# Interest Rate Swaps

Interest rates are unpredictable, especially over the long run. Issuers of bonds could issue short-term bonds to minimize the interest rate risk, but issuing bonds costs money, and the prices, and therefore their yields, will often depend on the bond market when they are sold. Hence, issuers of bonds generally want to issue long-term bonds; so does the United States government. Banks also are subject to interest rate risk when they make long-term fixed rate loans, such as mortgages or business loans. Interest rate swaps allow institutions to synthetically match the duration of their assets with their liabilities as a means of managing interest rate risk.

An interest rate swap can help protect the issuer of bonds, Treasuries, or loans against interest rate risk by transferring the risk to another party in exchange for a variable payment. A **swap contract** is an agreement to exchange future cash flows. Swaps can remove market risk but not credit risk. The most common type of swap agreement is the **fixed-floating interest rate swap**, otherwise known as a **plain-vanilla swap**, and is the most common type of **interest rate derivative** (aka **fixed-income derivatives**).

An **interest rate swap**, in its simplest form, is a private agreement between 2 **counterparties** to exchange a fixed interest obligation for a floating rate obligation over a specified duration. The payment is calculated by multiplying the interest rate times a **notional principal** (aka **notational principal**), which is not exchanged, but is simply a number used to calculate both interest payments. The counterparty paying the fixed amount is the **fixed-rate payer** and the counterparty paying the floating rate is the **floating rate payer**. The fixed payment of a swap is known as the **fixed leg** while the floating payment is referred to as the **floating leg**.

However, only the net difference between these obligations is paid, and who pays whom depends on whom the change in interest rates favors. For instance, if the float rate rises above the fixed rate, then the floating rate payer pays the fixed-rate payer the difference between the floating rate and the fixed rate, but if the floating rate falls below the fixed rate, then the fixed-rate payer pays the floating rate payer the difference in interest rates. It is possible for 1 counterparty to receive all the payments without paying anything, or it could go back and forth, depending on how interest rates fluctuate.

The frequency of the payment is the **tenor** or **coupon frequency**. Common tenors are 1 month, 3 months, 6 months, and annually. Sometimes, the 2 legs of a swap have different tenors.

The **fixed rate** is usually determined by a **benchmark** such as a Treasury with a maturity equal to the time period of the swap plus an additional risk premium, which equals the **swap rate**. The size of the swap rate is called the **swap spread**, which is sometimes used as an indicator of the systemic risk in the economy. The **floating rate** is usually determined by the **London Interbank Offered Rate** (**LIBOR**), which is the rate that large banks lend to each other, plus an additional risk premium.

Although there are other types of swaps, such as currency swaps and equity swaps, interest rate swaps are far more prevalent. According to the Bank for International Settlements, the notional principal for interest rate swaps was almost 347 trillion dollars (USD) in June, 2007, while the total for equity-linked and commodity derivatives was 9.2 trillion dollars for the same time period. Because swaps are private agreements, there is no organized exchange that lists them, and because they are tailored specifically for the counterparties, they are difficult to resell.

## Swap Credit Risks

With any derivative, there is always the chance that the counterparty will default on its obligation. To minimize this risk, the contract generally specifies that collateral must be posted.

When a swap agreement is reached, the net present value of both sides is zero, because no money changes hands at first. This must be so, because no one would agree to an arrangement where one party immediately benefits from the other without compensation. How does that transfer risk? So, if one party withdraws from the agreement before any liability is incurred, there is no loss, for another counterparty can usually be found. Only when interest rates change will there be a payment obligation. However, it is only the difference between the liabilities that is actually paid, which is considerably less than what would be suggested by the notional principal.

For example, consider an interest rate swap for a 5-year period with a fixed payment of 5% on the notional principal of $1,000,000 and the LIBOR rate, which was also at 5% when the contract was created. If the LIBOR rate rises to 6% during the swap period and stays there, then the floating rate payer must pay only the 1% difference or $10,000 for each of the 5 years. However, the present value of those payments is less than their sum. Hence, the credit risk is significantly less than if the principal were at stake.

## Basis Swaps and Currency Swaps

Other interest rate derivatives include the **basis swap**, which has 2 floating legs but no fixed leg. Thus, it is exchanging payments based on a floating interest rate on one index to that of another, such as the prime interest rate and the LIBOR. **Basis**, as used here, is the difference between 2 rates, such as the difference between spot prices and futures prices of a given commodity, so risk can arise when basis changes.

Another type of interest rate derivative is the **cross-currency interest rate swap**, or just **currency swap**, in which both legs of the swap are denominated in different currencies. Most of the swaps are set up to exchange a fixed interest rate in one currency with a floating rate in the other currency. To remove exchange rate risk, the notional amount of the swaps is generally exchanged. So if the exchange rate at the signing of the swap agreement is $1.25 to €1, and a company wants to exchange a fixed rate based on €1,000,000 for a floating rate in USD, then the euro party will give €1,000,000 to the other party and receive $1.25 million in United States dollars. This removes the exchange rate risk and the swap agreement itself removes interest-rate risk, which was its purpose. If a company wanted to remove foreign exchange risk without exchanging currencies, then that risk can be hedged with a forward agreement — specifically, an FX forward — or with interest rate futures or options to mitigate its risk.

## Swaptions

A **swaption** is an option for a swap at a specified rate before a specified time, the **expiration date**. The buyer of the swaption has the right, but not the obligation, to enter a swap and the swaption seller is obliged to be the counterparty. Swaptions can be American or European style. American style swaptions give the holder the right to enter a swap at any time before the expiration date, while the European style gives the holder the right only at expiry.

A **payer swaption** (aka **put swaption**) gives the buyer the right, but not the obligation, to pay a fixed rate and receive a floating rate. The buyer pays the premium to the seller for this right, which, like all options, may expire worthless. A **receiver swaption** (aka **call swaption**) gives the option holder the right to receive a fixed interest rate and pay a floating rate based on a specified benchmark.

Some swaps can be canceled or extended. A **cancelable swap** gives 1 party the right to cancel the swap on a specified day before the final maturity date without an additional cost. A cancelable swap can be created by combining a vanilla interest-rate swap with a swaption. An alternative to the cancelable swap is the **extendable swap**, where the buyer has the right to extend the option for a set period.