1010_Assignment_No4.ipynb

{
 "cells": [
  {
   "cell_type": "code",
   "execution_count": 8,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean =  0.0011148956211957017\n",
      "std =  0.7052256564092161\n",
      "1.959963984540054\n",
      "2.5758293035489004\n",
      "95% ci = [ -0.003256057963765855 ,  0.005485849206157259 ]\n",
      "99% ci = [ -0.00462951112168545 ,  0.006859302364076854 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 4-(a)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "T=0.5      #0.5년후 BM 예측(모델링)\n",
    "N=int(1e5) #10만 samples\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "W_T= np.random.randn(N)*np.sqrt(T) #T시점에서의 브라우니안모션(W) 도출\n",
    "mean_W_T=np.mean(W_T)\n",
    "std_W_T=np.std(W_T)\n",
    "\n",
    "print(\"mean = \", mean_W_T)\n",
    "print(\"std = \", std_W_T)\n",
    "\n",
    "ci_95 = norm.ppf(0.975) #norm.cdf(0.025)와 같은 의미\n",
    "ci_99 = norm.ppf(0.995) #norm.cdf(0.0025)와 같은 의미\n",
    "\n",
    "print(ci_95)\n",
    "print(ci_99)\n",
    "\n",
    "print(\"95% ci = [\", mean_W_T-ci_95*std_W_T/np.sqrt(N), \n",
    "      \", \", mean_W_T+ci_95*std_W_T/np.sqrt(N), \"]\") #좀 더 정확하게 쓰려면 자유도가 N-1이 되어야 하나, 근사에 의해 무시가능\n",
    "\n",
    "print(\"99% ci = [\", mean_W_T-ci_99*std_W_T/np.sqrt(N), \n",
    "      \", \", mean_W_T+ci_99*std_W_T/np.sqrt(N), \"]\") #좀 더 정확하게 쓰려면 자유도가 N-1이 되어야 하나, 근사에 의해 무시가능\n",
    "\n",
    "\n",
    "plt.hist(W_T, 1000)\n",
    "plt.show()\n",
    "\n"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 13,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean =  -0.001989172851050016\n",
      "std =  0.6110761831200245\n",
      "95% ci = [ -0.005776592677624254 ,  0.0017982469755242216 ]\n",
      "99% ci = [ -0.006966686239604144 ,  0.0029883405375041123 ]\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 4-(b)\n",
    "import numpy as np\n",
    "import matplotlib.pyplot as plt\n",
    "from scipy.stats import norm\n",
    "\n",
    "T=0.5      #0.5년후 BM 예측(모델링)\n",
    "N=int(1e5) #10만 samples\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "W_T= np.random.randn(N)*np.sqrt(T) #T시점에서의 브라우니안모션(W) 도출\n",
    "#W_1= np.random.randn(N)*np.sqrt(1) #<-- 이렇게 접근하면 안됨 !!\n",
    "\n",
    "W_1= W_T + np.random.randn(N)*np.sqrt(1) #<--W_1과 W_T는 독립이 아님 !! Cov(W_1, W_T) = T\n",
    "\n",
    "X_T = W_T - T*W_1\n",
    "mean_X_T = np.mean(X_T)\n",
    "std_X_T = np.std(X_T)\n",
    "\n",
    "print(\"mean = \", mean_X_T)\n",
    "print(\"std = \", std_X_T)\n",
    "\n",
    "ci_95 = norm.ppf(0.975) #norm.cdf(0.025)와 같은 의미\n",
    "ci_99 = norm.ppf(0.995) #norm.cdf(0.0025)와 같은 의미\n",
    "\n",
    "print(\"95% ci = [\", mean_X_T-ci_95*std_X_T/np.sqrt(N), \n",
    "      \", \", mean_X_T+ci_95*std_X_T/np.sqrt(N), \"]\") #좀 더 정확하게 쓰려면 자유도가 N-1이 되어야 하나, 근사에 의해 무시가능\n",
    "\n",
    "print(\"99% ci = [\", mean_X_T-ci_99*std_X_T/np.sqrt(N), \n",
    "      \", \", mean_X_T+ci_99*std_X_T/np.sqrt(N), \"]\") #좀 더 정확하게 쓰려면 자유도가 N-1이 되어야 하나, 근사에 의해 무시가능\n",
    "\n",
    "\n",
    "plt.hist(X_T, 1000)\n",
    "plt.show()"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 18,
   "metadata": {},
   "outputs": [
    {
     "name": "stdout",
     "output_type": "stream",
     "text": [
      "mean_S_T_actual =  105.14879109043557\n",
      "mean_S_T_RN =  102.04117467173837\n"
     ]
    },
    {
     "name": "stderr",
     "output_type": "stream",
     "text": [
      "/usr/local/lib/python3.7/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n",
      "/usr/local/lib/python3.7/site-packages/seaborn/distributions.py:2551: FutureWarning: `distplot` is a deprecated function and will be removed in a future version. Please adapt your code to use either `displot` (a figure-level function with similar flexibility) or `histplot` (an axes-level function for histograms).\n",
      "  warnings.warn(msg, FutureWarning)\n"
     ]
    },
    {
     "data": {
      "image/png": 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\n",
      "text/plain": [
       "<Figure size 432x288 with 1 Axes>"
      ]
     },
     "metadata": {
      "needs_background": "light"
     },
     "output_type": "display_data"
    }
   ],
   "source": [
    "# 26page ref.\n",
    "#!pip install seaborn\n",
    "import seaborn as sns\n",
    "\n",
    "S_0 = 100\n",
    "T = 1.0\n",
    "r = 0.02\n",
    "sig = 0.3\n",
    "mu = 0.05\n",
    "\n",
    "N = int(1e5)\n",
    "\n",
    "np.random.seed(0)\n",
    "\n",
    "W_T=np.random.randn(N)*np.sqrt(T)\n",
    "S_T_actual = S_0 * np.exp( (mu-sig*sig/2)*T + sig*W_T)\n",
    "S_T_RN = S_0 * np.exp ( (r-sig*sig/2)*T + sig*W_T)\n",
    "\n",
    "print(\"mean_S_T_actual = \", np.mean(S_T_actual))\n",
    "print(\"mean_S_T_RN = \", np.mean(S_T_RN))\n",
    "\n",
    "sns.distplot(S_T_actual, color='red', label = \"S_T_actual\")\n",
    "sns.distplot(S_T_RN, color='blue', label = \"S_T_RN\")\n",
    "\n",
    "plt.legend()\n",
    "\n",
    "#plt.hist([S_T_actual, S_T_RN], 1000)\n",
    "plt.show()"
   ]
  }
 ],
 "metadata": {
  "kernelspec": {
   "display_name": "Python 3",
   "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": "3.7.4"
  }
 },
 "nbformat": 4,
 "nbformat_minor": 4
}