Swaption

A swaption is an option on a swap. In its standard form it gives the buyer the right, without the obligation, to enter into an interest rate swap with a fixed rate, start date and maturity that are agreed when the swaption is traded. The buyer pays a premium for this right. If market rates at expiry make the underlying swap attractive, the buyer exercises; otherwise the swaption lapses.

Swaptions are traded over the counter between banks, asset managers, insurers, pension funds, hedge funds and corporations, usually under ISDA documentation. They form one of the largest markets in interest rate options and are used both to hedge and to take positions on the future level and volatility of interest rates.

• Payer swaption. The holder has the right to enter a swap paying the fixed rate and receiving the floating rate. It gains value when rates rise and is comparable to a put on a bond.
• Receiver swaption. The holder has the right to receive the fixed rate and pay floating. It gains value when rates fall.

The fixed rate of the underlying swap is the strike. A swaption is described by its expiry and the length of the underlying swap, so a one-year option on a ten-year swap is quoted as 1y10y. Exercise styles follow the usual conventions: a European option can be exercised only at expiry, an American one at any time, and a Bermudan swaption on a set of specified dates. On exercise the parties either enter the actual swap or settle its market value in cash.

The market standard for quoting European swaptions is Black's model of 1976. The value of a payer swaption is:

with:

• $N_0$ is the notional amount of the swap.
• $A$ is the annuity factor, the present value of receiving 1 on each fixed payment date of the underlying swap.
• $F$ is the forward swap rate for the underlying swap.
• $K$ is the strike rate.
• $\sigma$ is the volatility of the forward swap rate and $T$ the time to expiry in years.
• $N(\cdot)$ is the cumulative standard normal distribution function.

Consider a one-year payer swaption on a five-year swap with a notional of $10 million. The forward swap rate and the strike are both 4 percent, volatility is 25 percent and the annuity factor is 4.5. Then $d_1 = 0.125$ and $d_2 = -0.125$, with $N(d_1) = 0.5497$ and $N(d_2) = 0.4503$. The bracket equals $0.04 \times (0.5497 - 0.4503) = 0.00398$. Multiplying by 4.5 gives 0.0179, and by the notional about $179,000, or 1.79 percent of notional.

Black's model assumes the forward rate is lognormally distributed and cannot be negative. When interest rates in the euro area, Japan and Switzerland fell below zero in the 2010s, the market adopted alternatives: a normal model in which rate changes, not percentage changes, are assumed normally distributed, and a shifted version of Black's model. Swaption volatility is now commonly quoted as a normal volatility in basis points per year.

Volatility varies with the option expiry, the swap length and the strike. The full set of quotes forms a three-dimensional grid, the swaption volatility cube, which plays the role that the volatility surface plays for equity options. Dealers interpolate across strikes with models such as SABR, published by Patrick Hagan and co-authors in 2002.

• Hedging future borrowing. A company planning to issue fixed-rate debt can buy a payer swaption, which pays off if rates rise before the issue, while leaving it free to benefit if rates fall.
• Managing callable debt. An issuer of a callable bond holds an embedded right to refinance. Selling a receiver swaption turns that right into cash, and investors use swaptions to hedge it.
• Hedging mortgage portfolios. Holders of a mortgage-backed security face prepayments that rise when rates fall, and swaptions offset the resulting change in duration.
• Insurers and pension funds. Receiver swaptions protect institutions with long-dated guaranteed liabilities against a fall in rates.
• Volatility trading. Traders buy or sell swaptions, hedged with swaps, to take a view on interest rate volatility.

Swaptions are bilateral contracts, so each side bears counterparty risk, which is controlled through collateral agreements and, for many participants, regulatory margin requirements on uncleared derivatives. The underlying swaps reference overnight risk-free rates. In the United States dollar market the reference became SOFR after the last dollar LIBOR settings ceased in mid-2023.

A buyer's loss is limited to the premium. A seller's potential loss is large, since the underlying swap may have many years to run and its value moves substantially for each change in rates. Sellers therefore practise active hedging of both rate and volatility exposure. Bermudan swaptions have no simple formula and are valued with term-structure models and numerical methods, which introduces model risk.

• International Swaps and Derivatives Association (ISDA)
• Bank for International Settlements