# Interest Rate Swaps

The unprecedented interest rate volatility in the United States in the 1970s and 1980s created demand for risk management products and strategies. Swaps emerged from that time period and since then have become the primary derivative contract used in practice to hedge interest rate risk. There are some actively traded fixed-income and interest rate futures contracts, in particular, on Treasury notes and bonds and on 3-month LIBOR, but swaps have come to dominate because of their flexibility and operational ease for many * end users.* End users are those entities (including financial institutions, investment funds, companies, universities, and state and local governments) that either want or need an interest rate derivative. It's surely a vast simplification, but I like to think that those who

*derivatives essentially are*

**want***on rates and those who*

**speculating***them are*

**need***risk exposures. In reality, decisions regarding risk management often are a play between those two motivations, sometimes called*

**hedging**

**strategic hedging.**Interest rate swaps are also a great product to illustrate bond math techniques. We focus on swap valuation in this chapter. The traditional method is called LIBOR discounting. Later in the chapter we see how the financial crisis of 2007 to 2009 has led to some significant changes in derivatives valuation and what is called OIS discounting. To start, I use basic bond math to show that a standard (or * plain vanilla)* fixed- for-floating swap can be priced initially and valued later using the implied spot and forward curves corresponding to the reference rate, that is, LIBOR. “Pricing” here means determining the fixed rate at issuance. Typically, it is set so that the initial value of the swap is zero to each of the two counterparties to the contract. Subsequently, as time passes and swap market rates change, the swap will take on positive value to one of the parties and an equal but negative value to the other. Swaps are what we call a zero-sum game – gains to one side are offset by the losses to the counterparty.

The primary risk statistics (i.e., duration in its various forms) for an interest rate swap are calculated by interpreting the derivative as a “long- short” combination of a fixed-rate and a floating-rate bond. To the party paying the fixed rate and receiving the floating rate, the swap has * negative duration.* The idea is that the swap has the same net cash flows as owning a (low-duration) floater financed by issuing a (higher-duration) fixed-rate bond. Because swaps are a zero-sum game, the counterparty receiving the fixed rate and paying the floating rate has a swap having positive duration. It's like owning a fixed-rate bond financed by issuing the floater.

We calculate the duration of the implicit fixed-rate bond in the interest rate swap using the equations developed in Chapter 6. Unfortunately, the general formula in Chapter 7 for the duration of a floater that might be trading at a premium or discount is not used with interest rate swaps. Market practice traditionally has been to assume that the floater always is priced at par value on payment dates – that dramatically simplifies its duration calculations.