A collection of Python scripts for option pricing and volatility calculations.
If you find this project helpful, please consider supporting its development! Your contribution helps to maintain and expand this valuable resource for the options trading community.
This repository provides implementations of various option pricing models and volatility calculations in Python 2.7. It's a valuable resource for:
- Students learning about option pricing theory
- Quantitative analysts and traders
- Anyone interested in exploring financial modeling techniques
- Traditional Historical Volatility Calculation: Simple and easy-to-understand implementation.
- Garman-Klass Historical Volatility: More sophisticated volatility estimation.
- Black-Scholes Model: Classic option pricing model.
- Exotic Option Example (Shout Options): Demonstration of Monte Carlo approximation.
- Clear and Commented Code: Easy to follow and adapt for your own needs.
To use these scripts, you'll need:
- Python 2.7
- pandas
- pandas_datareader
- scipy
Install the dependencies using pip:
pip install pandas pandas_datareader scipy
# -*- coding: utf-8 -*-
# @Author: boyac
# @Date: 2016-05-02 18:28:28
# @Last Modified by: boyac
# @Last Modified time: 2016-05-02 19:09:29
from pandas import np
import pandas_datareader.data as web
def historical_volatility(sym, days): # stock symbol, number of days
"Return the annualized stddev of daily log returns of picked stock"
try:
# past number of 'days' close price data, normally between (30, 60)
quotes = web.DataReader(sym, 'yahoo')['Close'][-days:]
except Exception, e:
print "Error getting data for symbol '{}'.\n".format(sym), e
return None, None
logreturns = np.log(quotes / quotes.shift(1))
# return square root * trading days * logreturns variance
# NYSE = 252 trading days; Shanghai Stock Exchange = 242; Tokyo Stock Exchange = 246 days?
return np.sqrt(252*logreturns.var())
if __name__ == "__main__":
print historical_volatility('FB', 30) # facebook: 0.296710526109
# -*- coding: utf-8 -*-
# @Author: boyac
# @Date: 2016-05-02 18:28:28
# @Last Modified by: boyac
# @Last Modified time: 2016-05-02 19:09:29
from pandas import np
import pandas_datareader.data as web
def gk_vol(sym, days):
""""
Return the annualized stddev of daily log returns of picked stock
Historical Open-High-Low-Close Volatility: Garman Klass
sigma**2 = ((h-l)**2)/2 - (2ln(2) - 1)(c-o)**2
ref: http://www.wilmottwiki.com/wiki/index.php?title=Volatility
"""
try:
o = web.DataReader(sym, 'yahoo')['Open'][-days:]
h = web.DataReader(sym, 'yahoo')['High'][-days:]
l = web.DataReader(sym, 'yahoo')['Low'][-days:]
c = web.DataReader(sym, 'yahoo')['Close'][-days:]
except Exception, e:
print "Error getting data for symbol '{}'.\n".format(sym), e
return None, None
sigma = np.sqrt(252*sum((np.log(h/l))**2/2 - (2*np.log(2)-1)*(np.log(c/o)**2))/days)
return sigma
if __name__ == "__main__":
print gk_vol('FB', 30) # facebook: 0.223351260219
# -*- coding: utf-8 -*-
# @Author: boyac
# @Date: 2016-05-02 18:28:28
# @Last Modified by: boyac
# @Last Modified time: 2016-05-04 00:27:52
from __future__ import division
from scipy.stats import norm
from math import *
# Cumulative normal distribution
def CND(X):
return norm.cdf(X)
# Black Sholes Function
def BlackScholes(CallPutFlag,S,K,t,r,s):
"""
S = Current stock price
t = Time until option exercise (years to maturity)
K = Option striking price
r = Risk-free interest rate
N = Cumulative standard normal distribution
e = Exponential term
s = St. Deviation (volatility)
Ln = NaturalLog
"""
d1 = (log(S/K) + (r + (s ** 2)/2) * t)/(s * sqrt(t))
d2 = d1 - s * sqrt(t)
if CallPutFlag=='c':
return S * CND(d1) - K * exp(-r * t) * CND(d2) # call option
else:
return K * exp(-r * t) * CND(-d2) - S * CND(-d1) # put option
if __name__ == "__main__":
# Number taken from: http://wiki.mbalib.com/wiki/Black-Scholes期权定价模型
print BlackScholes('c', S=164.0, K=165.0, t=0.0959, r=0.0521, s=0.29) # 5.788529972549341
