Interest Rate Swaps: Valuation and Market Practice (Chapter 16)
Book: Fixed Income Securities: Tools for Today’s Markets | Author: Bruce Tuckman & Angel Serrat | ISBN: 978-0-470-89169-8
Previous: TED Spreads and Financial Stress (Chapter 15, Part 2) | Next: Arbitrage and Two-Curve Discounting (Chapter 17)
Parts One and Two already priced the fixed leg of swaps like a bond. Chapter 16 finally gives the floating leg, counterparty risk, and post-crisis market structure the attention they deserve.
Swap Cash Flows in Plain English
A vanilla USD swap: you pay fixed semiannually on 30/360 and receive three-month LIBOR quarterly on actual/360. The $100 million notional is never exchanged. It only sizes the interest.
Floating payments are set in advance and paid in arrears. On May 28, 2010, you observe LIBOR for the quarter starting June 2. You know the September payment three months before you pay it. Swap payment dates can slip to the next business day, and unlike bonds, extra days add extra interest on the fixed leg.
The Old LIBOR Discounting Story
Add a fictional principal payment to both legs at maturity. The fixed leg looks like a coupon bond. The floating leg looks like a floating-rate note.
The traditional trick: discount floating cash flows at LIBOR. Roll backward from maturity. Three months before the end, the floating leg is worth par because you earn and discount at the same rate. Keep rolling and the floating leg is par at every reset. So a par swap starts at zero NPV on both sides.
Between resets the floating leg is a short bond paying the last LIBOR setting until the next date. Reset risk jumps at each fixing and bleeds down to near zero just before payment.
That framework worked when LIBOR-OIS was a few basis points. It broke in 2007-2009. LCH.Clearnet moved to OIS discounting in June 2010. Chapter 17 explains why. This chapter still teaches LIBOR discounting first because you need the logic before the fix.
Credit Risk Is Two Different Things
LIBOR itself embeds bank credit risk. It is an unsecured interbank rate. Swap rates reflect expectations about future LIBOR plus premia.
Counterparty risk on the swap contract is separate. You only exchange interest, not principal at maturity. If your counterparty defaults, you lose the NPV of the swap, not the full notional. A 2-year swap might have NPV of $1.10 per 100. A bond with the same coupon puts you at risk for $101.15.
Dealers post collateral under CSA agreements. Non-collateralized trades often bake in a credit value adjustment (CVA) in the fixed rate. Swap books quoted in notional overstate true exposure.
Why People Trade Swaps
Corporates hedge future bond issuance by paying fixed now and unwinding at sale. They create synthetic floating debt by issuing fixed and receiving fixed in a swap. Mortgage desks pay fixed in huge size when rate risk on MBS rises, which can distort swap levels vs. Treasuries. Pension funds receive fixed to lengthen asset duration.
Each use comes with basis risk. Swap rates track bank credit, not your firm’s credit.
Clearing, Standardization, and Politics
Dodd-Frank pushed OTC swaps through central clearinghouses. A CCP sits between both sides and mutualizes default risk. Tuckman is skeptical: clearing does not eliminate risk, it spreads it. Forcing some exposures to a CCP while leaving others bilateral can increase total risk if diversification mattered.
Standardization fights customization. IMM-dated swap schedules are one compromise gaining traction.
Basis Swaps and CMS
Basis swaps exchange one floating index for another, usually with a spread. Three-month LIBOR vs. one-month LIBOR plus 25 bp is common. The spread exists because term and credit differ. You cannot assume both floating legs are worth par under one discount curve.
Constant Maturity Swaps pay a fixed rate against a market swap rate (e.g., five-year swap rate quarterly for two years). Fair CMS fixed must exceed the forward swap rate. An arbitrage with receiving that forward swap in five years shows why: convexity of the hedge beats the linear CMS payoff either way. The convexity correction depends on swap rate volatility. On a flat 4% curve with 60 bp vol, fair CMS might be 4.0325% vs. 4% forward.
My Read
Chapter 16 is the pivot point of the book’s crisis narrative. Everything before assumes LIBOR is the riskless investment rate. Everything after admits that was wrong. The swap chapter makes that admission explicit without yet giving you the full two-curve machinery. That comes next.