Callable Swaps

This product suits a company that wants to fix the interest on a loan it can repay early and also end the swap on the repayment date. Depending on who holds the right, the swap's fixed rate is higher or lower than that of a plain swap.

A swap with a termination right

A callable swap is a plain interest rate swap with a right added that lets one party end all future payments¹. The swap is called callable when the fixed-rate payer holds the right and putable when the fixed-rate receiver holds it. The Federal Reserve Board's 1998 manual for examiners groups both as cancelable swaps and counts them as a type of swaption². The holder of the right (the buyer of the right) pays an option premium for it², and in a callable swap that price appears in the difference in the fixed rate³.

A "3x5 cancelable swap" is a 5-year swap that one party can end starting in 3 years². The name gives the years until the right becomes exercisable, then the years in the whole swap.

When a plain swap without the right is ended before maturity, the parties settle an amount based on the market value of the remaining payments. For example, the party whose market value is negative pays the other party in a buy-back and pays the party taking over in a transfer⁴. The holder of the termination right can end the swap without paying the present value of those remaining payments². The price of the right corresponds to this difference. The glossary calls the amount settled when a plain swap is ended a termination payment.

Termination dates and the link to swaptions

A swap with one termination date is called European, and one that can be terminated on any of several dates fixed in advance is called Bermudan¹. A right that can be exercised on any of several dates is a Bermudan option. For a swaption, using the right is called "exercise," and for a swap, "termination."

A callable swap held by the fixed-rate payer corresponds to a plain swap combined with a receiver swaption¹. A putable swap held by the fixed-rate receiver is a plain swap combined with a payer swaption¹. The meaning of receiver and payer is covered in Swaptions.

Deep diveWhy the payer's termination is a receiver swaption

Suppose a swap in which one party pays a fixed rate $K$ and receives a floating rate is still running after the termination date. On the termination date, that party enters a new swap over the same period in which you receive the fixed rate $K$ and pay a floating rate. The fixed payments and the floating payments cancel, and no payments remain after the termination date.

If the payer terminates, the payments are the same as if the payer had entered this new swap. If the payer does not terminate, no new swap is entered and the original swap stays in place. The payer's termination right therefore has the same outcome as a receiver swaption with a strike rate of $K$ and a term equal to the remaining term⁵. This argument looks only at the cancellation of payments.

The value of the termination right corresponds to the value of the combined swaption.

An example of hedging debt

Institutions with debt that can be repaid early (such as callable bonds) use cancelable swaps. They do so to avoid a mismatch between the term of the debt and the term of the swap that hedges it². The case in which the issuer receives fixed is covered in Callable Bonds and Early Redemption Features. Here, the example is the form in which the fixed-rate payer holds the right.

Consider a hypothetical example in which Company H has a 5-year floating-rate loan with a notional of 10 billion yen, which it can repay early starting in 3 years. To turn the floating rate into a fixed rate, Company H pays fixed and receives floating in a swap with a dealer. The floating rate it receives is based on the same benchmark as the loan's floating rate, so Company H's cost becomes the fixed rate. The fixed rate of a plain 5-year swap is 2.0% per year. The fixed rate of a 3x5 callable swap that Company H can terminate starting in 3 years is 2.3% per year, because the price of the right is added to the fixed rate.

Suppose market rates have changed after 3 years, and compare two cases. Because the loan continues after termination, assume Company H enters a new 2-year swap at the market fixed rate. The floating-rate payments cancel against the interest on the loan, so the table shows only the fixed-rate payments, as a simple total without discounting. The difference is "with right − plain."

If rates fell, Company H terminates the 2.3% swap and re-enters at 1.0%. Its payments are 230 million yen for 3 years plus 100 million yen for 2 years, a total of 890 million yen, which is 110 million yen less than the 1,000 million yen of the plain swap. If rates rose, the market fixed rate is above 2.3%, so Company H does not terminate and keeps paying 2.3% for 5 years. It pays 1,150 million yen, which is 150 million yen more than the plain swap. This difference is the 0.3% gap between 2.3% and 2.0%, multiplied by the notional of 10 billion yen and 5 years. It is the price of a right that was not used.

Figure description

This figure shows the fixed-rate payments when rates fall and Company H terminates the swap after 3 years and re-enters a swap for the remaining 2 years. The amounts are the same as in the "Rates fell" row of the table in the text. Until termination, Company H pays the fixed rate of the swap with the right, and after termination the payments fall to the lower, re-entered fixed rate. The floating-rate payments cancel against the interest on the loan, so they are not drawn.

