5.98 swaption_bachelier

Function File: [SwaptionBachelierValue] = swaption_bachelier (PayerReceiverFlag, F, X, T, sigma, Annuity)

Compute the price of european interest rate swaptions according to Bachelier Pricing Functions assuming normal-distributed volatilities.

C = ((F-X)*N(d1) + sigma*sqrt(T)*n(d1))*exp(-rT) * multiplicator(m,tau)
d1 = (F-X)/(sigma*sqrt(T))
N1 = 0.5*(1+erf([-]d1/sqrt(2)))
n1 = exp(- d1 ^2 /2)/sqrt(2*pi)
C or [P] = sigma*sqrt(T)*Annuity*([-]d1*N1+n1)

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
• sigma: implied volatility of the interest rate measured as annual standard deviation
• Annuity: Annuity (Sum of discount factors for underlying term dates)

See also: option_bs.