Interest Rate Swaps and Their Derivatives

AMIR SADR, PHD, has experience as a quant, trader, financial software developer, and academic in fixed income markets. He traded options and exotics at HSBC in New York from 2005 to 2006 and traded at the proprietary desk for Greenwich Capital Markets (GCM) for four years prior to that. Sadr also has experience at Morgan Stanley as a vice president in the derivatives products group where he traded interest rate derivatives and exotics. Since 1996, Sadr has served as an adjunct professor at New York University in the Department of Finance and Accounting.

• Preface ix“Rates” Market ixBackground ixBook Structure xiAcknowledgments xviiAbout the Author xixList of Symbols and Abbreviations xxiPart One Cash, Repo, and Swap Markets 1Chapter 1 Bonds: It’s All About Discounting 3Time Value of Money: Future Value, Present Value 3Price-Yield Formula 5PV01, PVBP, Convexity 11Repo, Reverse Repo 16Forward Price/Yield, Carry, Roll-Down 19Chapter 2 Swaps: It’s Still About Discounting 25Discount Factor Curve, Zero Curve 26Forward Rate Curve 27Par-Swap Curve 31Construction of the Swap/Libor Curve 34Chapter 3 Interest Rate Swaps in Practice 43Market Instruments 43Swap Trading—Rates or Spreads 48Swap Spreads 51Risk, PV01, Gamma Ladder 56Calendar Rules, Date Minutiae 59Chapter 4 Separating Forward Curve from Discount Curve 67Forward Curves for Assets 67Implied Forward Rates 69Float/Float Swaps 70Libor/Libor Basis Swaps 73Overnight Indexed Swaps (OIS) 75Part Two Interest-Rate Flow Options 77Chapter 5 Derivatives Pricing: Risk-Neutral Valuation 79European-Style Contingent Claims 80One-Step Binomial Model 80From One Time-Step to Two 84From Two Time-Steps to 90Relative Prices 91Risk-Neutral Valuation: All Relative Prices Must be Martingales 92Interest-Rate Options Are Inherently Difficult to Value 93From Binomial Model to Equivalent Martingale Measures 94Chapter 6 Black’s World 97A Little Bit of Randomness 97Modeling Asset Changes 103Black-Scholes-Merton/Black Formulae 104Greeks 112Digitals 116Call Is All You Need 117Calendar/Business Days, Event Vols 120Chapter 7 European-Style Interest-Rate Derivatives 123Market Practice 124Interest-Rate Option Trades 124Caplets/Floorlets: Options on Forward Rates 125European-Style Swaptions 129Skews, Smiles 137CMS Products 140Bond Options 147Part Three Interest-Rate Exotics 149Chapter 8 Short-Rate Models 151A Quick Tour 152Dynamics to Implementation 153Lattice/Tree Implementation 154BDT Lattice Model 156Hull-White, Black-Karasinski Models 168Simulation Implementation 169Chapter 9 Bermudan-Style Options 175Bellman’s Equation—Backward Induction 176Bermudan Swaptions 177Bermudan Cancelable Swaps, Callable/Puttable Bonds 180Bermudan-Style Options in Simulation Implementation 183Chapter 10 Full Term-Structure Interest-Rate Models 185Shifting Focus from Short Rate to Full Curve: Ho-Lee Model 186Heath-Jarrow-Morton (HJM) Full Term-Structure Framework 186Discrete-Time, Discrete-Tenor HJM Framework 188Forward-Forward Volatility 191Multifactor Models 197HJM Framework Typically Leads to Nonrecombining Trees 199Chapter 11 Forward-Measure Lens 201Numeraires Are Arbitrary 201Forward Measures 206BGM/Jamshidian Results 208Different Measures for Different Rates 210“Classic” or “New Improved”: Pick Your Poison! 212Chapter 12 In Search of “The” Model 215Migration to Full-Term Structure Models 215Implementation Era 216Model versus Market: Liquidity and Concentration Risk 216Complexity Risk 217Remaining Challenges 218Appendix A Taylor Series Expansion 219Function of One Variable 219Function of Several Variables 220Ito’s Lemma: Taylor Series for Diffusions 220Appendix B Mean-Reverting Processes 223Normal Dynamics 224Log-Normal Dynamics 226Appendix C Girsanov’s Theorem and Change of Numeraire 229Continuous-Time, Instantaneous-Forwards HJM Framework 230BGM Result 232Notes 235Index 239