If the loan is repaid in 3 years, the termination right lets Company H end the swap on the same day as the repayment. Company H's payments end at 2.3% for 3 years, 230 million yen × 3 years = 690 million yen. With a plain swap, Company H pays 2.0% for 3 years, 200 million yen × 3 years = 600 million yen, and then the 2-year remainder of the swap stays in place. To end it, Company H settles the market value of the remaining payments²⁴. The swap with the right costs 90 million yen more than the plain swap over the 3 years until repayment, but no swap remains after repayment (simple totals, without discounting). The market value of the 2 remaining years of the plain swap could be an amount Company H receives or pays, depending on rates at that time.

How the premium is paid

For a swaption, the buyer pays the premium as an up-front fee⁶. For a callable swap, according to the Intercontinental Exchange (ICE) help, there is no premium paid at the start, and the price of the right appears in the difference in the fixed rate. The fixed rate is higher than that of a plain swap on the same terms when the payer holds the right, and lower when the receiver holds it³. The gap between 2.3% and 2.0% in Company H's example is this difference.

The size of the difference depends on the period until the right becomes exercisable and on interest rate volatility. The higher the volatility, the larger the difference from a plain swap³. A Bermudan swap, with several termination dates, has a more valuable right than a European one, so its fixed-rate difference is larger⁷.

What changes the value

For Company H, which holds the right as the payer, the value changes with the market fixed rate on the termination date. The more rates fall, the more the right is worth. If rates rise, the added fixed rate remains. The figures are in the two rows of the table above.

Seen from the party that granted the right (the seller of the right), gains and losses are the reverse. When the payer holds the right, the dealer is the fixed-rate receiver. If rates fall and the right is exercised, the dealer loses the rest of a contract that pays a fixed rate above the market. If rates rise and the right is not exercised, the dealer keeps receiving the added fixed rate.

When the receiver holds the right, the payer who sold it is worse off if rates rise, and better off by the lower fixed rate if rates do not rise.

In the ICE help's example, the fixed-rate payer gives the receiver a termination right and in return gets a fixed rate lowered from the plain 4.5% to 4.2%. If rates rise, the receiver uses the right, and the payer loses the swap's protection against the rise. If rates do not rise and the right is not used, the payer keeps paying the lower fixed rate of 4.2%⁸.

Risks and valuation

The Federal Reserve Board's manual for examiners (April 2001 edition) lists two risks of a swaption: the probability of exercise and the credit risk arising from the swap. The risk from the probability of exercise depends on the level of market interest rates and on interest rate volatility.

Credit risk is the cost of replacing the same transaction when one party cannot meet its obligations⁹. A cancelable swap is a type of swaption, so both risks apply to callable swaps².

When the payer holds the right, as the table above shows, the holder's risk is rising rates and the risk of the dealer who sold the right is falling rates.

Valuation changes with the model used. Swaption prices are set by models, and as of that manual the models dealers used differed widely. The more complex a structure is, and the harder to reverse, the more the bid-offer spread varies¹⁰. For a general explanation of risk arising from models, see model risk in the glossary.

As of that manual, swaptions were hedged with Eurodollar futures, U.S. Treasury securities, and interest rate swaps¹¹.

Notes

1. Intercontinental Exchange (ICE), "SDX Interest Rates Help," "Callable Swap," opening description. ↩ ↩² ↩³ ↩⁴

2. Board of Governors of the Federal Reserve System, "Trading and Capital-Markets Activities Manual" (February 1998), Section 4340.1 "Swaptions," page 1, "Cancelable Swaps." ↩ ↩² ↩³ ↩⁴ ↩⁵ ↩⁶ ↩⁷

3. The same help, "Callable Swap," on how the fixed rate differs depending on who holds the right, and on the breakeven rate. No premium is paid at the start: "Advantages of a Callable Swap." ↩ ↩² ↩³

4. The same manual (February 1998), Section 4325.1 "Interest-Rate Swaps," pages 5–6, "Secondary Market." Examples of a buy-back and an assignment. ↩ ↩²

5. An explanation by a calculation in which the payments cancel. The correspondence matches the opening of the ICE help's "Callable Swap." ↩

6. The same manual (February 1998), Section 4340.1 "Swaptions," page 1, "General Description." ↩

7. The same help, "Advantages of a Callable Swap." It explains why the seller of a Bermudan swap receives a higher rate. ↩

8. The same help, "Example of a European Callable Swap." In the source's example, the swap is a 5-year fixed-payer swap that the counterparty can terminate after 3 years, with a fixed rate of 4.2% against the plain 4.5%. ↩

9. The same manual (April 2001), Section 4340.1 "Swaptions," page 4, "Risks." ↩

10. The same manual (April 2001), Section 4340.1 "Swaptions," page 3, "Pricing." ↩

11. The same manual (April 2001), Section 4340.1 "Swaptions," page 3, "Hedging." ↩