Description
Book SynopsisAn up-to-date look at the evolution of interest rate swaps and derivatives
Interest Rate Swaps and Derivatives bridges the gap between the theory of these instruments and their actual use in day-to-day life. This comprehensive guide covers the main rates products, including swaps, options (cap/floors, swaptions), CMS products, and Bermudan callables. It also covers the main valuation techniques for the exotics/structured-notes area, which remains one of the most challenging parts of the market.
- Provides a balance of relevant theory and real-world trading instruments for rate swaps and swap derivatives
- Uses simple settings and illustrations to reveal key results
- Written by an experienced trader who has worked with swaps, options, and exotics
With this book, author Amir Sadr shares his valuable insights with practitioners in the field of interest rate derivatives-from traders and marketers to those in operations.
Table of ContentsPreface 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 C Girsanov’s Theorem and Change of Numeraire 229
Continuous-Time, Instantaneous-Forwards HJM Framework 230
BGM Result 232
Notes 235
Index 239
