Interest Rate Swap Valuation and Applications › Interest Rate Swap Valuation and Applications

In the previous chapter, we introduced the mechanics of interest rate swaps: the exchange of fixed-rate payments for floating-rate payments between two counterparties. You learned how these instruments work, what drives their use, and the basic terminology that market participants employ. Now we turn to the critical question: how do we determine the value of a swap?

Swap valuation connects present-value calculations to quoting, hedging and synthetic cash-flow construction. This chapter develops the bond and FRA approaches in a stated single-curve model, calibrates a curve to hypothetical par quotes, and applies the results to matched borrowing hedges, synthetic coupons and asset-liability management.

The key insight is that a swap can be decomposed into more fundamental instruments we've already studied. We can view it either as a portfolio of bonds or as a portfolio of forward rate agreements. The bond view groups cash flows by leg; the FRA view groups them by payment period. Under the assumptions below, the two constructions give the same value.

The examples use one curve for both projecting floating payments and discounting them, with no credit adjustment or floating spread. The reset-date examples assume that the current floating fixing matches the forward rate from that curve. Under these assumptions, the bond and FRA valuations agree. Later, we discuss why market pricing may require separate projection and discount curves.