The Black-Scholes model is used to determine the fair price or theoretical value of a call or put option based on certain variables. This code will showcase a simple python program utilizing various modules to calculate the Black-Scholes pricing model. The inputs of the variables can be changed in the “Test” variable.
import math
import numpy as np
import scipy.stats as si
import math
def BlackScholes(S,K,T,rf,q,vol):
"""
S = Stock price
K = Strike price
T = Time to maturity in years
rf = Risk-free rate
q = Divided rate
vol = Volatility (standard deviation)
"""
rf = rf / 100
q = q / 100
vol = vol / 100
d1 = ((np.log(S/K)) + ((rf+0.5*vol**2)*T)) / (vol*(T**0.5))
Nd1 = si.norm.cdf(d1,0.0,1.0)
d2 = d1 - (vol*(T**0.5))
Nd2 = si.norm.cdf(d2,0.0,1.0)
Call = (S*Nd1) - (K*(math.exp(-rf*T))*Nd2)
return Call
Test = BlackScholes(100,100,(30/365),5,0,25)
print(Test)
Breaking down the imported module functions:
- np.log(x) = ln() function
- si.norm.cdf = Cumulative normal distribution function
- math.exp = Return ‘E’ raised to the power of
Changes inputs in decimales:
- rf = rf / 100
- q = q / 100
- vol = vol / 100
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