WhatAreOptions.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 3,
   "id": "369e4d27-43d9-4472-9e23-0761e7880261",
   "metadata": {},
   "outputs": [],
   "source": [
    "import matplotlib.pyplot as plt\n",
    "plt.style.use('ggplot')\n",
    "plt.rcParams['lines.linewidth'] = 0.6"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5eca8678-d693-4310-943e-cf9a75575700",
   "metadata": {},
   "source": [
    "# Что такое опционы"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "4190c5a7-a723-4c22-88e9-6e16cfbfa991",
   "metadata": {},
   "source": [
    "### Что такое опцион\n",
    "\n",
    "Опцион - это контракт, который дает право (но не обязательство) купить/продать базовый актив в заранее оговоренный момент времени по заранее оговорённой цене.\n",
    "\n",
    "**Базовый актив** - это рассматриваемый актив, например акция либо криптовалюта.\n",
    "\n",
    "Здесь важно, что у покупателя есть право, но не обязательство. То есть он в момент экспирации (истечения) опциона может и не исполнять этот опцион. Например, если этот опцион будет для него невыгоден.\n",
    "\n",
    "В данной статьей будем рассматривать только **европейские опционы**, то есть те, которые можно исполнить только в момент истечения самого опциона.\n",
    "\n",
    "\n",
    "### Опционы call и put\n",
    "Есть два вида опционов - опцион на покупку **(call)** и опцион на продажу **(put)**.\n",
    "\n",
    "Рассмотрим пример\n",
    "\n",
    "Допустим человек купил опцион (call) на покупку эфира в размере 1 эфир по цене $\\$1600$ (то есть со страйком 1600) через 30 дней.\n",
    "Рассмотрим 2 случая:\n",
    "\n",
    "- 1-ый: цена эфира через 30 дней опустилась ниже $\\$1600$. В этом случае человеку не выгодно исполнять опцион (то есть покупать по $\\$1600$), так как он может купить на рынке дешевле. Такой опцион называется **Out-of-the-money** (\"не в деньгах\")\n",
    "- 2-ой: цена эфира через 30 дней стала значительно выше $\\$1600$. Тогда ему становится выгодно исполнить опцион, купив 1 эфир по $\\$1600$, так как он мгновенно может продать его на рынке дороже. \n",
    "\n",
    "\n",
    "\n",
    "#### В чём выгода для продавца опциона?\n",
    "\n",
    "Продавец опциона берёт на себя обязательство исполнить опцион (то есть купить/продать себе в минус), если покупатель захочет исполнить опцион. Таким образом, продавец берёт на себя риск, и хочет получить премию. Премия за взятый риск - это и есть цена опциона.\n",
    "\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "decfe7c4-63fe-4b43-9812-1effa3b8dd6e",
   "metadata": {},
   "source": [
    "### Как посчитать выплату по опциону\n",
    "\n",
    "Выплата - то есть сколько мы заработаем/потеряем, если купим данный опцион.\n",
    "\n",
    "Выплата по европейскому **call**-опциону на экспирации определяется формулой:\n",
    "\n",
    "$$Payoff = max(0, S_T - K) - C_0$$\n",
    "\n",
    "$S_T$ - цена базового актива на момент экспирации опциона <br/>\n",
    "$K$ - страйк опциона <br/>\n",
    "$C_0$ - цена call-опциона на момент покупки ($t=0$)\n",
    "\n",
    "#### Выплата в зависимости от цены на момент исполнения опциона будет выглядеть так:\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 2,
   "id": "fcfa0780-cc1f-4ee5-8564-bbe12313fc43",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "iVBORw0KGgoAAAANSUhEUgAAAkAAAAHMCAYAAAA9ABcIAAAAOXRFWHRTb2Z0d2FyZQBNYXRwbG90bGliIHZlcnNpb24zLjYuMiwgaHR0cHM6Ly9tYXRwbG90bGliLm9yZy8o6BhiAAAACXBIWXMAAA9hAAAPYQGoP6dpAABWPElEQVR4nO3dd1hTd/s/8HdC2CMBgQKiOCk+imDrqJu6tVZr66rar6PaPq6ux1GtClpEaV21auujuOoCqThaqdZR66y7DlSkiDhAQAjIJuT8/vCXPEZAMQSy3q/r6nWZcz7n5L5zgNz93GeIBEEQQERERGRGxPoOgIiIiKimsQAiIiIis8MCiIiIiMwOCyAiIiIyOyyAiIiIyOywACIiIiKzwwKIiIiIzA4LICIiIjI7LICIiIjI7LAAIiKDERQUBJFIpLHsjz/+gEgkQkhIiH6C0kJISAhEIhH++OMPfYdCRBVgAURElXbjxg1MnjwZzZo1g1QqhZWVFby8vPDWW28hIiICRUVF+g6xRmzYsAEikQgbNmzQdyhEpCUWQERUKfPmzUPTpk2xYsUKODk5YeTIkZgyZQp69+6NGzduYOzYsWjfvr2+wzQIkyZNwvXr19G6dWt9h0JEFZDoOwAiMnxhYWEIDg5GnTp1sGPHDrRp06bMmF9++QWLFy/WQ3SGx9XVFa6urvoOg4iegzNARPRcSUlJCAkJgaWlJfbt21du8QMAffv2xW+//aaxbMOGDXjvvffQoEED2NrawsnJCe3bt8fmzZurNeaioiIsXLgQ/v7+sLOzg5OTEzp27IioqKgyY5OSkiASiTBq1CjcuHED77zzDlxcXGBvb48OHTrgwIEDGuODgoIwevRoAMDo0aMhEonU/yUlJQF4/jlAhw4dQq9eveDi4gJra2v4+vriyy+/RHZ2dpmxqnOiFAoFwsLC0LhxY1hbW6NOnTqYPn06iouLq/5hEZkpzgAR0XOtX78eJSUlGDp0KJo1a/bcsdbW1hqvx48fj6ZNm6JTp07w9PTEo0ePsG/fPnzwwQe4efMmvv76a53HW1xcjJ49e+Lo0aPw8/PDxIkTkZ+fj+joaAwZMgSXLl1CWFhYme1u376Ntm3bwt/fHx9//DFSUlIQGRmJ3r17Y+vWrRgyZAgAYNSoUZDJZNi9ezf69++PwMBA9T5kMtlzY1u9ejXGjx8Pe3t7DBo0CO7u7vjjjz8QHh6OvXv34sSJE+XuY9iwYTh27