Interest Rate Swaps: Mechanics, Valuation, and the Comparative-Advantage Argument

An interest rate swap is the world's most traded derivative. At any moment, the Bank for International Settlements reports over $400 trillion in notional outstanding. The reason is simple: almost every corporation, bank, and government agency carries either fixed-rate debt it would prefer to be floating, or floating-rate debt it would prefer to be fixed. A swap converts one into the other without touching the underlying loan — no refinancing, no prepayment penalties, one OTC contract.

Pricing a swap requires a complete picture of forward rates across all payment dates. The bond valuation approach makes this transparent: a plain vanilla interest rate swap is the difference between a fixed-rate bond and a floating-rate bond, and the floating-rate bond always prices at par on coupon dates. The FRA valuation approach makes the cash-flow engineering explicit: each payment exchange is a forward rate agreement on a short-term rate, and the swap value is the sum of their present values evaluated at current forward rates. Both approaches give the same answer (as Example 7.2 / 7.3 confirm) and each reveals a different economic intuition.

• describe the cash flows in a plain vanilla interest rate swap and explain who pays what when;
• use the bond decomposition to value a swap given a LIBOR zero curve;
• use the FRA decomposition to value a swap via forward rates;
• explain the comparative-advantage argument, state its total gain formula, and identify the flaw in its reasoning;
• derive a LIBOR/swap zero rate via bootstrapping from swap rates;
• explain how yield curve shape affects the value of individual FRAs within a swap.

1. Mechanics of interest rate swaps
2. Day count conventions
3. The bond decomposition
4. The FRA decomposition
5. The LIBOR/swap zero curve
6. The comparative-advantage argument
7. Term structure effects on individual FRA values