Black Scholes Model implementation example written in Python

black_scholes.py

from scipy.stats import norm
from math import exp, log, sqrt

def BS_Call(S0, sigma, r, q, T, K):
  d1 = (log(S0 / K) + (r - q) * T) / (sigma * sqrt(T)) + sigma * sqrt(T) / 2
  d2 = (log(S0 / K) + (r - q) * T) / (sigma * sqrt(T)) - sigma * sqrt(T) / 2
  call = S0 * exp(-q * T) * norm.cdf(x=d1, loc=0, scale=1) - K * exp(-r * T) * norm.cdf(x=d2, loc=0, scale=1)
  return call

def BS_Put(S0, sigma, r, q, T, K):
  d1 = (log(S0 / K) + (r - q + sigma ** 2 / 2) * T) / (sigma * sqrt(T))
  d2 = d1 - sigma * sqrt(T)
  put = K * exp(-r * T) * norm.cdf(x=-d2, loc=0, scale=1) - S0 * exp(-q * T) * norm.cdf(x=-d1, loc=0, scale=1)
  return put

def put_call_parity(call, put):
  parity = call + K * exp(-r * T) - put -S0 * exp(-q * T)
  print(parity)

S0=100
sigma=30/100
r=5/100
q=0/100
T=1
K=100

call_ans = BS_Call(S0, sigma, r, q, T, K)
print(call_ans)

put_ans = BS_Put(S0, sigma, r, q, T, K)
print(put_ans)

put_call_parity(call_ans, put_ans)