[Tutor] How to calculate the cumulative normal distribution

[Michel Guirguis]

Good afternoon,

How to calculate the cumulative normal distribution function CND in order to use this figure to calculate the call option based on the Black and Scholes model.

>>> from math import*
>>> def CND(X):
	m = abs(X)
	[a1,a2,a3,a4,a5]=(0.31938153,-0.356563782,1.781477937,-1.821255978,1.330274429)
	k = 1/(1+0.2316419*m)
	CND1 = 1.0-1.0/ sqrt(2*3.1415)* exp(-m*m*0.5)
	CND2 =(a1*k + a2*k*k+a3*k*k*k+a4*k*k*k*k+a5*k*k*k*k*k)
	CND = CND1*CND2


>>> d1=(math.log(S/K)+(r-q+(sig*sig)*0.5)*T)/(sig*math.sqrt(T))
>>> d1
0.10606601717798211
>>> d2 =d1-sig*math.sqrt(T)
>>> d2
-0.03535533905932742

>>> call = 50*exp(-0.02*0.5)*CND(d1)-50*exp(-0.03*0.5)*CND(d2)
>>> call

Thanks,

Michel