boyac / pyoptionpricing

Option pricing based on Black-Scholes processes, Monte-Carlo simulations with Geometric Brownian Motion, historical volatility, implied volatility, Greeks hedging

pyOptionPricing

Content

• use python 2.7
• option pricing

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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

pyoptionpricing's Issues

Quick question about usage

Hello,
I recently stumbled across this repo but wanted to know what the repo usage is before downloading it for my self. I understand that the repo is for pricing options but what practical usage does it have?
Is it able to give a forecast of future value or is it merely trying to predict what the price of an option should be right now vs what it is on the exchange?

Typo in code demo of readme

The code in readme for B-S model has mismatched kwargs names between the function definition and function call inside main.