#修正BS公式
from scipy.stats import norm
from math import exp,log,sqrt
def BS_Call(S0, sigma ,r,T,K):
    d1 = (log(S0 / K) + (r + sigma**2 / 2) * T) / (sigma * sqrt(T))
    d2 = d1 - sigma * sqrt(T)
    BS_Call = S0 * norm.cdf(x=d1, loc=0, scale=1) - K * exp(-r * T) * norm.cdf(x=d2, loc=0, scale=1)
    return BS_Call
def BS_Put(S0, sigma ,r,T,K):
    d1 = (log(S0 / K) + (r + sigma**2 / 2) * T) / (sigma * sqrt(T))
    d2 = d1 - sigma * sqrt(T)
    BS_Put = K * exp(-r * T) * norm.cdf(x=-d2, loc=0, scale=1)-S0 * norm.cdf(x=-d1, loc=0, scale=1)
    return BS_Put