5.76 option_bs

Function File: [value delta gamma vega theta rho omega] = option_bs (CallPutFlag, S, X, T, r, sigma, divrate)

Compute the prices of european call or put options according to Black-Scholes valuation formula:

C(S,T) = N(d_1)*S - N(d_2)*X*exp(-rT)
P(S,T) = N(-d_2)*X*exp(-rT) - N(-d_1)*S
d1 = (log(S/X) + (r + 0.5*sigma^2)*T)/(sigma*sqrt(T))
d2 = d1 - sigma*sqrt(T)

The Greeks are also computed (delta, gamma, vega, theta, rho, omega) by their closed form solution.
Parallel computation for column vectors of S,X,r and sigma is possible.

Variables:

• CallPutFlag: Call: ’1’, Put: ’0’
• S: stock price at time 0
• X: strike price
• T: time to maturity in days
• r: annual risk-free interest rate (continuously compounded, act/365)
• sigma: implied volatility of the stock price measured as annual standard deviation
• divrate: dividend rate p.a., continously compounded

See also: option_willowtree, swaption_black76.