Listing 6.1/6.2: Black-Scholes function in R
Last updated 2011
bs = function(X, P, r, sigma, T){
d1 = (log(P/X) + (r + 0.5*sigma^2)*(T))/(sigma*sqrt(T))
d2 = d1 - sigma*sqrt(T)
Call = P*pnorm(d1,mean=0,sd=1)-X*exp(-r*(T))*pnorm(d2,mean=0,sd=1)
Put = X*exp(-r*(T))*pnorm(-d2,mean=0,sd=1)-P*pnorm(-d1,mean=0,sd=1)
Delta.Call = pnorm(d1, mean = 0, sd = 1)
Delta.Put = Delta.Call - 1
Gamma = dnorm(d1, mean = 0, sd = 1)/(P*sigma*sqrt(T))
return(list(Call=Call,Put=Put,Delta.Call=Delta.Call,Delta.Put=Delta.Put,Gamma=Gamma))
}
Listing 6.1/6.2: Black-Scholes function in Python
Last updated June 2018
import numpy as np
from scipy import stats
def bs(X, P, r, sigma, T):
d1 = (np.log(P/X) + (r + 0.5 * sigma**2)*T)/(sigma * np.sqrt(T))
d2 = d1 - sigma * np.sqrt(T)
Call = P * stats.norm.cdf(d1) - X * np.exp(-r * T) * stats.norm.cdf(d2)
Put = X * np.exp(-r * T) * stats.norm.cdf(-d2) - P * stats.norm.cdf(-d1)
Delta_Call = stats.norm.cdf(d1)
Delta_Put = Delta_Call - 1
Gamma = stats.norm.pdf(d1) / (P * sigma * np.sqrt(T))
return {"Call": Call, "Put": Put, "Delta_Call": Delta_Call, "Delta_Put": Delta_Put, "Gamma": Gamma}
