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import numpy as np
from scipy.stats import norm
def d1(F, K, sigma, T):
return (np.log(F / K) + sigma**2 * T / 2) / (sigma * np.sqrt(T))
def d2(F, K, sigma, T):
return d1(F, K, sigma, T) - sigma * np.sqrt(T)
def black(F, K, T, sigma, option_type = "payer"):
chi = 1 if option_type == "payer" else -1
if option_type == "payer":
return F * norm.cdf(d1(F, K, sigma, T)) - K * norm.cdf(d2(F, K, sigma, T))
else:
return K * norm.cdf(- d2(F, K, sigma, T)) - F * norm.cdf(- d1(F, K, sigma, T))
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