Swaptions

A payer swaption is the right to pay fixed and receive floating. A company that may need to borrow $100 million for ten years in six months can buy a payer struck at 4%. If the swap rate is then 5%, it exercises and pays 4% instead of 5%. If the swap rate is 3%, it lets the option expire and can enter a new swap at 3%.

A receiver swaption is the mirror. The holder has the right to receive fixed at 4% and pay floating. That right is the one a book uses when it wants protection if rates fall, because receiving 4% is then richer than the market rate.

A 5Y x 10Y payer is two clocks. The option lasts five years. If it is exercised, the holder enters a new swap that then runs for ten years. A 10Y x 5Y is a different contract: the option lasts longer, and the swap it delivers is shorter. A 1Y x 5Y receiver expires in one year and, if exercised, receives fixed on a five-year swap.

A European swaption has one exercise date, the expiry. A Bermudan swaption adds earlier dates, such as year 1, year 3, and year 5, and on each of those dates the holder compares exercising with waiting. That comparison is the Bermudan exercise lesson.

The forward swap rate is the fixed rate that would make a new swap worth about zero on the exercise date. The strike is the fixed rate already written into the swaption. The annuity is the present-value weight on the fixed leg: it turns a rate gap into money.

A payer payoff is notional times annuity times the amount by which the forward swap rate exceeds the strike. A receiver payoff uses the amount by which the strike exceeds the forward swap rate. In the lab the annuity is 8, so a 1 percentage-point gap on $100 million is $100 million × 8 × 0.01 = $8 million. The underlying in that product is a swap rate, not a share price.