5.99 swaption_black76

Function File: [SwaptionB76Value] = swaption_black76 (PayerReceiverFlag, F, X, T, r, sigma, m, tau)

Compute the price of european interest rate swaptions according to Black76 pricing functions.

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

Variables:

• PayerReceiverFlag: Call / Payer ’1’ (pay fixed) or Put / Receiver ’0’ (receive fixed, pay floating) swaption
• F: forward rate of underlying interest rate ( forward in T years for tau years)
• X: strike rate
• T: time in days to maturity
• r: annual risk-free interest rate (continuously compounded)
• sigma: implied volatility of the interest rate measured as annual standard deviation
• m: Number of Payments per year (m = 2 -> semi-annual) (continuous compounding is assumed)
• tau: Tenor of underlying swap in Years

See also: swaption_bachelier.