Bh69+4NJycn7Nu3D9988w3S0tKwfv36qnxcROZLICJ6ji5duggAhDVr1rz0tgkJCWWWFRUVCV26dBEkEolw7949jXWdO3cWnv2zdOTIEQGAEBwcXKn3DAsLEwAIvXv3FkpKStTLHz58KPj4+AgAhBMnTqiX3759WwAgABCmTJmisa+zZ88KEolEkMlkQnZ2tnr5+vXrBQDC+vXry40hODhYACAcOXJEvSwpKUmwsrISHB0dhevXr2uMHz9+vABAGDdunMZy1efx2muvCY8ePVIvz83NFRo2bCiIxWIhJSWlUp8LEWliC4yInislJQUA4O3t/dLbNmzYsMwyKysrTJw4EQqFAocOHapyfM9at24dRCIRlixZAonkf5Pc7u7umD17NgBg7dq1ZbaTSqWYM2eOxrKWLVti+PDhkMvliImJqVJcmzdvRnFxMSZNmgQ/Pz+NdfPnz4ejoyN++umncq+kCw8Ph4uLi/q1vb09hg8fDqVSiXPnzlUpLiJzxQKIiKpNcnIyJk6cCD8/P9jZ2anPlXnvvfcAAPfv39fp+z1+/BgJCQnw8vIqU2QAQJcuXQAAFy9eLLPutddeg6OjY5nlQUFBFW7zMi5cuKARw9OcnZ3RokULFBYW4saNG2XWt2zZssyyOnXqAACysrKqFBeRueI5QET0XJ6enrh+/fpLFyuJiYlo3bo1srKy0LFjR/To0QNSqRQWFhZISkrCxo0bdX7fINWJxJ6enuWuVy2Xy+Vl1r3yyivlbuPh4aGxb33EVt55QarZrdLS0irFRWSuWAAR0XN16NABhw8fxqFDh/Dhhx9WerslS5bg0aNHWL9+PUaNGqWxbtu2bdi4caOOI33SxgKA1NTUcter2nmqcU97+PBhuduo9lXeNtrG1rRp05eKjYh0jy0wInqu0aNHw9LSEj///DPi4uKeO/bpGZ2EhAQAULe7nnb06FHdBvn/OTo6omHDhrh//z5u3bpVZv2RI0cAPGl3PevChQt4/PhxmeWqS9lbtGihXmZhYQHg5WZfVNuXd2m8XC7HpUuXYGNjgyZNmlR6n0SkPRZARPRc9erVQ0hICIqLi/HWW29VeNLtb7/9ht69e2tsB5T9wt+/f3+5JyHrypgxYyAIAqZOnapRoGRkZKgvux8zZkyZ7bKzszFv3jyNZefOncOWLVsglUoxYMAA9fJatWoBeHKOU2WNGDEClpaW+P7779XFocrs2bORk5ODESNGlLmVABFVD7bAiOiFZs6cCYVCgblz56JVq1Zo164dWrZsCQcHBzx8+BB//vknbt26pXGy7oQJE7B+/XoMGjQIAwcOhJeXF65evYrffvsNgwcPRmRkZLXEOmXKFMTGxmL37t0ICAhAnz59kJ+fjx07diAtLQ3Tpk1Dhw4dymzXqVMnrF27Fn/99Rfat2+vvg+QUqnE6tWr4eTkpB7btm1b2NnZYdmyZXj06JH6PKHJkydX2MKqV68eli1bhokTJ+K1117D4MGD4ebmhqNHj+LUqVPw8/NDeHh4tXwmRFQOfV+HT0TGIy4uTpg0aZLQtGlTwdHRUbC0tBQ8PDyEXr16CWvXrhUKCws1xp84cUJ48803BZlMJjg4OAjt27cXYmJiKry3jy7uAyQIglBQUCDMnz9faNq0qWBjY6N+761bt5YZq7oP0MiRI4W4uDihX79+gkwmE2xtbYV27doJv/32W7nvERsbK7zxxhuCvb29+j5Ct2/fFgSh/PsAqezfv1/o3r27IJPJBCsrK6Fhw4bC1KlThaysrDJjy/s8VF50LyIiej6RIAiC3qovIiI9S0pKQv369TFy5Eg+3Z3IjPAcICIiIjI7LICIiIjI7LAAIiIiIrPDc4CIiIjI7HAGiIiIiMwOCyAiIiIyOyyAiIiIyOywACIiIiKzw0dhPEdWVhYUCoVO9+nm5ob09HSd7tPQMEfTYA45AuaRJ3M0DczxxSQSCZydnSs3Vut3MQMKhQIlJSU6259IJFLv11QvvmOOpsEccgTMI0/maBqYo+6xBUZERERmhwUQERERmR0WQERERGR2WAARERGR2WEBRERERGaHBRARERGZHRZAREREZHZYABEREZHZYQFEREREZocFEBEREZkdFkBERERkdlgAERERkdlhAURERERmhwUQERER1ZiEBAv88Ye1vsNgAUREREQ1o7QUmDpVBnt7Qd+hsAAiIiKimhERYY/mzUvQqlWxvkOBRN8BEBERkelLTLRAVJQd9u7N0HcoADgDRERERNVMqXzS+goNzYatrf7bXwALICIiIqpm69fbo0mTErzxhv5bXypsgREREVG1SUqywNatdtizxzBaXyqcASIiIqJqoVQCU6bIMG9etkFc+fU0FkBERERULTZtskPjxgq0b284rS8VtsCIiIhI55KTLbBpk73Btb5UOANEREREOiUIT676CgnJgYODYbW+VFgAERERkU5t3mwHHx8FOnUq0ncoFWILjIiIiHTm3j0LrFtnuK0vFc4AERERkU48aX1JERycA0dHw2x9qbAAIiIiIp3Yts0OtWuXIijIcFtfKmyBERERUZXdv2+BNWvssXu3Ybe+VDgDRERERFUiCMD06VLMmpUDJyfDbn2psAAiIiKiKomKsoWbmxJduxp+60uFLTAiIiLSWkqKGD/84IBdu4yj9aXCGSAiIiLSypPWlwwzZ+ZAJjOO1pcKCyAiIiLSSnS0LaRSJXr0MJ7WlwpbYERERPTSHj4UY+VKB8TEGFfrS4UzQERERPRSBAH48kspvvzyMZydjav1pcICiIiIiF7Krl22sLMT0KtXob5D0RpbYERERFRpaWlifPedA3bufKTvUKqEM0BERERUKYIAzJwpxdSpj+HiotR3OFXCAoiIiIgqZc8eG1hYAG+9ZbytLxW2wIiIiOiFMjLEWLrUEdHRxt36UuEMEBEREb3QV19J8cUXj+HqatytLxUWQERERPRce/faQKkE3n7b+FtfKmyBERERUYUePRJj8WJH7NjxCCKRvqPRHc4AERERUYVmz3bCZ5/lws3NNFpfKiyAiIiIqFyxsTYoLBShf/8CfYeic2yBERERURmZmSKEhzsiMtK0Wl8qnAEiIiKiMoKDpZg0KRevvGJarS8VFkBERESk4cABa+TkiPHee6bX+lJhC4yIiIjUsrJECAtzwvbtptn6UuEMEBEREamFhEgxfnwuPDxMs/WlwgKIiIiIAAAHD1ojM1OMwYNNt/WlwhYYERERITtbhPnznbBli2m3vlQ4A0RERESYN88JH32UBy8v0259qbAAIiIiMnNHjlgjJcUCQ4fm6zuUGsMWGBERkRnLyRHh66+d8NNPmWbR+lLhDBAREZEZCw11wujReahdu1TfodQoFkBERERm6s8/rXHnjgQjRphP60uFLTAiIiIzlJsrQkiIEzZuNK/WlwpngIiIiMxQaKgTRo7MQ5065tX6UmEBREREZGaOH7dCYqIEH3xgfq0vFYNqgSmVSkRFReHYsWOQy+VwcXFB586d8d5770H0/+fnBEFAVFQUDh06hLy8PPj5+WHs2LHw9PRU7yc3Nxfr1q3D+fPnIRKJ0KZNG4wePRo2Njb6So2IiMgg5OWJEBwsxbp1mRCb8TSIQaW+a9cu/P777/jwww+xdOlSDB8+HHv27EFsbKx6zO7duxEbG4tx48YhLCwM1tbWmD9/PoqLi9Vjli9fjrt372LWrFn48ssvcf36daxevVofKRERERmUsDAnjBiRBx8f82x9qRhUARQfH4+WLVvitddeg7u7O9544w00b94cCQkJAJ7M/uzbtw/vvvsuWrVqBR8fH0yaNAlZWVk4e/YsAODevXu4dOkS/v3vf6Nx48bw8/PDmDFjcPLkSWRmZuozPSIiIr06dcoKN29KMHKk+ba+VAyqAPL19cXVq1fx4MEDAEBSUhJu3ryJFi1aAADS0tIgl8vRvHlz9TZ2dnZo1KgR4uPjATwpouzt7dGwYUP1GH9/f4hEInUhRUREZG7y80WYPVuKb7+Vm3XrS8WgzgF65513UFBQgM8//xxisRhKpRJDhw5Fx44dAQByuRwAIJVKNbaTSqXqdXK5HE5OThrrLSws4ODgoB7zrJKSEpSUlKhfi0Qi2Nraqv+tK6p96XKfhoY5mgZzyBEwjzyZo2nQRY4LFzph6NB8NGigBGB4n1VNH0eDKoBOnTqF48eP45NPPkGdOnWQlJSEDRs2wNnZGUFBQdX2vjExMYiOjla/rl+/PsLDw+Hm5lYt7+fh4VEt+zUkzNE0mEOOgHnkyRxNg7Y5HjsG3LoF/Pe/gFgsffEGelRTx9GgCqDNmzejf//+aN++PQCgbt26SE9Px65duxAUFASZTAYAyM7OhrOzs3q77Oxs1KtXDwAgk8mQk5Ojsd/S0lLk5uaqt3/WgAED0LdvX/VrVfWZnp4OhUKho+ye7NfDwwOpqakQBEFn+zUkzNE0mEOOgHnkyRxNQ1VyzM8H/v1vV/z3v1l4+NBwT3zWxXGUSCSVnrwwqAKoqKgI4mcak2KxWP1BuLu7QyaT4cqVK+qCJz8/HwkJCejRoweAJ+cR5eXlITExEQ0aNAAAXL16FYIgoFGjRuW+r6WlJSwtLctdVx2/TIIgmOwvqQpzNA3mkCNgHnkyR9OgTY7h4U4YODAf9esrYAwfT00dR4MqgF5//XXs3LkTrq6u8Pb2RlJSEn755Re8+eabAJ5Uh3369MHOnTvh6ekJd3d3bN++Hc7OzmjVqhUAwNvbG4GBgVi9ejXGjRsHhUKBdevWoV27dnBxcdFnekRERDXq7FlLXLpkidmzc1482MwYVAE0ZswYREZGYu3atcjOzoaLiwu6d++OgQMHqsf0798fRUVFWL16NfLz8+Hn54eZM2fCyspKPeaTTz5BREQE5s2bp74R4pgxY/SREhERkV4UFAAzZ8rwww9ZsLDQdzSGx6AKIFtbW4waNQqjRo2qcIxIJMKQIUMwZMiQCsc4ODjg008/rYYIiYiIjMOiRU4YMKAAjRrp7lxWU2JQBRARERFV3fnzljh71go7d2boOxSDxQKIiIjIhBQWAjNmyLBiRRYk/JavEO8FSUREZEKWLnVE374F8PVl6+t5WBsSERGZiEuXLHHihDV27WLr60VYABEREZmAoiJg+nQpvvtOztZXJbAFRkREZAKWLXNE796F8PNj66syWCMSEREZucuXLfHnn2x9vQwWQEREREasuBiYNk2KxYvlqOCpTlQOtsCIiIiM2PLljujRoxBNm7L19TI4A0RERGSkrl6V4PBhtr60wRkgIiIiI1RSAkybJsM338jx1OMwqZJYABERERmhFSscEBRUhGbN2PrSBltgRERERiYuToL9+22wezdbX9riDBAREZERUbW+wsOzYW2t72iMFwsgIiIiI7JqlQPaty9CQECJvkMxamyBERERGYkbNyTYt88Ge/aw9VVVnAEiIiIyAgoFMHWqFAsXsvWlCyyAiIiIjMDixUCbNsVo0YKtL11gC4yIiMjA3bolwbZtQEzMY32HYjI4A0RERGTASkuB//xHilWrABsbfUdjOlgAERERGbA1a+zx+uvFaNdO35GYFrbAiIiIDFRCggWio+2wd28GAAd9h2NSOANERERkgEpLgalTZQgLy4adnb6jMT0sgIiIiAxQRIQ9/P1L0Lp1sb5DMUlsgRERERmYxEQLREXZ8YaH1YgzQERERAZEqXzS+goNzYadnaDvcEwWCyAiIiIDsmGDPZo0KcEbb7D1VZ3YAiMiIjIQd+5YYMsWtr5qAmeAiIiIDIBSCUyZIsO8edmwt2frq7qxACIiIjIAmzbZoVEjBdq3Z+urJrAFRkREpGfJyRb46Sd77N7N1ldN4QwQERGRHgnCk6u+goOz4eDA1ldNYQFERESkR5s328HHR4FOndj6qklsgREREenJvXsWWL+erS994AwQERGRHggCMG2aFHPm5MDRka2vmsYCiIiISA+2bbODl1cpgoKK9B2KWWILjIiIqIbdvy/GmjVsfekTZ4CIiIhqkCAA06fLMHt2Dpyc2PrSFxZARERENSgqyhZubkp06cLWlz6xBUZERFRDUlLE+PFHB8TEsPWlb5wBIiIiqgGq1tfMmTmQydj60jcWQERERDUgOtoWMpkS3buz9WUI2AIjIiKqZg8firFyJVtfhoQzQERERNVI1fqaMeMxnJ3Z+jIULICIiIiqUUyMLRwclOjZs1DfodBT2AIjIiKqJmlpYixf7oCdO9n6MjScASIiIqoGggDMnCnFtGmP4eLC1pehYQFERERUDfbssYFEAvTpw9aXIWILjIiISMcyMsRYutQRP//8SN+hUAU4A0RERKRjM2dK8cUXj1GrllLfoVAFWAARERHp0N69NhAE4O232foyZGyBERER6cijR2IsXuyIHTseQSTSdzT0PJwBIiIi0pFZs6T47LNcuLmx9WXoWAARERHpQGysDYqLgf79C/QdClUCW2BERERVlJkpQni4IyIj2foyFpWaATp37hwyMzOrOxYiIiKjFBwsxeTJuXjlFba+jEWlCqBvv/0WcXFx6teTJk3CuXPnqi0oIiIiY3HggDVycsR49122voxJpVpgtra2yMvLU79OT09HYSEv7yMiIvOWlSVCWJgTtm9n68vYVKoAatSoEXbu3Ins7GzY2dkBAC5cuAC5XP7c7fr27fvSAWVmZmLz5s24dOkSioqK4OHhgQkTJqBhw4YAAEEQEBUVhUOHDiEvLw9+fn4YO3YsPD091fvIzc3FunXrcP78eYhEIrRp0wajR4+GjY3NS8dDRERUkZAQKcaPz4WHB1tfxqZSBdDYsWOxYsUK/Pzzz+plJ06cwIkTJ5673csWQLm5uZg9ezaaNm2KmTNnwsnJCSkpKbC3t1eP2b17N2JjYzFx4kS4u7sjMjIS8+fPx5IlS2BlZQUAWL58ObKysjBr1iyUlpZi1apVWL16NT799NOXioeIiKgiBw9aIzNTjMGD2foyRpUqgDw8PBAaGori4mLk5ORg4sSJGDlyJFq1aqXTYHbv3o1atWphwoQJ6mXu7u7qfwuCgH379uHdd99Vv/ekSZMwbtw4nD17Fu3bt8e9e/dw6dIlLFiwQD1rNGbMGCxYsAAffPABXFxcdBozERGZn+xsEebPd8KWLWx9GatKFUD79u1DYGAgvLy84OrqioEDB6JZs2Zwc3PTaTDnzp1DQEAAlixZgri4OLi4uKBHjx7o1q0bACAtLQ1yuRzNmzdXb2NnZ4dGjRohPj4e7du3R3x8POzt7dXFDwD4+/tDJBIhISEBrVu31mnMRERkfubOleKjj/Lg5cXWl7GqVAG0ceNGODk5wcvLCwAQHR0NT09P1K1bV6fBpKWl4ffff8dbb72FAQMG4J9//sH69eshkUgQFBSkPudIKpVqbCeVStXr5HI5nJycNNZbWFjAwcGhwnOWSkpKUFJSon4tEolga2ur/reuqPaly30aGuZoGswhR8A88mSOunfkiDVSUy3w/vsFNfaePI66V6kC6HnFgy4plUo0bNgQw4YNAwDUr18fycnJ+P333xEUFFRt7xsTE4Po6Gj16/r16yM8PFznM1wqHh4e1bJfQ8IcTYM55AiYR57MUTeys4H584HYWMDLy/PFG+gYj6PuVKoA+te//oUdO3YgKSlJfRXY0aNHER8fX+E2IpEIo0ePfqlgnJ2d4e3trbHM29sbf/31FwBAJpMBALKzs+Hs7Kwek52djXr16qnH5OTkaOyjtLQUubm56u2fNWDAAI0TtlXVZ3p6OhQKxUvl8DwikQgeHh5ITU2FIAg6268hYY6mwRxyBMwjT+aoW1OnSjFqVDEsLQuQklKtb6WBx7FyJBJJpScvKn0V2IYNG3D58mVkZ2cDAC5fvozLly8/d7uXLYBeffVVPHjwQGPZgwcP1Mm4u7tDJpPhypUr6oInPz8fCQkJ6NGjBwDA19cXeXl5SExMRIMGDQAAV69ehSAIaNSoUbnva2lpCUtLy3LXVccPmiAIJvsDrMIcTYM55AiYR57MseqOHrVGcrIFwsPzoa+PksdRdypVAEmlUo1LyIcMGYLJkyejQ4cOOg3mrbfewuzZs7Fz5060a9cOCQkJOHToED766CMAT6rDPn36YOfOnfD09IS7uzu2b98OZ2dn9VVh3t7eCAwMxOrVqzFu3DgoFAqsW7cO7dq14xVgRESkldxcEebOdcLGjZm86stEaPUw1PHjx8PX11fXsaBRo0aYMmUKtm7dip9//hnu7u4YOXIkOnbsqB7Tv39/FBUVYfXq1cjPz4efnx9mzpypvgcQAHzyySeIiIjAvHnz1DdCHDNmjM7jJSIi8xAa6oSRI/NQp06pvkMhHdGqAHr6hOR79+4hPT0dAODm5lbmHJ6X9frrr+P111+vcL1IJMKQIUMwZMiQCsc4ODjwpodERKQTx45Z4Z9/JAgLy9Z3KKRDWhVAAHD27Fls2rQJaWlpGstVszYtW7ascnBERET6lJcnQnCwFOvXZ0JcqceHk7HQqgC6cOECFi9eDDc3N7z//vvqWZ979+7h0KFDWLRoEb788ksEBgbqMlYiIqIaFRbmhA8+yIOPD1tfpkarAujnn3+Gj48P5s6dq/GA0ZYtW6JXr16YM2cOduzYwQKIiIiM1smTVrh5U4Kvv2bryxRpNaGXnJyMzp07l/t0dRsbGwQFBSE5ObnKwREREelDfr4Ic+ZI8e23cra+TJRWh9XS0hK5ubkVrs/Nza3wvjpERESGbuFCRwwZko/69dn6MlVaFUDNmjXDvn37yr0T9K1btxAbGwt/f/8qB0dERFTT/vrLClevWmLMmDx9h0LVSKtzgEaMGIGvvvoKs2fPRqNGjdQPSX3w4AESEhIglUoxfPhwnQZKRERU3QoKRPjqKylWr86EhYW+o6HqpFUB5O7ujkWLFiEmJgaXLl3CyZMnATy5D1CfPn3wzjvvlHliOxERkaH75htHDByYj4YN2foydVrfB0gqlWLUqFE6DIWIiEh/zp61xIULVti5M0PfoVAN0OocoF27diEzM1PXsRAREelFQQEwY4YMixbJ2foyE1rNAG3fvh3bt29HkyZN0KlTJ7zxxhuwtbXVdWxEREQ1YvFiJwwYUIDGjRX6DoVqiFYzQKtWrcKwYcOQm5uLH3/8ER999BGWLVuGCxcuQKlU6jpGIiKianPhgiX++ssKH39c8e1dyPRoNQPk4uKCfv36oV+/fkhOTsbx48dx4sQJnDp1Co6OjmjXrh06duyIxo0b6zpeIiIinSksBL78Uobvv8+CROuzYskYVflw161bF8OGDcOwYcNw/fp1/Prrr9i/fz/2798PDw8PdOrUCd26deNVYUREZHCWLnXE228X4NVX2foyNzq5wXdxcTFOnDiB3bt34/z58xCLxWjRogXq1KmDn3/+GZMnT8aZM2d08VZEREQ6cemSJU6csMb48Wx9mSOtZ4AEQcDly5dx7NgxnD17FoWFhahXrx5GjBiBDh06qGd8srKy8N1332HTpk1o3bq1zgInIiLSVlERMH26FMuWydn6MlNaHfYNGzbg1KlTkMvlcHZ2Rvfu3dG5c2fUqVOnzFhnZ2d06dIFK1eurHKwREREurBsmSN69y5EkyZsfZkrrQqgQ4cOoXXr1ujcuTP8/f0hEomeO97Pzw/jx4/XKkAiIiJdunLFEseOWSMmhjc8NGdaFUBr1qyBjY1Npce7u7vD3d1dm7ciIiLSmeJiYNo0KRYtksPSUt/RkD5pdRL0yxQ/REREhmL5ckd061aEpk3Z+jJ3Wp/6JZfLcfjwYSQmJqKgoKDMDRBFIhHmzJlT5QCJiIh04epVCQ4ftsauXWx9kZYF0J07dxASEoLi4mJ4eXkhOTkZ3t7eyM/PR2ZmJl555RXUqlVL17ESERFppaQEmDZNhm++kcPKSt/RkCHQqgDaunUrbGxs8O2338LKygrjxo3D6NGj0axZM5w6dQpr167FJ598outYiYiItLJihQPefLMIzZqx9UVPaHUO0I0bN9C9e3e4urpCLH6yC1ULrG3btujQoQN++ukn3UVJRESkpbg4Cfbvt8Gnnz7WdyhkQLQqgARBUN/o0M7ODmKxGLm5/7uTZt26dZGYmKibCImIiLSkan2Fh2ez9UUatCqA3N3dkZaW9mQHYjHc3d1x5coV9fqbN2/C3t5eNxESERFpadUqB7RvX4SAgBJ9h0IGRqtzgJo3b47Tp0/j/fffBwB0794dP/30E9LS0iAIAq5du4a3335bp4ESERG9jBs3JNi3zwZ79vCqLypLqwLo3XffRYcOHaBQKCCRSPDWW2+hqKgIf/31F8RiMd577z28++67uo6ViIioUhQKYOpUGRYuzIa1tb6jIUOkVQHk4OAABwcH9WuRSIT33nsP7733ns4CIyIi0taPPzqgTZtitGjB1heVr8rPwM3OzkZ6ejoAwM3NTX1yNBERkT7Ex0uwe7ct9u5N13coZMC0LoCuXLmCLVu24Pbt2xrL69evj2HDhqF58+ZVDo6IiOhllJY+aX0tWCAHn9pEz6NVAXTmzBksWbIEUqkU/fv3h6enJwDgwYMH+PPPP7FgwQJ8/vnnaN26tU6DJSIiep41a+zx+uvFaNmSrS96Pq0KoO3bt6NOnTqYN28ebG1tNdYNGDAAc+bMwfbt21kAERFRjbl1ywLR0XZsfVGlaHUfoIcPH+LNN98sU/wAT26M2KVLF/V9goiIiKrb/1pf2Sjnq4moDK0KoNq1ayM7O7vC9XK5XN0WIyIiqm7LlwMBAcVo1apY36GQkdCqABoxYgR+//13nD17tsy6M2fO4ODBg/jggw+qHBwREdGLJCZaYP16YPp0PuuLKk+rc4BiY2Ph5OSERYsWwcXFBR4eHgCA1NRUZGZmwsvLC7GxsYiNjVVvIxKJMG3aNN1ETUREBECpBKZMkeL77wE7O0AQ9B0RGQutCqDk5GQAgKurKwBoPBfM1dUVxcXF6jEqIpGoKnESERGVsX69Pf71LwU6d7ZGSoq+oyFjolUBtHLlSl3HQURE9FKSkiywdasdfvnlEQA+gJtejlbnABEREenTk9aXDPPmZcPOjn0venksgIiIyOhs2mSHxo0VaN+eV32Rdqr8LDAiIqKalJxsgU2b7LFnT4a+QyEjxhkgIiIyGoLw5IaHISHZcHBg64u0xwKIiIiMxubNdvDxUaBTJ7a+qGrYAiMiIqNw754F1q1j64t0gzNARERk8AQBmDZNiuDgHDg6svVFVafVDJAgCDh48CAOHz6MtLQ05ObmlhkjEomwffv2KgdIRES0bZsdvLxKERRUpO9QyERoVQBt3rwZv/zyC+rVq4eOHTvC3p43oCIioupx/74Ya9bYY/dutr5Id7QqgI4ePYo2bdrgiy++0HU8REREaoIATJ8uw6xZOXByYuuLdEerc4CKi4vRvHlzXcdCRESkISrKFq6uSnTtytYX6ZZWBVCzZs2QkJCg61iIiIjUUlLE+OEHB4SEZOs7FDJBWhVAY8eOxa1bt7Bz5048fvxY1zEREZGZU7W+Zs7MgUzG1hfpnlbnAH322WcQBAGRkZGIjIyElZUVxOKytdTGjRurHCAREZmf6GhbSKVK9OjB1hdVD60KoDZt2kAkEuk6FiIiIjx8KMbKlQ6IieFVX1R9tCqAJk6cqOs4iIiI1K2vL798DGdntr6o+vBO0EREZDBiYmxhb69Er16F+g6FTJzWzwLLz8/Hr7/+igsXLiAj48k0paurK15//XX06dMHdnZ2OguSiIhMX1qaGMuXO2Dnzkf6DoXMgFYzQJmZmZg+fTqio6NRWFiIV199Fa+++iqKioqwY8cOTJ8+HVlZWbqOlYiITJQgADNnSjF16mO4uCj1HQ6ZAa1mgLZs2QK5XI7p06fjtdde01h38eJFLFmyBFu2bMGkSZO0DmzXrl3YunUr+vTpg1GjRgF4cgPGTZs24eTJkygpKUFAQADGjh0LmUym3i4jIwNr1qzBtWvXYGNjg86dO2PYsGGwsLDQOhYiIqpee/bYQCIB3nqLrS+qGVrNAF26dAl9+vQpU/wAQIsWLdC7d29cvHhR66ASEhLw+++/w8fHR2P5xo0bcf78eXzxxReYO3cusrKysHjxYvV6pVKJBQsWQKFQIDQ0FBMnTsQff/yByMhIrWMhIqLqlZEhxtKljpg/nzc8pJqjVQFUVFQEqVRa4XqZTIaiIu3u3VBYWIjvv/8eH3/8scZDVvPz83H48GGMHDkSzZo1Q4MGDTBhwgTcvHkT8fHxAIC///4b9+7dw+TJk1GvXj20aNECQ4YMwf79+6FQKLSKh4iIqtdXX0nxxRePUasWW19Uc7RqgXl7e+PEiRPo0aMHJBLNXSgUCpw4cQLe3t5aBbR27Vq0aNECzZs3x86dO9XLExMTUVpaCn9/f/Wy2rVrw9XVFfHx8fD19UV8fDzq1q2r0RILDAzE2rVrcffuXdSvX7/c9ywpKUFJSYn6tUgkgq2trfrfuqLalynfQ4k5mgZzyBEwjzwNPcdffrGBUgn061ekdYyGnqMuMEfd06oA6t+/P5YtW4YZM2agZ8+e8PT0BAA8ePAAv//+O+7cuYPPP//8pfd74sQJ3L59GwsWLCizTi6XQyKRaMwKAYBUKoVcLlePebr4Ua1XratITEwMoqOj1a/r16+P8PBwuLm5vXQOleHh4VEt+zUkzNE0mEOOgHnkaYg5ZmQAS5cCR44Ar7xiW+X9GWKOusYcdUerAqht27YoKirCli1bsGbNGo11Tk5OGD9+PN54442X2mdGRgY2bNiAWbNmwcrKSpuwtDZgwAD07dtX/VpVfaanp+u0dSYSieDh4YHU1FQIgmne4Is5mgZzyBEwjzwNOcfx42WYNKkQSmUhUlK0348h56grzLFyJBJJpScvtL4PUFBQEDp27Ih//vlH4z5ADRs21OqKq8TERGRnZ2P69OnqZUqlEtevX8dvv/2Gr776CgqFAnl5eRqzQNnZ2epZH5lMVuYp9dnZ2ep1FbG0tISlpWW566rjB00QBJP9AVZhjqbBHHIEzCNPQ8sxNtYGhYVA//4F0FVYhpZjdWCOuqN1AQQAFhYW8PX1ha+vb5UD8ff3x6JFizSW/fDDD/Dy8kL//v3h6uoKCwsLXLlyRT279ODBA2RkZKjf39fXFzt37kR2dra69XX58mXY2tpqfU4SERHpVmamCOHhjoiMfAQTPqWFDFylCqC4uDgAwL/+9S+N1y+iGl8Ztra2qFu3rsYya2trODo6qpd36dIFmzZtgoODA+zs7LBu3TqNAiwgIADe3t5YsWIFhg8fDrlcju3bt6Nnz54VzvAQEVHNCg6WYvLkXLzyCq/6Iv2pVAE0d+5cAE9ugCiRSNSvX0TX998ZOXIkRCIRFi9eDIVCob4RoopYLMaXX36JtWvXYtasWbC2tkbnzp0xZMgQncZBRETaOXDAGo8fi/HuuwX6DoXMnEioRKOtJmaADFF6errG5fFVJRKJ4OnpiZSUFJPt4TJH02AOOQLmkach5SiXizBggCu2bXsEDw/dzf4YUo7VhTlWjqWlpW5Pgn62kDH2woaIiGpeSIgU48fn6rT4IdKWVneCnjt3Lq5cuVLh+qtXr1a6TUZERKbv0CFrPHokxqBBbH2RYdCqAIqLi1NfXl6enJycSrfJiIjItGVnixAa6oTwcDmv+iKDoVUB9CKpqanqR0kQEZF5mzfPCR9/nAsvL7a+yHBU+j5Af/zxB44ePap+vXPnThw6dKjMuPz8fNy5cwctWrTQTYRERGS0jhyxRmqqBYYMYeuLDEulC6Di4mLk5OSoXxcUFJR5YJlIJIK1tTW6d++OgQMH6i5KIiIyOjk5Isyb54TNmzPZ+iKDU+kCqEePHujRowcAYOLEiRg9ejRatmxZbYEREZFxCw11wtixeahdu1TfoRCVodWjMFauXKnrOIiIyIQcPWqNu3ctEB5e8QUzRPpUpWeBnT9/HhcvXkR6ejoAwM3NDS1atMDrr7+uk+CIiMj4PH4swty5Tti4ka0vMlxaFUB5eXlYtGgR4uLiIBaL4ezsDODJg0d///13NGnSBFOnTtV4ajsREZmH0FAnjByZhzp12Poiw6VVAbR+/Xpcv34dw4cPR48ePWBjYwMAKCwsxIEDB7B161asX78ekyZN0mmwRERk2I4ds8Lt2xIsWMDWFxk2rQqgs2fPokePHujXr5/GchsbG/Tr1w8ZGRkal8wTEZHpy8sTIThYivXrMyGulrvMEemOVj+iEokEXl5eFa738vKCRFKl04uIiMjIhIU54YMP8uDjw9YXGT6tCqA2bdrg9OnTUCrL3tWztLQUp06dwhtvvFHl4IiIyDicPGmFmzclGDkyX9+hEFWKVtM0HTt2xLp16zBr1ix069YNHh4eAICUlBQcPHgQCoUCHTt2RGJiosZ2DRo0qHrERERkUPLzRZg9W4q1a9n6IuOhVQEUEhKi/vc///xT7pjg4OAyyyIjI7V5OyIiMmALFzri/ffzUb8+W19kPLQqgMaPH6/rOIiIyAj99ZcVrl61REhIzosHExkQrQqgoKAgHYdBRETGpqBAhK++kmL1ara+yPhU+VKtwsJCZGRkAABcXV3V9wQiIiLTFh7uiEGD8tGwIVtfZHy0LoASEhKwZcsW3LhxQ301mFgshp+fH0aMGIGGDRvqLEgiIjIsZ89a4tIlS8yezdYXGSetCqBbt24hJCQEEokEXbp0Qe3atQEA9+/fx4kTJxAcHIyQkBA0atRIp8ESEZH+FRQAM2fK8MMPWbCw0Hc0RNrRqgDavn07XFxc8PXXX0Mmk2msGzRoEGbPno1t27Zh9uzZuoiRiIgMyOLFThgwoACNGin0HQqR1rQ6be3WrVvo3r17meIHAGQyGbp164Zbt25VNTYiIjIw589b4swZK3z0Ua6+QyGqEq1mgEQiEUpLKz7pTalUQiQSaR0UEREZnsJCYMYMGVasyAKfdkTGTqsZoFdffRX79+9Henp6mXUZGRk4cOAA/Pz8qhwcEREZjqVLHfH22wXw9WXri4yfVjX8+++/j+DgYHz22Wdo3bo1PD09AQAPHjzAuXPnYGFhgffff1+ngRIRkf5cumSJEyessWtXhr5DIdIJrQqg+vXrIywsDNu2bcO5c+dQXFwMALCyskJgYCCGDh0Kb29vnQZKRET6UVQETJ8uxXffydn6IpOh9Y+yt7c3pk6dCqVSiZycJ/eBcHJygpi3AyUiMinLljmid+9C+Pmx9UWmo8q1vFgsLvdqMCIiMn6XL1vizz/Z+iLTw8lMIiIqV3Hxk9bXokVyWFrqOxoi3WK/ioiIyrV8uSO6dStC06ZsfZHp4QwQERGVcfWqBIcPs/VFposzQEREpKGkBJg2TYbw8GxYWek7GqLqwQKIiIg0rFjhgKCgIvj7l+g7FKJqwxYYERGpxcVJsH+/DXbvZuuLTBtngIiICIBm68vaWt/REFUvFkBERAQA+OEHB7RvX4SAALa+yPSxBUZERLh5U4JffrHFnj1lH3JNZIo4A0REZOYUCmDKFBkWLpTDxkbf0RDVDBZARERmbvVqB7RpU4zXXmPri8wHW2BERGbs1i0Jdu1i64vMD2eAiIjMVGnpk9bXggVy2NrqOxqimsUCiIjITK1ZY4/XXitGy5ZsfZH5YQuMiMgMJSRYIDraDnv38oaHZJ44A0REZGZKS4GpU2UIC8uGra2g73CI9IIFEBGRmYmIsIe/fwlaty7WdyhEesMWGBGRGUlMtEBUlB327GHri8wbZ4CIiMyEUvmk9RUamg07O7a+yLyxACIiMhMbNtijSZMSvPEGW19EbIEREZmBpCQLbNnC1heRCmeAiIhM3JPWlxTz5mXD3p6tLyKABRARkcn78UegUSMF2rdn64tIhS0wIiITlpxsgR9+AHbufKzvUIgMCmeAiIhMlCA8aX0tXQo4OLD1RfQ0FkBERCZq82Y7+Pgo0K2bviMhMjxsgRERmaB79yywfr099ux5BMBe3+EQGRzOABERmRhBAKZNk2LOnBw4OrL1RVQeFkBERCZm2zY7eHmVIiioSN+hEBksg2qBxcTE4MyZM7h//z6srKzg6+uLESNGwMvLSz2muLgYmzZtwsmTJ1FSUoKAgACMHTsWMplMPSYjIwNr1qzBtWvXYGNjg86dO2PYsGGwsLDQQ1ZERDXn/n0x1qyxx+7dvOEh0fMY1AxQXFwcevbsifnz52PWrFkoLS1FaGgoCgsL1WM2btyI8+fP44svvsDcuXORlZWFxYsXq9crlUosWLAACoUCoaGhmDhxIv744w9ERkbqIyUiohojCMD06TLMnp0DJye2voiex6AKoK+++gpBQUGoU6cO6tWrh4kTJyIjIwOJiYkAgPz8fBw+fBgjR45Es2bN0KBBA0yYMAE3b95EfHw8AODvv//GvXv3MHnyZNSrVw8tWrTAkCFDsH//figUCn2mR0RUraKibOHmpkSXLmx9Eb2IQbXAnpWfnw8AcHBwAAAkJiaitLQU/v7+6jG1a9eGq6sr4uPj4evri/j4eNStW1ejJRYYGIi1a9fi7t27qF+/fpn3KSkpQUlJifq1SCSCra2t+t+6otqXLvdpaJijaTCHHAHTyvPBAzF++MEBu3c/0sjHlHKsCHM0DTWdo8EWQEqlEhs2bMCrr76KunXrAgDkcjkkEgns7TUv6ZRKpZDL5eoxTxc/qvWqdeWJiYlBdHS0+nX9+vURHh4ONzc33STzDA8Pj2rZryFhjqbBHHIEjD9PQQDGjQMWLwaaNCk/F2PPsTKYo2moqRwNtgCKiIjA3bt3MW/evGp/rwEDBqBv377q16rqMz09XadtM5FIBA8PD6SmpkIQTLM/zxxNgznkCJhOnjt22MLW1gotW2YjJUVznank+DzM0TToIkeJRFLpyQuDLIAiIiJw4cIFzJ07F7Vq1VIvl8lkUCgUyMvL05gFys7OVs/6yGQyJCQkaOwvOztbva48lpaWsLS0LHdddfygCYJgsj/AKszRNJhDjoBx55maKsaKFfaIicl4bg7GnGNlMUfTUFM5GtRJ0IIgICIiAmfOnMGcOXPg7u6usb5BgwawsLDAlStX1MsePHiAjIwM+Pr6AgB8fX2RnJysLnoA4PLly7C1tYW3t3fNJEJEVAMEAfjySxlmzHgMZ2fT/lIk0jWDmgGKiIjA8ePHMW3aNNja2qrP2bGzs4OVlRXs7OzQpUsXbNq0CQ4ODrCzs8O6devg6+urLoACAgLg7e2NFStWYPjw4ZDL5di+fTt69uxZ4SwPEZExiomxhb29Ej17Fr54MBFpMKgC6MCBAwCAkJAQjeUTJkxAUFAQAGDkyJEQiURYvHgxFAqF+kaIKmKxGF9++SXWrl2LWbNmwdraGp07d8aQIUNqKg0iomqXlibG8uUO2Lnzkb5DITJKBlUARUVFvXCMlZUVxo4dq1H0PMvNzQ0zZszQZWhERAZDEICZM6WYOvUxXFyU+g6HyCgZ1DlARET0Ynv22EAiAd56i60vIm0Z1AwQERE9X0aGGEuXOuLnn9n6IqoKzgARERmRmTOl+Pzzx6hVi60voqpgAUREZCT27rWBIAD9+rH1RVRVbIERERmBR4/EWLzYETt2PIIJPw6KqMZwBoiIyAjMnu2Ezz7LhZsbW19EusACiIjIwO3bZ4OiIhH69y/QdyhEJoMtMCIiA5aZKcI33zgiKoqtLyJd4gwQEZEBCw6WYvLkXLi7s/VFpEssgIiIDNT+/TbIyRHj3XfZ+iLSNbbAiIgMUFaWCAsWOGL7dra+iKoDZ4CIiAxQSIgUEybkwsODrS+i6sACiIjIwBw8aI3MTDEGDWLri6i6sAVGRGRAsrNFmD/fCVu2sPVFVJ04A0REZEDmzpXio4/y4OXF1hdRdWIBRERkII4cscbDh2IMHZqv71CITB5bYEREBiAnR4R585yweXMmW19ENYAzQEREBiA01AkffpiH2rVL9R0KkVlgAUREpGd//mmN5GQJhg9n64uoprAFRkSkR7m5IoSEOGHjRra+iGoSZ4CIiPQoNNQJI0fmoU4dtr6IahILICIiPTl+3Ar//CPBBx+w9UVU09gCIyLSg7w8EYKDpVi3LhNi/q8oUY3jrx0RkR6EhTlhxIg8+Piw9UWkDyyAiIhq2MmTVrh5U4KRI9n6ItIXtsCIiGpQfr4Ic+ZIsWYNW19E+sRfPyKiGrRwoSOGDs1H/fpsfRHpEwsgIqIa8tdfVrh2zRJjxuTpOxQis8cWGBFRDSgoEOGrr6RYvZqtLyJDwF9DIqIaEB7uiEGD8tGwIVtfRIaABRARUTU7e9YSf/9tibFj2foiMhRsgRERVaOCAmDmTBl++CELFhb6joaIVDgDRERUjRYtcsK77+ajUSOFvkMhoqdwBoiIqJqcP2+Js2etEBOToe9QiOgZLICIiKpBYSEwY4YMK1aw9UVkiNgCIyKqBkuWOOLttwvg68vWF5Eh4gwQEZGOXbpkiZMnrbFrF1tfRIaKBRARkQ4VFQHTp0vx3XdySPgXlshgsQVGRKRDS5c6onfvQvj5sfVFZMj4/ydERDpy+bIljh+35lVfREaABRARkQ4UFwPTpkmxeLEclpb6joaIXoQtMCIiHVi+3BE9ehSiaVO2voiMAWeAiIiq6OpVCQ4f5lVfRMaEM0BERFVQUgJMmybDN9/IYWWl72iIqLJYABERVcGKFQ54880iNGvG1heRMWELjIhIS3FxEuzfb4M9e9j6IjI2nAEiItKCqvUVHp7N1heREWIBRESkhVWrHNC+fRECAkr0HQoRaYEtMCKil3TjhgT79rH1RWTMOANERPQSFApg6lQZFi7MhrW1vqMhIm2xACIiegmrVzvgjTeK0KIFW19ExowtMCKiSoqPl2DXLlvs3Zuu71CIqIo4A0REVAmlpU9aXwsWyGFjo+9oiKiqWAAREVXCmjX2eO21YrRsydYXkSlgC4yI6AUSEiwQHW3H1heRCeEMEBHRc6haX2Fh2bC11Xc0RKQrLICIiJ4jIsIezZuXoHXrYn2HQkQ6xBYYEVEFEhMtEBVlh717ecNDIlNjsgXQb7/9hr1790Iul8PHxwdjxoxBo0aN9B0WERkJpfJJ6ys0NBu2toK+wyEiHTPJFtjJkyexadMmDBw4EOHh4fDx8cH8+fORnZ2t79CIyEisX2+PJk1K8MYbbH0RmSKTLIB++eUXdO3aFW+++Sa8vb0xbtw4WFlZ4ciRI/oOjYiMQFKSBbZutcOMGY/1HQoRVROTa4EpFAokJibinXfeUS8Ti8Xw9/dHfHx8uduUlJSgpOR/9/YQiUSw/f+Xe4hEIp3FptqXLvdpaJijaTCHHIHy81QqgWnTZPj66xw4OACAcX8G5nAsmaNpqOkcTa4AysnJgVKphEwm01guk8nw4MGDcreJiYlBdHS0+nX9+vURHh4ONze3aonRw8OjWvZrSJijaTCHHAHNPFetApo3BwYONK0nnZrDsWSOpqGmcjS5AkgbAwYMQN++fdWvVdVneno6FAqFzt5HJBLBw8MDqampEATTPKmSOZoGc8gRKJtncrIFli93xt69j5CSYhp5m8OxZI6mQRc5SiSSSk9emFwB5OTkBLFYDLlcrrFcLpeXmRVSsbS0hKWlZbnrquMHTRAEk/0BVmGOpsEccgSe5KlUCpgyRYqQkGzY2ythammbw7FkjqahpnI0uZOgJRIJGjRogKtXr6qXKZVKXL16Fb6+vnqMjIgM2ebNdvDxUaBTJ171RWQOTG4GCAD69u2LlStXokGDBmjUqBH27duHoqIiBAUF6Ts0IjJA9+5ZYN06e+zZwxseEpkLkyyA2rVrh5ycHERFRUEul6NevXqYOXNmhS0wIjJfggBMmSJFcHAOHB1Nu7VARP9jkgUQAPTq1Qu9evXSdxhEZODWrgVq1y5FUFCRvkMhohpksgUQEdGL3LsnxrJlwM6dOfoOhYhqGAugGvTggRj//S/w+LEDAFOdahfB0ZE5Gj9zyBH44w8bfPst4OQkmNxVX0T0fCyAapC1tQA/PyArS2GylzGKRCI4OzNHY2cOOQJAq1aP0adPLaSk6DsSIqppLIBqUK1aAoYMAVJSCk32S0UkEsHTkzkaO3PIETDtxwoQ0fOZ3H2AiIiIiF6EBRARERGZHRZAREREZHZYABEREZHZYQFEREREZocFEBEREZkdFkBERERkdlgAERERkdlhAURERERmhwUQERERmR0WQERERGR2WAARERGR2WEBRERERGaHBRARERGZHYm+AzBkEkn1fDzVtV9DwhxNgznkCJhHnszRNDBH3W0rEgRB0PqdiIiIiIwQW2A1qKCgANOnT0dBQYG+Q6k2zNE0mEOOgHnkyRxNA3PUPRZANUgQBNy+fRumPOnGHE2DOeQImEeezNE0MEfdYwFEREREZocFEBEREZkdFkA1yNLSEgMHDoSlpaW+Q6k2zNE0mEOOgHnkyRxNA3PUPV4FRkRERGaHM0BERERkdlgAERERkdlhAURERERmhwUQERERmR3Tf6hINYuKikJ0dLTGMi8vLyxbtgwAUFxcjE2bNuHkyZMoKSlBQEAAxo4dC5lMph6fkZGBNWvW4Nq1a7CxsUHnzp0xbNgwWFhY1GAmFZs4cSLS09PLLO/RowfGjh2LkJAQxMXFaazr1q0bPvroI/VrQ8sxLi4Oe/bswe3bt5GVlYUpU6agdevW6vWCICAqKgqHDh1CXl4e/Pz8MHbsWHh6eqrH5ObmYt26dTh//jxEIhHatGmD0aNHw8bGRj3mzp07iIiIwD///AMnJyf06tUL/fv313uOCoUC27dvx8WLF5GWlgY7Ozv4+/tj2LBhcHFxUe+jvGM/bNgwvPPOOwaRI/DiY7ly5UocPXpUY5uAgAB89dVX6tfGfCwBYPDgweVuN2LECPTr1w+AYR/LmJgYnDlzBvfv34eVlRV8fX0xYsQIeHl5qcfo6m/ptWvXsGnTJty9exe1atXCe++9h6CgIL3nmJubi6ioKPz999/IyMiAk5MTWrVqhaFDh8LOzk69n/KO9aeffor27dsbfI4AdPZ9oYscWQDpQJ06dTB79mz1a7H4fxNrGzduxIULF/DFF1/Azs4OERERWLx4Mb7++msAgFKpxIIFCyCTyRAaGoqsrCysWLECFhYWGDZsWI3nUp4FCxZAqVSqXycnJyM0NBRt27ZVL+vatSuGDBmifm1lZaX+tyHmWFRUhHr16qFLly5YtGhRmfW7d+9GbGwsJk6cCHd3d0RGRmL+/PlYsmSJOrfly5cjKysLs2bNQmlpKVatWoXVq1fj008/BQDk5+cjNDQU/v7+GDduHJKTk/HDDz/A3t4e3bp102uOxcXFuH37Nt577z3Uq1cPubm52LBhA7755hssXLhQY+zgwYM14n26KNB3jsCLjyUABAYGYsKECerXzz4w0ZiPJQD897//1Xh98eJF/Pjjj2jTpo3GckM9lnFxcejZsycaNmyI0tJSbNu2DaGhoViyZIk6Rl38LU1LS8PChQvRvXt3TJ48GVevXsWPP/4ImUyGwMBAveaYmZmJzMxMfPDBB/D29lYXAVlZWfjPf/6jsa8JEyZoxPt0gWTIOapU9ftCZzkKVCWRkZHClClTyl2Xl5cnDB06VDh16pR62b1794RBgwYJN2/eFARBEC5cuCAMHjxYyMrKUo/Zv3+/8H//939CSUlJtcaurfXr1wuTJk0SlEqlIAiCEBwcLKxfv77C8Yae46BBg4S//vpL/VqpVArjxo0Tdu/erV6Wl5cnDBs2TDh+/LggCIJw9+5dYdCgQUJCQoJ6zMWLF4XBgwcLjx49EgThSY6jRo3SyHHz5s3Cp59+Ws0ZlfVsjuW5deuWMGjQICE9PV29bMKECcIvv/xS4TaGlKMglJ/nihUrhPDw8Aq3McVjGR4eLsydO1djmTEdy+zsbGHQoEHCtWvXBEHQ3d/Sn376Sfjiiy803mvp0qVCaGhoNWdU1rM5lufkyZPC+++/LygUCvWyFx1/Q89RF98XusqR5wDpQGpqKj7++GNMmjQJy5cvR0ZGBgAgMTERpaWl8Pf3V4+tXbs2XF1dER8fDwCIj49H3bp1NaZxAwMDUVBQgLt379ZoHpWhUChw7NgxvPnmmxCJROrlx44dw4cffoj//Oc/2Lp1K4qKitTrjC3HtLQ0yOVyNG/eXL3Mzs4OjRo10jhu9vb2aNiwoXqMv78/RCIREhIS1GOaNGmiMdsQEBCABw8eIDc3t4ayqbz8/HyIRCKN/5sEgF27dmHMmDGYNm0a9uzZg9LSUvU6Y8kxLi4OY8eOxaeffoo1a9bg8ePH6nWmdizlcjkuXryILl26lFlnLMcyPz8fAODg4ABAd39Lb926pbEP4EmOqn3UpGdzrGiMra1tmVMFIiIi8OGHH2LGjBk4fPiwxrOzjCHHqn5f6CpHtsCqqHHjxpgwYQK8vLyQlZWF6OhozJkzB4sXL4ZcLodEIoG9vb3GNlKpFHK5HMCTP1ZPH2jVetU6Q3PmzBnk5eVp9Fo7dOgAV1dXuLi44M6dO9iyZQsePHiAKVOmADC+HFUxqWJUefa4OTk5aay3sLCAg4ODxhh3d3eNMarPQS6XP/cPX00rLi7Gli1b0L59e40CqHfv3qhfvz4cHBxw8+ZNbNu2DVlZWRg5ciQA48gxMDAQbdq0gbu7O1JTU7Ft2zaEhYVh/vz5EIvFJncsjx49ChsbG41zhADjOZZKpRIbNmzAq6++irp166rfXxd/S+Vyebm/1wUFBSguLtZoxVSn8nJ8Vk5ODn7++ecy7cfBgwejWbNmsLa2xt9//42IiAgUFhaiT58+AAw/R118X+gqRxZAVdSiRQv1v318fNQF0alTp2rsB60mHTlyBIGBgRonyj79C1q3bl04Oztj3rx5SE1NhYeHhz7CpJegUCiwdOlSAMDYsWM11vXt21f9bx8fH0gkEqxZswbDhg0zmlvyP31yaN26deHj44PJkyfj2rVrZf4v0hQcOXIEHTt2LPP3x1iOZUREBO7evYt58+bpO5Rq86Ic8/PzsXDhQnh7e2PQoEEa6wYOHKj+d/369VFUVIS9e/eqCyBDUVGOhvR9wRaYjtnb28PLywupqamQyWRQKBTIy8vTGJOdna2ucGUyWZlZkOzsbPU6Q5Keno7Lly+ja9euzx3XqFEjAE9ag4Bx5Qj8LyZVjCrPHrecnByN9aWlpcjNzX3usVW9NpS8VcVPRkYGZs2aVab99azGjRujtLRUfTWRMeT4rFdeeQWOjo4aP5+mcCwB4Pr163jw4EG57a9nGeKxjIiIwIULFxAcHIxatWqpl+vqb6lMJiv399rW1rbG/oe1ohxVCgoKEBYWBltbW0yZMqXMCfvPaty4MR49eoSSkhIAxpHj07T5vtBVjiyAdKywsFBd/DRo0AAWFha4cuWKev2DBw+QkZEBX19fAICvry+Sk5M1Dubly5dha2sLb2/vGo//eY4cOQKpVIrXXnvtueOSkpIAAM7OzgCMK0cAcHd3h0wm0zhu+fn5SEhI0DhueXl5SExMVI+5evUqBEFQ/0L7+vri+vXrUCgU6jGXL1+Gl5eXQbRMVMVPamoqZs+eDUdHxxduk5SUBJFIpG4ZGXqO5Xn06BFyc3M1fj6N/ViqHD58GA0aNEC9evVeONaQjqUgCIiIiMCZM2cwZ86cMq04Xf0tbdy4scY+VGNU+6hOL8oR+N+VeBKJBNOmTavUl3lSUhLs7e3Vs3iGnuOztPm+0FWOLICqaNOmTYiLi0NaWhpu3ryJb7/9FmKxGB06dICdnR26dOmCTZs24erVq0hMTMSqVavg6+urPlABAQHw9vbGihUrkJSUhEuXLmH79u3o2bOnQU1LK5VK/PHHH+jcubPGCXmpqamIjo5GYmIi0tLScO7cOaxcuRJNmjSBj48PAMPMsbCwEElJSepfvrS0NCQlJSEjIwMikQh9+vTBzp07ce7cOSQnJ2PFihVwdnZGq1atAADe3t4IDAzE6tWrkZCQgBs3bmDdunVo166duj3YoUMHSCQS/Pjjj7h79y5OnjyJ2NhYjVaEvnJUKBRYsmQJEhMTMXnyZCiVSsjlcsjlcvUXYHx8PH799VckJSXh4cOHOHbsGDZu3IiOHTuqvxD1neOL8iwsLMRPP/2E+Ph4pKWl4cqVK/jmm2/g4eGBgIAAAMZ/LFXy8/Nx+vTpcmd/DP1YRkRE4NixY/j0009ha2ur/lksLi4GAJ39Le3RowfS0tKwefNm3L9/H/v378epU6fw1ltv6T3H/Px8zJ8/H0VFRfj3v/+NgoIC9RjVbUjOnTuHQ4cOITk5GampqThw4ABiYmLQu3dv9fsYco66+r7QVY58GnwVLVu2DNevX8fjx4/h5OQEPz8/DB06VN3LVN2868SJE1AoFOXevCs9PR1r167FtWvXYG1tjc6dO2P48OEGcyNEAPj7778xf/58LFu2TOOmVhkZGfj+++9x9+5dFBUVoVatWmjdujXeffddjXaKoeV47do1zJ07t8zyzp07Y+LEieobIR48eBD5+fnw8/PDhx9+qJF7bm4uIiIiNG6eN2bMmApvnufo6IhevXpp3HiuOj0vx0GDBmHSpEnlbhccHIymTZsiMTERERERuH//PkpKSuDu7o5OnTqhb9++GoWrPnMEnp/nuHHj8O233+L27dvIy8uDi4sLmjdvjiFDhmj8DhrzsZw4cSIA4ODBg9iwYQP++9//lmllGvqxrOhGjhMmTFBfcKGrv6XXrl3Dxo0bce/evRq9SeCLcqzoGAPAihUr4O7ujkuXLmHr1q1ITU2FIAjw8PBAjx490LVrV437zxlqjrr8vtBFjiyAiIiIyOywBUZERERmhwUQERERmR0WQERERGR2WAARERGR2WEBRERERGaHBRARERGZHRZAREREZHZYABGRzkVFRVV4U7SqCAkJQUhIyEtvd+3aNQwePBjXrl3TeUw1ZfDgwYiKitJ3GEQmgwUQERERmZ3nP2aWiMgENGnSBJs3b37hk7UN2ebNmw3q8ThExo4zQERk8IqKiqq0vVgshpWVlcbzkoyBUqlUP0jSysqKBRCRDhnv/w4R0UtZuXIl4uLisHLlSo3lUVFRiI6O1ji/ZPDgwejZsyf8/f0RGRmJlJQUeHh44P/+7/8QGBiosf2NGzewceNGJCcnw8XFBf369aswhj///BO//vor7t27BysrKwQEBGDEiBFwdXVVjwkJCcHjx48xceJEbNy4Ef/88w+6deuGUaNGaeyrsLAQ48aNQ5cuXTB69GiNdY8ePcKECRMwdOhQDBgwQP2gSdWDXp9+n88//xwRERG4desW7O3t0adPH/Tv319jf+np6Vi3bh2uXr0Ka2trdOjQAYGBgQgLC9PYZ3lUn+/SpUsRGRmJv//+GxYWFujYsSOGDx8OKyurMp+7r68vYmJikJKSgs8//xytW7fG4MGDMXDgQI1zqzIzMxEZGYlLly7h8ePHcHZ2RmBgIEaPHq2e7crLy8OOHTvw119/ITs7G7Vq1ULXrl3Rr18/oysIiXSJBRARlevGjRs4c+YMevToAVtbW8TGxmLx4sVYtWoVHB0dAQDJyckIDQ2Fk5MTBg0ahNLSUkRFRWk8oVtl586diIyMRNu2bdG1a1fk5OQgNjYWwcHB+Oabb2Bvb68e+/jxY4SFhaFdu3bo2LEjpFJpmf3Z2NigVatWOHnyJEaOHKnxZX7ixAkAQMeOHZ+bY25uLubPn482bdqgbdu2OH36NLZs2YK6deuiRYsWAJ4UWvPmzUNWVhb69OkDmUyG48ePv/QJ1UuXLoWbmxvef/993Lp1C7GxscjLy8OkSZM0xl29ehWnTp1Cr1694OjoCHd393L3l5mZiRkzZiA/Px9du3ZF7dq1kZmZidOnT6OoqAgSiQRFRUUICQlBZmYmunXrBldXV9y8eRPbtm2DXC4vU1QSmRMWQERUrvv372PJkiXw8PAAADRt2hRTp07FiRMn0KtXLwBAZGQkBEHAvHnz1LM4bdq0wZQpUzT2lZ6ejqioKAwZMgTvvvuuennr1q0xffp07N+/X2O5XC7HuHHj0L179+fG2LlzZxw/fhyXL1/WmJk6duwYmjRpojGzVJ6srCxMmjQJnTp1AgB06dIFEyZMwOHDh9UF0MGDB/Hw4UNMnToVrVq1AgB069YN06dPf+6+n+Xu7o5p06YBAHr16gVbW1scOHAAb7/9Nnx8fNTjHjx4gMWLF8Pb2/u5+9u6dSvkcjnCwsLQsGFD9fIhQ4ZAEAQAwC+//ILU1FR888038PT0BAB0794dLi4u2LNnD/r27fvCz4jIVHH+k4jK5e/vry5+AMDHxwe2trZ4+PAhgCfnp/z9999o1aqVxpeot7c3AgICNPb1119/QRAEtGvXDjk5Oer/ZDIZPDw8ysymWFpa4s0336xUjM7Ozjh27Jh6WXJyMu7cufPC2R/gySzS0+MkEgkaNWqEtLQ09bJLly7BxcUFLVu2VC+zsrJC165dX7j/p/Xs2VPjde/evQEAFy9e1Fj+r3/964XFj1KpxNmzZ/H6669rFD8qIpEIAHD69Gk0adIE9vb2Gp+7v78/lEolrl+//lI5EJkSzgARUbnKmxlwcHBAXl4eACAnJwfFxcXqmYWneXl5aXyxp6amQhAEfPLJJ+W+17NXZ7m4uFTqii2xWIyOHTviwIEDKCoqgrW1NY4fPw5LS0u0bdv2hdvXqlVLXSyo2Nvb486dO+rX6enpeOWVV8qMe7o4rIxnPyfVPp8utgBU2PJ6Wk5ODgoKClC3bt3njktJScGdO3cwduzYctdnZ2e/8L2ITBULICIz8ewXuIpSqSx3eUUnyKraKy9DqVRCJBJhxowZ5e7XxsZG4/XTJwa/SKdOnbBnzx6cPXsW7du3x/Hjx/H666/Dzs7uhdvq8yTgio7Hy+T+IoIgoHnz5hWemO7l5aWz9yIyNiyAiMyEvb29evbmaRkZGVrtz8nJCVZWVkhJSSmz7sGDBxqvPTw8IAgC3N3ddf6lW7duXdSvXx/Hjh2Di4sLMjIyMGbMGJ3t383NDffu3YMgCBpFS2pq6kvtJyUlRWN2RzUrVpkZn2c5OTnB1tYWycnJzx33yiuvoLCwEM2bN3/p9yAydTwHiMhMvPLKK8jPz9do72RlZeHMmTNa7U8sFiMgIABnz57VKKLu3buHv//+W2Ns69atIRaLER0dXWYGSRAEPH78WKsYVDp27IjLly9j3759cHR0LHOpflUEBAQgMzMT586dUy8rLi7GoUOHXmo/+/fv13gdGxsLAFrFKhaL0apVK5w/fx7//PNPmfWqz7ht27aIj4/HpUuXyozJy8tDaWnpS783kangDBCRmWjfvj22bNmCRYsWoXfv3igqKsKBAwfg6emJ27dva7XPwYMH49KlS5gzZw569OgBpVKJ2NhY1KlTR6PQ8vDwwNChQ7F161akp6ejVatWsLGxQVpaGs6ePau+L422OnTogC1btqgv29flHZ+7d++O3377Dd99953GZfCWlpYAKm5lPSstLQ3h4eEIDAxEfHw8jh07hg4dOqBevXpaxTVs2DBcvnwZISEh6Nq1K7y9vZGVlYXTp09j3rx5sLe3R79+/XDu3DmEh4ejc+fOaNCgAYqKipCcnIzTp09j5cqVcHJy0ur9iYwdCyAiM+Ho6IipU6di48aN2Lx5M9zd3TFs2DCkpKRoXQD5+Pjgq6++wqZNmxAVFYVatWph8ODByMrK0iiAAOCdd96Bp6cnfv31V+zYsQPAkxOtmzdvrnGFlTZkMhmaN2+Oixcvqi9p1xUbGxsEBwdj3bp12LdvH2xsbNCpUye8+uqrWLx4sboQepHPPvsMUVFR2Lp1K8RiMXr16oURI0ZoHZeLiwvCwsKwfft2HD9+HAUFBXBxcUFgYCCsra0BANbW1pg7dy527tyJ06dP488//4StrS28vLwwePDgSp0nRWSqRII2ZzQSERmYb7/9FsnJyfj+++9r5P1+/fVXbNy4ET/++CNcXFwqHKe6E/TatWs520JkQHgOEBEZvaysLFy4cEHnsz8qqudxPf364MGD8PT0fG7xQ0SGiy0wIjJaaWlpuHHjBg4fPgyJRPLCO0dra9GiRXB1dUW9evWQn5+PY8eO4f79+xXe14iIDB8LICIyWnFxcVi1ahVcXV0xceLEcp9BpgsBAQE4fPgwjh07BqVSCW9vb3z22Wdo165dtbwfEVU/ngNEREREZofnABEREZHZYQFEREREZocFEBEREZkdFkBERERkdlgAERERkdlhAURERERmhwUQERERmR0WQERERGR2WAARERGR2fl/5ABcbSxpxpQAAAAASUVORK5CYII=\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = 1500 # strike price\n",
    "C0 = 25\n",
    "\n",
    "prices = [price for price in range(500, 2500, 25)]\n",
    "calls = [max(0, price - K) - C0 for price in prices]\n",
    "\n",
    "plt.plot(prices, calls, 'b')\n",
    "plt.title('Call option')\n",
    "plt.xlabel('underlying price')\n",
    "plt.ylabel('option payoff')\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "5931b95c-a8a7-48c2-9a2e-a2680835ec63",
   "metadata": {},
   "source": [
    "#### Для put-опциона:\n",
    "\n",
    "Схожим образом считается выплата по европейскому **put**-опциону:\n",
    "\n",
    "$$Payoff = max(0, K - S_T) - P_0$$\n",
    "\n",
    "$S_T$ - цена базового актива на момент экспирации опциона <br/>\n",
    "$K$ - страйк опциона <br/>\n",
    "$P_0$ - цена put-опциона на момент покупки ($t=0$)\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 4,
   "id": "9a9cd4e2-1c46-474c-a583-3cb487825148",
   "metadata": {},
   "outputs": [
    {
     "data": {
      "image/png": "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\n",
      "text/plain": [
       "<Figure size 640x480 with 1 Axes>"
      ]
     },
     "metadata": {},
     "output_type": "display_data"
    }
   ],
   "source": [
    "K = 1500 # strike price\n",
    "P0 = 45\n",
    "\n",
    "prices = [price for price in range(500, 2500, 25)]\n",
    "calls = [max(0, K - price) - P0 for price in prices]\n",
    "\n",
    "plt.plot(prices, calls, 'b')\n",
    "plt.title('Put option')\n",
    "plt.xlabel('underlying price')\n",
    "plt.ylabel('option payoff')\n",
    "plt.show()\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "ab1a86d0-dfd9-4456-b8fd-6f473a382f7b",
   "metadata": {
    "tags": []
   },
   "source": [
    "### Как посчитать стоимость опциона?\n",
    "\n",
    "Здесь начинается самое интересное. Стоимость опциона - это премия за риск, который готов на себя взять продавец опциона. Причем цена теоретически может пойти совершенно любым образом. И в идеале хотелось бы иметь модель, которая бы говорила сколько конкретный опцион должен стоить (конечно, на практике идеально такое невозможно).\n",
    "\n",
    "#### Почему это сложно?\n",
    "\n",
    "Никто не знает как пойдёт цена в будущем. В зависимости от движения цены, будут получаться разные выплаты по опциону. Соответственно не понятно, как вообще искать цену опциона, которая будет устраивать продавца и покупателя.\n",
    "\n"
   ]
  },
  {
   "cell_type": "markdown",
   "id": "b21c179b-9e7b-44f3-8e7d-bfca4fa82b5e",
   "metadata": {},
   "source": [
    "#### Модель Блэка-Шоулза\n",
    "\n",
    "Модель Блека-Шоулза позволяет аналитически вычислить честную стоимость опциона. \n",
    "\n",
    "В следующих статьях покажу как выводится формула Блека-Шоулза."
   ]
  },
  {
   "cell_type": "markdown",
   "id": "bd1491fc-81cf-4200-a4d2-9fe548cd1e52",
   "metadata": {},
   "source": [
    "#### Спасибо что дочитали до конца:)\n",
    "\n",
    "\n",
    "##### Мой twitter:\n",
    "https://twitter.com/kirrya95\n",
    "\n",
    "##### Мой telegram:\n",
    "https://t.me/kirr_ya"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3 (ipykernel)",
   "language": "python",
   "name": "python3"
  },
  "language_info": {
   "codemirror_mode": {
    "name": "ipython",
    "version": 3
   },
   "file_extension": ".py",
   "mimetype": "text/x-python",
   "name": "python",
   "nbconvert_exporter": "python",
   "pygments_lexer": "ipython3",
   "version": "3.9.13"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 5
}