gLTDuSq12qW4urkJHVtJv8eJu8Mum5P7RWA5x1k983VKatPdjnXbMZ8bx2G6T447x1/qq98t+sqOp2HPMwka7YrzPthX57HUR/s7X16A+IpwM/isHgCdtDlobE6omks6eR7Hja/GvE6vp5bZnzvAch8D5/cTwfnQt181zZWghZKQTpb56qJmxYoMRbadwyvyBkJSeiV2Cxej4JpCu8VP+jnY3DaWzYfIMj6ojWxXCqT21m1UuCJ/cdIOAx8Qd1qe01Vruj+2bZ/7chHgIsXzNPtgO9mlazZ8EA6HJcEHrcpcVenMBps56VwBPqve62QuRnINqyY9J8n74H4YBvUsvyeH1CtYI89zfRHOB895MYyG9CzYV9PLEzdJHbP8WWr0ww/5SRfg4AlIepYdrI7dtwu+1t0EOmEuPLcBdVKXe0Htdoa+shE07DV6LY3GwxlF2XGEv4V7YDjUtbXJfRmSkA5cVxzt2EgqfQ10WgPR1uGi1OnM0sU5cJN+VfkWP7AoU/XQm5/bCRyk9pxgW7H9KTwRrO8kcg3o9Ey7HVK7hxLvS9uZxtO5mnmwXS37UKU6KXRs6iTPAB/qhWCw23AEeAJuhdkyMUYQ16En7a4h7k4vt7SLdefXyHajQGrLiboVW4/CTpDWfxJc7Ni3l+AGSO2WJ26yOmo6YMe/5zuuhZbXKeqkfvr8as5ttpPmzJNM7ICpbxr/6uQ87P1Lz/IxxNvdQVK1pjnXnwyb1CzxnwzPvzucAeoxM1RaciBWcEKaPSt1PfF3suNWok9T+NhWKmRlXU2PBW9oJ+0JGruqQw1uVLTzh1J7ToA+7DprbTNYBJ71oLC0q7k6JdQIHcDpFZoO4tUa5aqSHfhfAR+ob8Ep8AZ8Bi6ENSDZtSnSR+FDWbtLZvFa0X+QcTz8CGbLCjk21y34EqH383/hXBis5qQ5Cm4AdzHJniHiynKPImFjwk8WaUXShzYsIo7ZRjYiK+Dk16ztTMEfg/dRR3YwvAArg5PT+pDsFiKdfuZT24ZvgQ7Oc7srce5rZn5LOlG8x67hX+ufBlv1pLz/zycIXBw5ftux6amkVnsWlY07vm3P+Xk9+CXsBKfC/0EnTS10Fu810aj36eyCJoq/vzV14FhRylvuphrpUCEnj9SPTobP0a6vtnprDswrwcl7iYrGvEl5vw/KyqTVuQ5j7iy9KjoHiQ+AbVk+d/4c1jQdezr/URWlXCmmfCdpH5ZGNrRRgTr5+WuQ0+uUK2d9lQTHYeprVfgy+Y6XwWqHceHqsmOFAGuR5hhNunnfkzlheay+S6XEOqGvUVM7i9Upl2fpXLw/1nNSHgK5lZ8T+1vPZq6X2UReevZSf2Ztos6HKXMFpGv3OdwU7oVJ4CI85RluA+2Y53FOSW2dUNHITKS5KLXMkhX5XZ20OL3LH+ZmJsC+uiAH/6pNskpRzjBnZY5zVuK4UzdFJ+XEfAvoBMo2nAQHXxosNxNP5dJkmz/s5frp2InfgWw7f4RmHgh3TC8Xde4jrHIeY4t82x0HrpxqmQ/1FuBqbWitQg3SR5GftHCiasXWpPAxoNb5+EztGf4VFoVaNoQMH+CBZt6PK0Fdqib9fEJSpwngc67ND44Px+ZcUM88zwVgG47rEdDI3LU/DtaZDOtA2ZYiwXzxebJPZXNsjoEz4fwi3I5wRmjV5qSC85rnewAaXTdFep4f+5b6eQ9x9Va7VaHsxK8lrZ2+HUK9dA7vSb5z57DHNuZftfSNwAw9Kf3gn9RR389KskeIuJWdFqbQ3shuNR/SUTAenMzLNpEEHciXiwwfrk/CONikSHPCbGTp3ljOQfVugwrev4Mg7XSuIf5cRR37kuxOIuV2VyNNRzgS1oMN4G7wwXkbWrV/UUEnoGPWnDTK5+zJqPjndtLEB05nqZZbg31K12n6VnAylM0+nw2PwffgPWjXlqNis/1udA774QTcG3NFvgyozz8qGnqTtAsgjbnhxPeFr4F1VwK1eRHqmfdruqLAc4S+SmlkX6HAkkUh+1f1PH8ma+RR4v/Mjo0OAfu/LvwGfB68z3vA72AM/B2aNcdu0kn9dZyNbAkKjMoKrUL856COz8NMcCdsBNrqsCKY1qx5X8Zmhb0nXqsOd3pYDGz/v8D7cBw0cw8o1j2mYMmDGl7Ui64dTt0jQJEGoh3KRanRrnUuzoHmaiNpqnNRDx2PactAI1uUAk7slr8QHGz1bHMy0/kMnYzLNg8JaRVnmTXLBTg+FybBXeCDbTnjTvLtmA7ACcZ2roZZoJY1u9PYkwZ07rYpx0OV7U+i+VeCk0G79nUqpnN1InyN9ka025minhOvfal17RbTkeT3+z6O54M0hscQb2QuXFIb9xK3fj1z3Dp+kk7fqVE4PQuW+1ZFmcNIc/ynhYnPz8rwF7DOJdDKHOPz43Nk3YlgPxuZfbd84n8qKuyW5VtOB9CKfZHCqX3DP4J6q7WkPJ3W1tCvLN0gLyq3O/KDFuKLUVZPeyP0Oy/bxHWq12rwKtxcp7wDZDxsUZRZj3BDWAoegH9AI1O/NOFOR9wHpN4KOh98nsNVe9mccFxhaU/C00ZK5mJDJ/AG7ASbQW9sSFb5deI+MFX2eRK3BcePzqOe/YrMMbB2Uahq0lO7tYp8r9UVfbt2FhW9B++120Cp3ksc/6WU1urhxkWFG+pUdJxdC+mer0R8c1gdHMO3QCP7FwUeAdtQgzRnEK20DUhNTsECv6go5ThcOksfn8WNzgX2cxQ4Ho4AnwcdpPficPgCnAbjoRlzHOosteeg1jjsKcA/Xucq6YDQOfLE7DhF3U3dD2qr7Qg6fZ1YM7ZxVshn9iFw7MqLcC7oXG6DfmeKqCnGXyENDB/ck6BV248Ks0HVjWilLbeHnXqY03nfJtJo4kpla4U+GB8FB9vztQqR7rl8EJKDURMHnoPQlVu9umT32Fv86yDTRoL3ynarbHYS7Veyx4n8Mx1k4SZZ/FHiTkBle40E6ZT5YKcH1XadKMo2lIRdwUlnVmh0n16gzDOwNmi3vx9M8e8cHKXzjp8ip/UD79cPoNGk1HrL7dVQL6/NZ/bBBk38mPydID3bY4j7WsYxXHX/SZ7CHIdp9+wzmeaMKQplB/nO+QHSq8ahz5EOS9P5/7kn9p9/XOCsVhx+htDXn+mZsc1kPk/j00GDUM1GFmWmI6wah0V2T+CiZdkswefFcVc2Nfw9JAejztvDSdDIZqaA4z2ZDvSL8C406l+q09VhGiyT6eXfIQ3CRYg7aZnerFl3R3BFdXezlSrKbUTacdDph9lBvBv0ZvJcjPqjYDw00uYmytwPaeCNIa7d8n7Q8N+3KJEcjIMw3auqig5UH8pkD6dIKcwffidlB7LtOrHXqkNWr8wHO5nnckVctnlJsA/eG2lkc1JgRFHoFcKrswqO3cXBycE2dVYLgPf+WpgE7Vinx2M7fUh11GsZeBiqJvBUzvApuBF28ABzPPpsj4eXoBl7ryi0CmFyNlX1HK8fyTL+QtxVeNnyhY7X8LeiwPKEfwId5xmwGfwGknMhOsWvnnIcNGuOw3QP7efbDSo6hpbMyvwhi5ejp5MwGtL8+TniP4VGc4SLr3kg2R1EfO4HjKVJS898J6RVxUjis0EjgSjSY05u54F1XG30xvv+hfpuyV1ldNKcWKomt1bOkR6MeoMttaeml4EPdG75ZJinl+MONB++FcAH3AekluXOyDIO1LI5kJ1wk40vIkcT7gmrwhNFWicDH6JkE1OkFC7O8ZJwPziWdAr1zAlSZ6+Ngz/3xN7/MOrYySe5OTj+SZH/BcKfF/H+HIyi8+r1a3i1iQs5nzLJwaid5gKoWXs8K1hvHDpO8+fWe1E1F6yTtXcPcSf+LeEK2A3s7z7gmP0b5LZ+dqDjbNYch8nBuOt4vUHF9Uv515WO88P/42A87Fgken3rgWOznjm/5s/Em/UKF3kjCJ9polzXFVmQHjnBeBPkbGjGZqLQT+EVSAI3U69eGScZB3InqbfyqteXlOcAvRK8ziVSYoPQwTAJkqY3Ex/WoE6e7crIug7ENKHm+SnuQuESSOdZNmVk4XZZvhOGryHnBft0DeRbdQ57bC/+tc07IZ+0ezKb/GddyqV+7V+jzneyMmvXKJMn/6wory6r5RnEvaaF4Jfgeb9fHJuWT34c9ls7gZ57bTs3eQXeO+9xug+OYR1UszaagqmujqCefZXMVHa/ioKed0JWZs2izE8J3bksWhxXBY7Ru8D2b4CZoVlzZ2v71vVZqWczkqmzs6y48Jkb6tnmZKbyhtZvZs7Jx/6X652AvDHgfLIx9EtzwPrQJqFOJK4DqWWrkHE5uOLcrVahfp7uIHHSGg0vgTfY69YJNmOnUyjpeVYzFbIynjPVdSdTzw4lM5UtO/rtyXs4y7+UuNe1VpF2IGGVJQfjQz1bVYEm0g6jTOrX8hXlk+NOZa6izAIV5VLSN4ikst9OiaVwLo4fLcptUMrrz4fD6LwONd3LHYh7Xz4MjWxfCiTdbiHuzq5ZW5qCOiXrN5oEN6NMmkNOI57bKA7ug9SPx4n7bC0Axi+CejaaTOt6b3UYrdgnKJzOW+saXIDMAPYzOSPr/BzqOQvrLQj5tTkn6giGQj3zOtK5XDhVLYLmJF1nbZtPwUjot/ZNep4GiOJeBw4aVx4OBMV3FePD7WSrqNvCQLS9uagrIB84auJ7YleEx4IDsp45iSc9x9QrWJGn5unBrloN5lWcVB8E+3czOBE5MRwKDsyHwIfY/CdgRbgaHoOFoMp662B8KMdBOufwipOkycUyzxVl7yUcC441H1z79wm4GCwnR0Et0xlbZgK4U+vvtjYXcAncD2kseX3Pwq1wBswK9Uwdve/WO7NewYq8YaQ5pqzruRrZLymQ9N+Y+AjYAx4HJ1MdnPnyGfgheF2bQi1blgzHsc+er1RbtXyn4K66bPuScBFcADdB6p/h3UW6429/yM1dlHreBnkd4xPhQtBx6CRqmfOM5V8E++lz7zUuA4eB9938y6HdhR5Vu8ecnK4BLyrnHo7ThGd4PDhwB6I5YTsp59dfjl9B/kwNLn4o+deDei3aoGw520GZHsazypkVx4uQ5iBM/fSc4qRgW1sVx3n+NqTVsr3IsGy7O5j5qJucs7umIVC2dUjwHFfDLKDTzidRx5xOMPXZ9naBenYAmZa/Ehrdn3rtdEOeuxMnqHT9VeH95DfzHKqt9XeCVs3xZ13H4xwNKruwcNJ17FknhY7Nj8EIeBLMSxxNvJYtQYbfc+6EdpyLGl4CnksntxDkNoyDWyH1pV54el6RuNdTr7x5OtVGz/6ulHFBZPlXIX8Gfs/xPjAD9Cur2o6lC/Bh3w5GwdIF/yR8Bh4Eb4gTz0A2V7+zFxfojdd8eN4Db/az4GBoZK46nGyfalSwIv840r4CN8MW8BLUs5nJdIGwCrwIt4MTdDIf1s+C99576ENby3QwP4G7YUNwomjFHDe+ztB2h5/2xKb8Z2cOv1DwRpFl/3eAhWEZeBcmwKXwW/g71DInk4vh83ACqJ3m9aZ72JPQj/5J48drEC1dj07b57KeJpbXHLNLgruAVs0J8DxwDKwEf4ZGtgIFNigKXUfo+H+zONYhbgou5GzrSqgynz8Xu38DHWN63r5E/B04BxrZ3BS4Fuz32bAHlG1eEuYEdfX5dhyl0HHjsXn29W3IbRQH6X5YNo0z07w/Pof2v5EtToHlYUXwWRB1mwSTYcCa4g4DJ6+wqavAxzmdg8tB62p/apoOxvO2u4PROVrfB6S8aiSpx3wIa40rx50PvWPPybEZc8JyAvW8WxcVfMiPhKWK4whaV8BJ+n5Q10Nar95WDceFbwnGQb4T/QjHf4DdoRlzYWa/Ze1mKkSZUGAwKfAzLtaH49ipfNG9cTCuUJ8o+n30VOz3iOKcLxMuUJzXXZK7OB1VWPsKHEhVx+HVUGtR0H7rU9Z0QaFjcdezG3gPdynCfQm9v1tCI3NxcSXY78vA47BQIBTIFFiT+CswEUZCX5qvYxaFheF08MH0/fdGMBLmh2YsTUb3UrjZOs2026hMcjC++tOhrA7uaJqZjCgWVkeB+ci7DxwTn61TrhNZxxfn8Vy1cJw2Mp+dyQVrNCoc+aHAYFUgTfan9bEAB9B+rQfa9D9Co9XrHJRJr1PGEp+aNj0n8xuMfb0F/gbuxMI6o8D+NKO2N8MsnWnyA60MJ6XeGDRvEszzgZofTLiAJMtf+MGsSAkFQoGkgA/zNeCrgU+lxD4IdR6LgA+5LJTFPfZdfCM7kwLpofY7ytQ2ncxWMAbsf1hnFTiB5ry/3+pss1O05hh0h1KLZnbFo6lvP91Fu/sKCwVCgToK+JA8CY/CR+uUm5ZZ6aG+ik74MTZs4CmgA/f7iIudTbv08lalX75S9ln5WJf2MboVCnSdAovRI51MN07gq9AvH+qrIf+pHw7DBpgC7nSvBSfwlbrs2uakP74efQIW77K+DaruuBIJ618KvER3rwHvnf/H5R3oFpudjrwIX4E3u6VT0Y8+UcBx90sYAn6XewG6xfzRd53MYaCTCQsFQoFQIBQIBUKBUCAUCAVCgVAgFAgFQoFQIBQIBUKBUCAUCAVCgVAgFAgFQoFQIBQIBUKBUCAUCAVCgVAgFAgFQoFQIBQIBUKBUCAUGBgKxP+DGRj3Ma6iOxTw/1/4K3389TjvgsdhnVVgWvzqoc5ewSBqLRzMILrZcal9qoB/nuAk+CR8Cd6AfeE60NmE9V4Bfw/eN8Df5PwMPA9hoUAoEAoMaAX8tTi3gb+Xa0bwt0l77C+FDOuMAu5cToe1YUXQwfTVb3Om6bBOKOAf9QkLBUKB3ingTmUCpN3KW8T9K6A3QVhnFHiPZh4AQ/++j79lOd7AIEJYKBAKDFwFXFkfDw/CEpB+yecXiA+FsM4rsDlNXgzxjavz2kaLoUAo0GUK7E5//LsjcjMcBN1s/dnxrYmwvirz7UstB1MrvZvvyYDsW2wxB+RtjYuaygrcx/l8ffM6jIJd4RXwO4zm3+75Z09s2v+zEF3YD+6Gf0377lT2wD8FsAKsAUuD+uk0nK+OBHcv+4C/kv9tKJv6+z3s1nJGHIcCoUAo0EkFXPGeDKfAIdDpRZV/Ayf96KyhH/gfAl+baTOCuxp/rf20Nl/h6VhWm9YdqXN+HaCOYyK4I3wWdBT+wMTRRdzj38NQqLJhJPoNbKeqzEgLBUKBUKBTCoymocvAyepOqDUpkdWy2ZYf9vOfZtKhOAF+GVx5Hw5OhivCtDT76PV/c1p2osG5ZyVfh/JVsL97wcMwN+i8fS2moxbj9WxVMm3LBUY926peZuSFAqFAKNBIgXko0BcOZg7anQybQJoAP038EZgZnASPgC9C+vhPtC2z/V3AsB2z7gSwz31h9stXU9P3onG10jmrnbY1uBvMHbjpzZh1zoHLwIVAlR1JouPCXVNYKBAKhAJtKeArk75wMDqWnxZcT+hfGr0U5gVNB+OEOdyDXpqO4R5IbbfSnHVvh++3UqnFsrNR3v7N12K9VFytzoTjUgLhWfBzMK8dc/fifV+rorK7pdtAp+tfvwzrAwXavXF90JVoMhToMwX8QFxlrrpdcaeP3b7e8qOxk1IzlpyKz5ErZs/zGrwDmu3NDu5ytgFX0+1arWtopr3lKOQHc189VZl99wcUkrniV4dWzP71po9q9ldQe/VcGVYAdzFJT6It2ROU9v/M2IbOJDcdog7oCng1z4h45xRod7vduR5ES6FA3ytQdhhOqKfDSXA1uOo+DK6C8+BT0Iy9WxRyAtSJvAz5ZOh/uPR12X/DjdAbK19DK22tXxR+tKLShqTZt6PAiX1/cBd2LLTqMHrTR073oRPB3YT3ZTRsA5OgXVN/HYzfY9Jrtx2J/xi8/5oLgFNgBw/COqtA7GA6q2e01p0KpInSCTDh/wjfAFzdO7H5rv/z4CsaX8usBo9Db0xnswvoiJIzare9dA2t1neHtgzcAWmnltoYReQnoFP5HTihXwnj4DS4Fy6CZqzd/uVtP8/BV8CP+DoH71Fv7G0qPwcbg4uKN8D7771YELQn3w8+VOV8i6wIQoFQIBSorcDcZDmx3Am+/kn2IyKmfyMlEH6hSHNF303myv4emLfFTjmx6lwkreJTE98m8k34NKjDdeB51MnjdaBZS9+I3A12k32HzngtC2Sd8vuLeri7tN9hfaRA7GD6SNhotl8okFbdf856m9Jmy9LKUSfRQ8uJLRz7Leb6GuV9bT0Wli3luxPxvEdC/hrOYr6a01lU7ZLSa3Cvq7wjmECau5QtQDsOXoI9YX64BcpWq3+m27//hXL/XiFNR1bVP5I/tBi4c+mNeV53K2V7ukgYRpjyvberwwUQ318Qoa8sHExfKRvtdpMCrmC1FL5/9J/jfOJNZZKjSWXz0Lw0cefpnYi7w/KHA8rnT+f0vOW8en1J11PVt3NJ9HzfhclwF2gPvB9U/juE1Kr+pX6lsLJyjcR0bTWyO5Kca7Zh0eLDhLWcXkdOGo2EAqHAwFeg1iuyU7l0J+DtMwnSKzJfn3WTtfuKTGdwHfjaa6aKC3Jl/yxcC+VXaBXFayZ1+yuy9M3FC/D7kvd9LQ+wRSB/ddqTGP/0XoF6K5/etx4thALdoUCtVXzaueSr29TjqrSUVxU6QTmBJ9Kz5autlObqf2qbr6v8gO21Vk2iy5C+MPiqzI/g3Wg6vqq+N+qrdXzVp/nBX/sIrAQT4U9g21fAqhDWYQXSQ9DhZqO5UKBrFPB9+4iiN04uTji+Gl4IhoPmJONKfh5YAjTrueptxtHoOL4K48CdgD/iuwJo7o7cQYyHPUCHMzXNV0BOpGtAlYP7ZNGZ8UXYTYHa/xDccVwJW0ErpoPx4767t7eKis55LjgmgU7X+2b+bRAWCoQCoUBLChxB6bvh9oJ7CD8H90GaWPz28Ev4OaSy5rmqnwuaMR3S1fB7mL2ooCP7FpwAvobpjXNp9xUZp+35gQEn1fJPhTmBHwWPgO33xjr9isy+nQR7gQsAnbPXsBE0a3NT0O8svgrNzTYnwI1gnucKCwVCgVCgZQVcxTr5zwIfKeKuYo2LP7Jq6GssJzLjqazxZs1zvAxHFBXcIZ0LGxbHvQ1642C8jjvg+xWdUB816K112sF4L24FdxbeD4//AmdCsw5hTcrqlNK3FqL/tnmJSVgoEAqEAl2vwAb00MlMh+I7/kvBXUunTKe4K7S7C9qZun53SLsroh01J33718mfTPX13ZZFL10APAPHg1o0Mp3SOeB98AcdwkKBQamAD6YPpSvJ/mb23ff6PvyD3Q5HAHcwo8HXMg9CN01s7lL8PvQN6I+2DZ2eDCs22fmPU87XYH57CgsFBqUCq3DVP4Zz4U7wNUt/sZXp6E/gHLDvviIZrKaTvQp8hfM12A7SboZo19hi9OQeWK1retRcR/xhjIeg/A2pVu1hZDgmv16rQKSHAoNBAV+lOEm/BE5IPhj9xXQwOkf77fv9TrzHp5l+aen7y3eL3vt6RmfzC2j3lVbRVMcDJ+tDoL/sOuenr44vX5eppTsSd871bDcyD6pXIPJCgcGigK/G/JDZ3xyM9+ejRb91NIPZNuDivX+GyQ4nYtpI6DZzx9UfzH6eAsuDP+SwHPwIwvqJAs18LOsnl9Jvu+lqTPqjbVh0+ub+2PkO9Xk92vEDuuaPxaaP3H6H0dwtODF2k/2rmzpToy/OTS5cxoLfs14EX5P9GcL6iQLpYegn3e3abuog1PI9SA4jxe20ae9Ael3iyjalEZ3CwbhqmxVeg1oTgfm+hrHN9HqNaM8Hd+v7cFrfj8zukPw4mptlXBHaj1fhTWjWPLfX+jr4Y6Da9e8Hg+5ftf0cqOGJoLO5BZ6HdcE0NTaeHA7RsCYVuIhyv83K+sy42w/rJwp4w8J6r4A/SrkH/AXU1J/Zd5J/A3Q0c8GFsByMAM1wR3gb/gC+W14V/DC5ILwAZ8JvILcdOPBcrpbng3EwFnQmZ8NI8Nw/AlfWOpIT4BLQFgUnPs/veZz4xsBEqGe2uTd8DmaHX8P28ApsUoQEU8XU2Ik7LBQIBUKBAa/A4lzhGHCn8CxsDZvB+eBEeDT4fyLWgUfASX0fcCfgKvgOsJyTtk5Ip3Ad2Fb+4X8vji3n/zew3nbwEpwC08PmcDlYZgJsWsT9iRqdgv20zVPBHdBH4XawP/V+Csy2r4CHYD1YFqzneWyrtwuV/WjjtBY4lrJDICwUCAVCgUGhgBNemtyXKa7484ROwkcVx+4yboRPF8cGOoo0Wa+Vpe9G3LruQjQdjc5BB6Vz0GaGa0EnMy9oO4H1LgAnfn9VycagM0v9W5p4sm8Tsbz1atn3ybCMO65kXydi2r4pgdBz2Dcdn86rWdMxjqlADfL00RzL7qDTCwsFQoEuVsAJIawzCvyLZn4BW4ET7JGwLfgKaQv4HswK/tqO2yCZTiDtAJ5KiRWhzmdh+BOcnOXreNx9LAn/gNSWjkgHYD+0uWF9I9g34L2e2H/+dOwnOL6oSMsDHZdOZCL8rshwcl+hiF9fhDrPs0AHsw1sDfa1GftNM4VaLKMmv2qxThQPBQ5GgntChs4oEA6mMzqmVn5PxInYXce5sAr8ENwl+KOW68N4eBmqLE365ukccpuzOHiO8DpI+e5gnPB9zaalNp7uOfrPP97r9BrsJuJv/CerZ7fj668q25REX6/5iiz1Wye5KuhAJoH2FuwNltXBtGL2zR1gs+Y1er56Zr47trBQoBUF/t5K4ShbX4FwMPX1aTX3RSqMBx3MrvA4XAQ6mM/Bx8HdQ25OlslZ5OlpJ5LS/lxE3CH8GianDEJ3D+9mx0bLbepQdAjpu4s7nGQ6qA+ng1K4TnF8J2Fqczhx27kAbPez4C7kVRgKrZiO5RRQm2bNXeFWkBxeVb03SbTdsFAgFJhGCoSD6azwOouLQQfzTXBF/xS449gM1PtBaMbSZJ7KPkDESX4NWAw81pygT4bj4DFIjsK+5KZDGgc6hk0gdzD7cPw6nA1le7hIcOeUbNsi4qu+L8HK8OsiLQXl/qf0cvgvEnS6vj5s1nS+9ZxLs+1EuVAgFAgF+pUCvsqaAM/C3EXPxxI64R5VHKfAnYAf158B83cDHYg7AlffphnqnNxlrAi27aS/GswDh8B54C7Gcjob650EO8BCkMwyd4E7LZ3fMNgSdFypr0SnsKU4cjI/Grw2600EzzEaboS1IZltmrd1SogwFAgFBqcCrgTDOq/AD4omDyZ0snVi9lvJXnAvJNuUyIHwNPiKa1F4EHQ8vuJxF+I3DXcpu4Ovo0bBd2BZcLdyN/wXzAQ6I3cE6XXZSOIngOdOZrkjYCPw/v8NbPs5qGUbkvEt8PXXo/BlOA0WBts+EpLpYJ6HbeDylBhhv1TA8eH4DQsF2lIgHExbsjWsNAMl1NbJPpkfxl9NB0VoGcv6EIsOQ6diqKWHu9yWdXQUWt6mjkizXrq37xTHpuc2Cwc6jNcg72deJo9b3vO+ArbvuUwrv6oKB4MoA8Acgy4iloQ0DvPLeoCDg/KEiIcCZQWcMMI6r4CTetlyR5DyfHDzyT3tPFKYypVD269qL2+rXKd87DcXadbKZT1X2bm425qnaNBwjooyRXYEXa7AWvRPzoCqcTWpy/sf3esCBdIqtwu6El3o5wq4WPk6LAA6SHc4TkLHwtsQ1n8U8FvdL+FiuKj/dDt6GgqEAqFAKNDtCvhDG37bq/rJvvT6ttuvIfoXCoQCoUAo0GUKuBMdBztX9MsfWjkSwslUiBNJoUAoEAqEAvUVWJNsf1WKP5SSmz/G/hJcCumHSfL8iIcCH1AgViIfkCQSQoFBq4D/1+oA8Efbyz9Esilp/tCG/4+q6qM/yWGhwJQKxE+RTalHHIUC/VEBJ36dgz+0k/+I+gvFMUFT5o8kLw17Z6XdyfjRf4Mi7V7CueDF4jiCUCAUCAVCgQGowBJc0w/gEdCxlNmLtGZN53Q6fCOroOOaAOV2/b9Q82XlIhoKhAKhQCgwgBRYl2t5CJ6FU+Ba0BH401+nwjEwHHJbKj8oxc17HPytE7n5H2eXAf/P0xWwEJgWFgqEAqFAKDAAFXCCnwjXgL9eyNdj/v8jdzK3w2yQm99afe3lR3qdRZX9hMRvVmWQ9lnQedXKr1EtkkOBUCAUCAX6kwK+ynKH4oS/ctZxf7JLh6OT8RtJMp3LheDuxDo/BtvIbRQH5tfamfiLTq3rT5iFhQKhQCgQCgxQBdyduEvxN2rnP0rs9xLTrgM/yidzdzMG5gO/p/iqy4/5ufk67ZA8IYv7++Z8/earuFoOKCse0VAgFAgFQoH+qsC8dNzdhLuY3NbmwPRv5YmluLsXy3w/S/f/t/jdxrDKdEyTwd+MPbTgMMLciXEYFgp8UIH4fzAf1CRSQoFuVuAtOndHqYPuao6A8XAC1DLzdBa7QHIo+xL34/3zUGWrkGj7j8LbsCcsBPYjLBQIBUKBUGCAKbAj1+OrrrGwOVwPvsZyt1HP/PZyPriL8YO9TuZxWAJq2WpkWP4o2B/c7cTuBRHCGiswfeMiUSIUCAW6TAF/PPmPsBH4U2HnwHfB3Ukj+ysFvgQLwuzwDzgPatkkMty9LA1+8xkD/uG7sFAgFAgFQoFQYAoF/I7i9xR3JTqP8gd/kiptSGVqJIYCoUAoEAqEApkC6xDXwZyWpUU0FAgFQoFQIBTotQLuYsbBIr1uKRoIBUKBUCAUCAVKCsQrr5IgcRgKhAKhQCgQCoQCoUAoEAqEAqFAKBAKhAKhQCgQCoQCoUAoEAqEAqFAKBAKhAKhQCgQCoQCoUAoEAqEAqFAKBAKhAKhQCgQCoQCoUAoEAqEAqFAKDBoFCj/IbNBc+FxodUKzFCdHKmhQCgQCrSswLepsTz4a2jK9ncSDiwnxvHAViAczMC+v91wdY4x/+7QuwWt9slVsW2If4PkPeh287eU21/D17u9sx3qn780cwz8Ct6Esr1YTojjUCAUCAXaVUDHsAecA/6J30OhVfPvjvjnfM8B/8jWltDtthId/AlcA3fCXDAYzGuu99c0B4MGcY0lBeIvWpYEicOOKvAUrTnBrgH+/ZFWzV3P0/BRWB382yXdbq7UJ8DGMCt4DQPdRnGBG0D5tzOvR9p+A/3i4/pCgVBg2ikwnFP7Tv7UNrvgH7lyB/Qs9JfdgH8EzGs+H6aHgW7uMg8pXaTO9U/gvfNPLocNQgViBzMIb/pUvuSqD76tdMGJyh3QPfBqKxWnYdkNi3M7uQ70Hcw8XKPXW969LEyajvYJeA3CBqECfogMG7wKzMKlO4G70Hgbyh9i/ZXu/u0Q8/3Abpk5wO8rL0Ets92ZwD+ta9lWzW8v9stz+qpJ83vGv3pi3fmPOy31egXWLrp4fRF2W+Cuyr56b1wApHvkx/lWFwR7U+cu+Cdoqe1N3j/syXMMVX34L4pEMFAVCAczUO9s4+vy1dWF4OsLJ0edwjHwQ9AcG+fCYuAE5Cuu5WFZmA9uhm+ATieZk8s+MAZeByer06EVW53C34RhoEN5DrTxPf923z9q4yT7edART4KPga+HjHeT6VQ+DZ+DpcC+5w7mTI6lWSfjPdoVNgfN9k+GVSF9cxtLfDTsAO5mwgaRAuFgBtHNzi7VHcIpsB7sAT8DJ8izQcdzMPhq5xzYCvaFOeECcEJZDm6C5+F/QXNyPRe2ACcUV+/zg05La2bS+gzlLgbrOFH5Xv+/YSI8ArmlyTFPqxfXce0JVf1IabaZ2684uCpPKMUt79+3XxnUxT7af53w+eBupltsCB35BXg/bwd/cGJ2mAyPgn19FpIWRBuajnU8PFmUdEGgHreB40In+wN4B56CsFAgFBgkCuzFdd4B7ko0dzFOPE4OvgZLpuNx0rkMnKQ0nY1lxUlK2wks930PMtuFuOmnZmlV0TVJfAkuhemLAvMSWtdJK53bSX1P0AEdBjNBMzaSQmNgdAW7kSbm5fGVOK5nY8m0fztmhZIO5iVzITczbAsrpMQmQuupRTPUa07tXBw8A+5evL+Lgg7xWXC3Yf/KVu+HKhwDj4E7obItQ4K6eE4XHmGDVAEHcNjgVMBXV7+GxeCbsCQ40UyCKvsria5QNSd5J5A8/IQZ2B/fD/79r6vXRuYE+HVw4jsL3gVtk/eDKb6/fJc0z302+IrubrCc/atnT5N5Tr0CLebNTXnPPxGuKuqqR9LhhiJtCOGZMBtsAzqZB6GRrUuB3SFp0aj8zRQ4D9SmbDqVneE74C5GexnGwz7gOd6A3Dbl4CSwDy46yma9G+HxcgbHGxZptxK+V5EfSYNEgXAwg+RGV1ymE9gxsAhcDE6Ia0B5gkrHKaRIz6ThcXIw7iJWMQNrZ0JxNbwxTAAnpWRpsh5fJMxKOBqc0HVkTvB/hh3gBGhkszQqUMp30s2vO8/+FAcLg7srJ2vNXaA6+GpIx6PplJ2Mk4MxrRlzd2j7atyM3UShqr7q4NyF+grsTEg2lMiSYF/fSolFqLP/MrjgOBi2h3cgmbtWr/+/UkIWfpj42sXx9Vl6RAehAuFgBuFN55J99XRJcelO7I+Ck/dYcEJbAHzNcUdxTDCFWSZNfIZvwr2wepZOdAqrmvxSASc7J+A7wbY0++Nk7UTtJLgV6Fh+Ae4AXHX/AzSdZCPbkgKHQ71+lNs4m4QflROL42FF6A7Kvmg6GDU4H5y07fOV8DrMCK2YE3q6R63UK5fVqc4PavhClqmTsK/XwRtZunOCqL3X5jWMAsdIMrV8oiClpTB3spOKxC0Ifw9pB5zKRjjAFXAghQ0+BTbhkofDj+Gx4vJdeTrpuANZB1yF3gtVliZpw8TNxPeGxUoVdBSa7deyNPE4CabJbgniToBXwMzgx+Ib4WtgH7WNwN2DE3oj+x0F7mlUqJT/z9JxfvhicfBEluirKE3HvDHsCDqY3FLf87S+jKut2uuokyP0fOqoHQxv98Te/0fHdmRx/GPC78GB4C5M04EcBPtC1bWY/1G4AF6DNeErcD2k+0w0LBQIBQaqAgtwYZPhGVgRhsHR8CzoMI6Dk+DTcDKYdinsDEvDbmBdGQ2Lw/TgpPISuOqdC7YGz2P922AXGAJlM+1KsMx8sBbcDbb1E/g2nAa5LcjBwzA2T5yKca95Aqib16ozcRL3WtVkHKwDySxj3jYpYSqGamTfVoK54YDieBPCejYPmY6Jl2HJoqBj4Nfg/a4y74vX6f1aFryPn4KwUCAUGEQKrMC1Xg6u6u8DV6TDwVcmV4BOSEfjKtbXRKeCr2w2g9OLY9ONrweak46TmTsNdz8XwRfhTrgDTJsNqkzHch7YHycwJ7S9wLr2Z35INoTIL2CDImHmlDGVQ52zenldajULqNddcBTkNhcH08rB2A/vi9p6r3Xao6AZ877bb538rGAba0E924fM28FxkMZGvfKRFwqEAgNQASfq2cCJMZnxGYoDHYb4iqUqntKmK8qnwAnfdm3HusZN83z1zPZmh7ycdWfMKtneubApzFSEToLTyuyDfUxm/7yGsk1rB2N/vLc6ifL9Mq+WLU3Gy/AsfAl0/vn94bDS1GBaOf7KDkViKBAKhAKNFDiTAk52txQ8RLgtdLPNSedWB3cCh4GvqVqZ5Ck+zUyHeQHYd193+m0uLBRoSoH+MsibupgoNOAVcOV8LDjZJXPX4/t+v8d0o9m/g8FXjn5k91gOgvzjOodda2vSM7+P+Up1B3gLwkKBUCAUCAVCgV4r4KtOv7V9vNctRQOhQCgQCoQCoUBJgaGl4zgMBUKBUCAUCAVCgVBg2ijw/wG6Rc0JOoFHIgAAAABJRU5ErkJggg==)"
      ],
      "metadata": {
        "id": "R4F_SDodpqwq"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "S = torch.Tensor([80]).requires_grad_()\n",
        "t = torch.Tensor([0]).requires_grad_()\n",
        "sigma = torch.Tensor([0.3]).requires_grad_()\n",
        "r = torch.Tensor([0.05]).requires_grad_()\n",
        "K = torch.Tensor([70])\n",
        "T = torch.Tensor([1])\n",
        "t2m = T-t\n",
        "\n",
        "d1 = (torch.log(S / K) + (r + 0.5 * sigma**2) * t2m)/(sigma * torch.sqrt(t2m))\n",
        "d2 = d1 - sigma * torch.sqrt(t2m)"
      ],
      "metadata": {
        "id": "7yjo1vjyoA6k"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "N0 = lambda value: 0.5 * (1 + torch.erf((value/2**0.5))) #normal cdf\n",
        "Nd1 = N0(d1)\n",
        "Nd2 = N0(d2)\n",
        "C = S* Nd1 - K* Nd2 *torch.exp(-r*t2m)\n",
        "print(\"Option Price:\", C.item())"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "XTzHGhF9oB_-",
