# Derivatives: Valuation and Risk Management

By David A. Dubofsky; Thomas W. Miller Jr. | Go to book overview

CHAPTER 13

Pricing and Valuing Swaps

Determining the theoretical price of a swap is quite simple. In Chapter 11, you learned that a swap is equivalent to an asset and a liability and that an at-market swap has zero value (ignoring the impact of the bid-ask spread) when it is originated. This means that to determine the fixed price for a swap, a firm should find the present value of the swap's payments and the swap's receipts. The price that equates the two present values results in a zero net value for the two parties. Then the swap dealer, to make a profit in her service as a market maker, can adjust the price to quote a bid-ask spread. Thus, valuing swap cash flows involves no more work than valuing two sets of cash flows.1

After its origination, the swap can be valued by comparing the new present value of the remaining cash payments to the new present value of the remaining cash receipts. Current interest rates and exchange rates must be used to compute these two present values. The remaining fixed cash flows are the same as they were when the swap was originated, although they will be discounted at new, current rates. The remaining expected floating cash flows will likely be different, and they too will be discounted at new current rates. Remember that a swap is a zero sum game, so that if the swap has a positive value for one party, it must have the same negative value for the counterparty.

Another way to value swaps after origination is to compare the price of the old swap with the current price for a swap with a tenor equal to the remaining time to maturity of the old swap. Then, one compares the present value of the old swap's fixed cash flows with the present value of the fixed cash flows for a new swap. This shortcut is valid because the same LIBOR serves as the floating rate in both cases.

If valuation is properly done, the value of the swap will be the same regardless of which approach is used. The differences between the two approaches will become apparent when an example is worked out, later in the chapter.

This chapter begins with an example of the method that prices and values plain vanilla fixed-floating interest rate swaps.

13.1 PRICING AND VALUING PLAIN VANILLA FIXED–FLOATING INTEREST
RATE SWAPS

In a fixed-floating interest rate swap, one party agrees to make a series of fixed payments and receive a series of floating, or variable, payments. Thus, the goal of swap pricing is to determine the fixed interest rate that makes the present value of the fixed payments equal to the present value

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