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@rubik
Created December 18, 2017 18:05
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{
"cells": [
{
"cell_type": "code",
"execution_count": 1,
"metadata": {},
"outputs": [],
"source": [
"import numpy as np\n",
"import matplotlib.pyplot as plt\n",
"plt.style.use('ggplot')\n",
"%matplotlib inline"
]
},
{
"cell_type": "code",
"execution_count": 2,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"5.992557444469406\n",
"CPU times: user 8.73 s, sys: 101 ms, total: 8.83 s\n",
"Wall time: 8.83 s\n"
]
}
],
"source": [
"%%time\n",
"from random import gauss\n",
"from math import exp, sqrt\n",
"\n",
"S0 = 100\n",
"Kc = 110\n",
"Kp = 90\n",
"T = 1.0\n",
"r = 0.05\n",
"sigma = 0.2\n",
"M = 252\n",
"dt = T/M\n",
"I = 30000\n",
"\n",
"S = []\n",
"for i in range(I):\n",
" path =[]\n",
" for t in range (M+1):\n",
" if t == 0:\n",
" path.append(S0)\n",
" else:\n",
" Z = gauss(0.0, 1.0)\n",
" St = path[t - 1] *exp((r - 0.5*sigma**2)*dt + sigma*sqrt(dt)*Z)\n",
" path.append(St)\n",
" S.append(path)\n",
"\n",
"C0 = exp(-r*T) * sum([max(path[-1]-Kc, 0) for path in S]) / I\n",
"print(C0)"
]
},
{
"cell_type": "code",
"execution_count": 3,
"metadata": {},
"outputs": [],
"source": [
"def mc_option_price(S0, T, M, I, r, sigma):\n",
" dt = T / M\n",
" S = np.empty((I, M + 1))\n",
" Z = np.random.normal(size=S.shape)\n",
" S[:,0] = S0\n",
" F = np.exp((r - 0.5*sigma**2)*dt + sigma*np.sqrt(dt)*Z)\n",
" for t in range(1, M + 1):\n",
" S[:,t] = S[:,t - 1] * F[:,t]\n",
" return S\n",
"\n",
"def payoff(type_, price, strike, I, T, r):\n",
" if type_ == 'call':\n",
" target = price - strike\n",
" elif type_ == 'put':\n",
" target = strike - price\n",
" else:\n",
" raise ValueError(f'unknown option type: {type_}')\n",
" return np.exp(-r*T) * np.maximum(target, 0).sum() / I"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"6.01714641804 2.32301078213\n",
"CPU times: user 2.68 s, sys: 150 ms, total: 2.83 s\n",
"Wall time: 2.83 s\n"
]
}
],
"source": [
"%%time\n",
"S0 = 100\n",
"Kc = 110\n",
"Kp = 90\n",
"T = 1.0\n",
"r = 0.05\n",
"sigma = 0.2\n",
"M = 252\n",
"I = 100000\n",
"\n",
"S = mc_option_price(S0, T, M, I, r, sigma)\n",
"C0 = payoff('call', S[:,-1], Kc, I, T, r)\n",
"P0 = payoff('put', S[:,-1], Kp, I, T, r)\n",
"print(C0, P0)"
]
},
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f12f40e9cf8>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40e9ef0>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fc080>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fc1d0>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fc320>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fc470>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fc5c0>,\n",
" <matplotlib.lines.Line2D at 0x7f12ff285b38>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fc828>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fc978>,\n",
" <matplotlib.lines.Line2D at 0x7f12f40fcac8>]"
]
},
"execution_count": 5,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
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H5BUcpgrKbW2EU92lInWuKwR9q+9+FC3PsaFv47U2TXu2JmOSrEiiGa9Vnx3E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3H93e8wMjRATU0V5ZWXqJqSMjtK3iCd/Gjc0q6Gj0egBwzJSdazDqec5d7bd7Bnzx5EUeQPbqhi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\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f12ff2519e8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.plot(S[:11].T)"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [],
"source": [
"Is = np.round(np.logspace(0, 5), 100).astype(np.int32)\n",
"C0s = [payoff('call', mc_option_price(S0, T, M, i, r, sigma)[:,-1], Kc, i, T, r) for i in Is]"
]
},
{
"cell_type": "code",
"execution_count": 8,
"metadata": {},
"outputs": [
{
"data": {
"text/plain": [
"[<matplotlib.lines.Line2D at 0x7f12f409ae80>]"
]
},
"execution_count": 8,
"metadata": {},
"output_type": "execute_result"
},
{
"data": {
"image/png": 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p6EsLfRzwiLX20Hn+2zn3ZFaiygMzY/bh8ehpJnQaFgctzwkTey7TMWth41FD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\ngg==\n",
"text/plain": [
"<matplotlib.figure.Figure at 0x7f1324944ba8>"
]
},
"metadata": {},
"output_type": "display_data"
}
],
"source": [
"plt.semilogx(Is, C0s)"
]
}
],
"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": "3.6.3"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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