black_scholes.py

# -*- 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