        "outputId": "0a0a734a-17a9-4eb3-ab19-1189f349f17d"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "stream",
          "name": "stdout",
          "text": [
            "Option Price: 17.01496124267578\n"
          ]
        }
      ]
    },
    {
      "cell_type": "markdown",
      "source": [
        "### Differential eqn\n",
        "\n",
        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)"
      ],
      "metadata": {
        "id": "7xdTg1bFqO-R"
      }
    },
    {
      "cell_type": "code",
      "source": [
        "dCdt = tgrad.grad(C, t, create_graph=True, only_inputs=True)[0]\n",
        "dCdt"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "Vb07WKHooCNM",
        "outputId": "1fd6c8ca-dd0f-485c-b2c8-1b2ae337f50e"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([-5.8385], grad_fn=<NegBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 23
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [
        "dCdS = tgrad.grad(C, S, create_graph=True, only_inputs=True)[0]\n",
        "d2CdS2 = tgrad.grad(dCdS, S, create_graph=True, only_inputs=True)[0]\n",
        "dCdvol = tgrad.grad(C, sigma, create_graph=True, only_inputs=True)[0]\n"
      ],
      "metadata": {
        "id": "5uYOabG7qC1p"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [
        "dCdt.item() + ((0.5*sigma**2) * (S**2)*d2CdS2.item() )+ r*S*dCdS.item() - r*C"
      ],
      "metadata": {
        "colab": {
          "base_uri": "https://localhost:8080/"
        },
        "id": "VqrUVGolqC5_",
        "outputId": "b5d6fab7-a48b-40fc-d084-e870f169ae67"
      },
      "execution_count": null,
      "outputs": [
        {
          "output_type": "execute_result",
          "data": {
            "text/plain": [
              "tensor([0.], grad_fn=<SubBackward0>)"
            ]
          },
          "metadata": {},
          "execution_count": 26
        }
      ]
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "s0OayooKqC90"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "qMelkap1qDBX"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "3vh3ud8AoCcM"
      },
      "execution_count": null,
      "outputs": []
    },
    {
      "cell_type": "code",
      "source": [],
      "metadata": {
        "id": "AJqP2e0ZoCm2"
      },
      "execution_count": null,
      "outputs": []
    }
  ]
}