import math
import numpy as np
import matplotlib as mpl
import matplotlib.pyplot as plt
from scipy.integrate import quad
def dN(x):
return math.exp(-0.5 * x **2)/math.sqrt(2 * math.pi)
def N(d):
return quad(lambda x: dN(x),-20,d,limit=50)[0]
def d1f(St,K,t,T,r,sigma):
d1 = (math.log(St/K) + (r + 0.5*sigma**2)
*(T - t)) /(sigma*math.sqrt(T - t))
return d1
def BSM_call_value(St,K,t,T,r,sigma):
d1 = d1f(St,K,t,T,r,sigma)
d2 = d1 - sigma*math.sqrt(T - t)
call_value = St*N(d1)- math.exp(-r*(T - t) * K * N(d2))
return call_value
