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cxh1996108 committed Dec 27, 2021
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227 changes: 227 additions & 0 deletions .ipynb_checkpoints/Black-Scholes Calculator-checkpoint.ipynb
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{
"cells": [
{
"cell_type": "markdown",
"metadata": {},
"source": [
"# Black-Scholes Calculator"
]
},
{
"cell_type": "code",
"execution_count": 4,
"metadata": {},
"outputs": [],
"source": [
"import scipy\n",
"m = 6\n",
"n = 61\n",
"S0 = 70\n",
"S1 = 130\n",
"K = 100\n",
"r = 0.12\n",
"T = 1.0\n",
"sigma = 0.10"
]
},
{
"cell_type": "code",
"execution_count": 7,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:6: RuntimeWarning: divide by zero encountered in true_divide\n",
" \n",
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in true_divide\n",
" \n"
]
}
],
"source": [
"time = scipy.linspace(T, 0.0, m)\n",
"S = scipy.linspace(S0, S1, n)\n",
"logSoverK = scipy.log(S/K)\n",
"n12 = (r + sigma **2/2) * (T - time)\n",
"numerd1 = logSoverK[scipy.newaxis, :] + n12[:, scipy.newaxis]\n",
"d1 = numerd1 / (sigma * scipy.sqrt(T - time)[:, scipy.newaxis])"
]
},
{
"cell_type": "code",
"execution_count": 9,
"metadata": {},
"outputs": [
{
"name": "stderr",
"output_type": "stream",
"text": [
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:879: RuntimeWarning: invalid value encountered in greater\n",
" return (self.a < x) & (x < self.b)\n",
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:879: RuntimeWarning: invalid value encountered in less\n",
" return (self.a < x) & (x < self.b)\n",
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\scipy\\stats\\_distn_infrastructure.py:1738: RuntimeWarning: invalid value encountered in greater_equal\n",
" cond2 = (x >= self.b) & cond0\n",
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:4: RuntimeWarning: divide by zero encountered in true_divide\n",
" after removing the cwd from sys.path.\n",
"C:\\ProgramData\\Anaconda3\\lib\\site-packages\\ipykernel_launcher.py:6: RuntimeWarning: invalid value encountered in multiply\n",
" \n"
]
}
],
"source": [
"from scipy.stats import norm\n",
"Delta = norm.cdf(d1)\n",
"denom1 = (scipy.sqrt(2 * scipy.pi) * sigma * scipy.sqrt(T - time))[:,scipy.newaxis]\n",
"factor1 = 1/(denom1 * S)\n",
"factor2 = scipy.exp(-d1 ** 2/2)\n",
"Gamma = factor1 * factor2\n"
]
},
{
"cell_type": "code",
"execution_count": 15,
"metadata": {},
"outputs": [
{
"data": {
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]
},
"execution_count": 15,
"metadata": {},
"output_type": "execute_result"
}
],
"source": [
"Delta"
]
},
{
"cell_type": "code",
"execution_count": null,
"metadata": {},
"outputs": [],
"source": []
}
],
"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",
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"version": "3.7.0"
}
},
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}
124 changes: 124 additions & 0 deletions .ipynb_checkpoints/Finding the implied volatility-checkpoint.ipynb
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{
"cells": [
{
"cell_type": "code",
"execution_count": 5,
"metadata": {},
"outputs": [],
"source": [
"# http://www.codeandfinance.com/finding-implied-vol.html\n",
"import numpy as np\n",
"import pandas as pd\n",
"import math\n",
"from scipy.stats import norm\n",
"import datetime"
]
},
{
"cell_type": "code",
"execution_count": 16,
"metadata": {},
"outputs": [],
"source": [
"def find_vol(target_value, call_put, S, K, T, r):\n",
" MAX_ITERATIONS = 100\n",
" PRECISION = 1.0e-5\n",
" i = 0\n",
" sigma = 0.5\n",
" for i in range(0, MAX_ITERATIONS):\n",
" price = bs_price(call_put, S, K, T, r, sigma)\n",
" vega = bs_vega(call_put, S, K, T, r, sigma)\n",
"\n",
" price = price\n",
" diff = target_value - price # our root\n",
"\n",
" print (i, sigma, diff)\n",
"\n",
" if (abs(diff) < PRECISION):\n",
" return sigma\n",
" sigma = sigma + diff/vega # f(x) / f'(x)\n",
" i = i + 1\n",
"\n",
" # value wasn't found, return best guess so far\n",
" return sigma"
]
},
{
"cell_type": "code",
"execution_count": 17,
"metadata": {},
"outputs": [],
"source": [
"n = norm.pdf\n",
"N = norm.cdf\n",
"\n",
"def bs_price(cp_flag,S,K,T,r,v,q=0.0):\n",
" d1 = (np.log(S/K)+(r+v*v/2.)*T)/(v*np.sqrt(T))\n",
" d2 = d1-v*np.sqrt(T)\n",
" if cp_flag == 'c':\n",
" price = S*np.exp(-q*T)*N(d1)-K*np.exp(-r*T)*N(d2)\n",
" else:\n",
" price = K*np.exp(-r*T)*N(-d2)-S*np.exp(-q*T)*N(-d1)\n",
" return price\n",
"\n",
"def bs_vega(cp_flag,S,K,T,r,v,q=0.0):\n",
" d1 = (np.log(S/K)+(r+v*v/2.)*T)/(v*np.sqrt(T))\n",
" return S * np.sqrt(T)*n(d1)"
]
},
{
"cell_type": "code",
"execution_count": 19,
"metadata": {},
"outputs": [
{
"name": "stdout",
"output_type": "stream",
"text": [
"0 0.5 -21.669539271534063\n",
"1 0.21879739316064523 0.03217154881230044\n",
"2 0.21921383628613422 1.9891615465894574e-08\n",
"Implied vol: 21.92%\n",
"Market price = 17.50\n",
"Model price = 17.50\n"
]
}
],
"source": [
"V_market = 17.5\n",
"K = 585\n",
"T = (datetime.date(2014,10,18) - datetime.date(2014,9,8)).days / 365.\n",
"S = 586.08\n",
"r = 0.0002\n",
"cp = 'c' # call option\n",
"\n",
"implied_vol = find_vol(V_market, cp, S, K, T, r)\n",
"\n",
"print('Implied vol: %.2f%%' % (implied_vol * 100))\n",
"print('Market price = %.2f' % V_market)\n",
"print('Model price = %.2f' % bs_price(cp, S, K, T, r, implied_vol))"
]
}
],
"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": "3.7.0"
}
},
"nbformat": 4,
"nbformat_minor": 2
}
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