pyOptionPricing

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.

Description

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

Key Features

• 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.

Usage

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

---

Traditional Historical Volatility Calculation

# -*- 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

Garman-Klass Historical Volatility

# -*- 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

Black-Scholes Model

# -*- 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

Exotic Options Example: Shout Options by Monte Carlo Approximation

Support

This project is made possible by the generous support of its users. If you find this project helpful, please consider:

• Becoming a GitHub Sponsor
• Buying me a coffee on Ko-fi