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