# How to Price an Interest Rate Swap

by Leslie McClintock

Investors use interest swaps to hedge their portfolio credit risk exposure to a specific creditor, as well as to lower overall borrowing costs. The potential for arbitrage arises because of the difference in pricing, or interest rates, between two loans. Alternatively, it provides a way for a lender to trade a floating-rate debt for a fixed-rate debt, or vice versa. By trading a floating-rate obligation for a fixed-rate stream of payments, a lender can hedge its exposure to interest rate risk. The two lenders can trade, or "swap," the stream of payments from two loans. The lender receiving the larger stream of obligations compensates the other, so that both parties benefit.

## Determining Net Present Values

The net present value, or NPV, of a stream of payments is essentially what a market will pay you today for the right to receive those payments in the future. To determine the NPV of the two streams of payments, you may use a time value of money calculator. Different calculators use different variables, but usually I = the interest rate, P = payment, FV = future value, PV = present value, and P(x) is the number of payments per year.

## Comparison of Two Streams

Compare the two net present values. Remember, though, that streams of payments are not guaranteed, other than with Treasury debt. Some bonds are riskier than others. The risk, however, is accounted for, to some extent, in the issue with the higher interest rate. Traders should be cognizant of their own liquidity positions, however, in the event a borrower should default.

## The Swap Rate

The swap rate is the rate someone exchanging a variable stream of payments for a fixed rate should be willing to pay a counterparty for the privilege. To find it, calculate the net present value of both loans combined. Then divide the result by the total principal of the period in question times the number of days in the loan period times a floating-rate discount factor. Normally, traders use the LIBOR as the floating-rate discount factor, but there are other markets you could use. The swap rate is usually expressed as a percentage.

Calculate the "swap spread." Typically, traders will use the difference between the swap rate and a risk-free security of similar maturity -- a five-year Treasury, for example. Normally, the swap rate will come out higher than the risk-free rate.

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