1014_HW1_No4_LeeSeHa.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) by LeeSeHa \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) by LeeSeHa\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()"
   ]
  }
 ],
 "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
}