Swaptions: Payer, Receiver, the Annuity Measure, and Black's Formula

A swaption is an option to enter an interest-rate swap at a future date at a pre-agreed fixed rate. Unlike caps — which are strips of independent period-by-period options — a swaption gives optionality on the entire term structure from the expiry date forward. The exercise decision depends on the level of the swap rate at expiry, not on individual LIBOR resets. Swaptions are the hedging instrument of choice for banks with callable deposits, insurance companies with embedded interest-rate guarantees, and mortgage issuers with prepayment exposure. Black's swaption formula, derived by modelling the forward swap rate as lognormal under the annuity measure, is the market standard — analogous to Black-Scholes for equities but with the annuity as the natural numeraire.