Interest Rate Swaps and Their Derivatives: A Practitioner's Guide

Preface.

"Rates" Market.

Background.

Book Structure.

Acknowledgments.

About the Author.

List of Symbols and Abbreviations.

PART ONE Cash, Repo, and Swap Markets.

CHAPTER 1 Bonds: It's All About Discounting.

Time Value of Money: Future Value, Present Value.

Price-Yield Formula.

PV01, PVBP, Convexity.

Repo, Reverse Repo.

Forward Price/Yield, Carry, Roll-Down.

CHAPTER 2 Swaps: It's Still About Discounting.

Discount Factor Curve, Zero Curve.

Forward Rate Curve.

Par-Swap Curve.

Construction of the Swap/Libor Curve.

CHAPTER 3 Interest Rate Swaps in Practice.

Market Instruments.

Swap Trading—Rates or Spreads.

Swap Spreads.

Risk, PV01, Gamma Ladder.

Calendar Rules, Date Minutiae.

CHAPTER 4 Separating Forward Curve from Discount Curve.

Forward Curves for Assets.

Implied Forward Rates.

Float/Float Swaps.

Libor/Libor Basis Swaps.

Overnight Indexed Swaps (OIS).

PART TWO Interest-Rate Flow Options.

CHAPTER 5 Derivatives Pricing: Risk-Neutral Valuation.

European-Style Contingent Claims.

One-Step Binomial Model.

From One Time-Step to Two.

From Two Time-Steps to . . .

Relative Prices.

Risk-Neutral Valuation: All Relative Prices Must be Martingales.

Interest-Rate Options Are Inherently Difficult to Value.

From Binomial Model to Equivalent Martingale Measures.

CHAPTER 6 Black's World.

A Little Bit of Randomness.

Modeling Asset Changes.

Black-Scholes-Merton/Black Formulae.

Greeks.

Digitals.

Call Is All You Need.

Calendar/Business Days, Event Vols.

CHAPTER 7 European-Style Interest-Rate Derivatives.

Market Practice.

Interest-Rate Option Trades.

Caplets/Floorlets: Options on Forward Rates.

European-Style Swaptions.

Skews, Smiles.

CMS Products.

Bond Options.

PART THREE Interest-Rate Exotics.

CHAPTER 8 Short-Rate Models.

A Quick Tour.

Dynamics to Implementation.

Lattice/Tree Implementation.

BDT Lattice Model.

Hull-White, Black-Karasinski Models.

Simulation Implementation.

CHAPTER 9 Bermudan-Style Options.

Bellman's Equation—Backward Induction.

Bermudan Swaptions.

Bermudan Cancelable Swaps, Callable/Puttable Bonds.

Bermudan-Style Options in Simulation Implementation.

CHAPTER 10 Full Term-Structure Interest-Rate Models.

Shifting Focus from Short Rate to Full Curve: Ho-Lee Model.

Heath-Jarrow-Morton (HJM) Full Term-Structure Framework.

Discrete-Time, Discrete-Tenor HJM Framework.

Forward-Forward Volatility.

Multifactor Models.

HJM Framework Typically Leads to Nonrecombining Trees.

CHAPTER 11 Forward-Measure Lens.

Numeraires Are Arbitrary.

Forward Measures.

BGM/Jamshidian Results.

Different Measures for Different Rates.

"Classic" or "New Improved": Pick Your Poison!.

CHAPTER 12 In Search of "The" Model.

Migration to Full-Term Structure Models.

Implementation Era.

Model versus Market: Liquidity and Concentration Risk.

Complexity Risk.

Remaining Challenges.

APPENDIX A Taylor Series Expansion.

Function of One Variable.

Function of Several Variables.

Ito's Lemma: Taylor Series for Diffusions.

APPENDIX B Mean-Reverting Processes.

Normal Dynamics.

Log-Normal Dynamics.

APPENDIX C Girsanov's Theorem and Change of Numeraire.

Continuous-Time, Instantaneous-Forwards HJM Framework.

BGM Result.

Notes.

Index.