INTEREST RATE SWAPS AND THEIR DERIVATIVES
Interest rate swaps and their derivatives have become an integral part of the fixed income market, but many of the pricing and risk management issues for these now mainstream products can only be learned on a trading floor. While there are many books on fixed income and interest rate derivatives, they generally suffer from being either too elementary and bond–centric, mentioning swaps in passing, or too technical and focused on exotics and the myriad implementation issues and algorithms used to tackle them.
Rather than focusing on exotics, Interest Rate Swaps and Their Derivatives thoroughly covers the mainstream productsswaps, flow options, Bermudans, semi–exoticsshowing the common pricing techniques while also explaining how to generalize the concepts to more nuanced products.
Author Amir Sadr, experienced as a quant, trader, financial software developer, and academic in the fixed income field, begins by presenting plain–vanilla swaps as an extension of fixed rate bondsrevealing how techniques for pricing these instruments are a generalization of similar methods used for pricing bonds and repos, and for the most part involve the concepts of financing cost, discount factors, and projection of forward curves. He then moves on to cover the options markets for flow products, including options on futures, caps and floors, and European swaptionswith detailed attention to the actual trading practice of these products. Sadr explains how, as with any option product, the pricing and risk management of these requires dealing with volatility as the main risk factorand he shows that one does not need to have a PhD in math to understand options. Sadr presents risk–neutral valuation as the fundamental pricing paradigm for derivatives, and illustrates the core idea of dynamic replication in a simple binomial setting. This unified framework is used to derive industry–standard Black formula for flow products, and is developed into short–rate and full term–structure models for more complex interest rate exotics including Bermudans.
For current or aspiring practitioners in interest rate products, Interest Rate Swaps and Their Derivatives provides a sound working knowledge and appreciation of the main features of these products and their pricing and risk management issues.
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.
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.
Construction of the Swap/Libor Curve.
CHAPTER 3 Interest Rate Swaps in Practice.
Swap Trading—Rates or Spreads.
Risk, PV01, Gamma Ladder.
Calendar Rules, Date Minutiae.
CHAPTER 4 Separating Forward Curve from Discount Curve.
Forward Curves for Assets.
Implied Forward Rates.
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 . . .
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.
Call Is All You Need.
Calendar/Business Days, Event Vols.
CHAPTER 7 European–Style Interest–Rate Derivatives.
Interest–Rate Option Trades.
Caplets/Floorlets: Options on Forward Rates.
PART THREE Interest–Rate Exotics.
CHAPTER 8 Short–Rate Models.
A Quick Tour.
Dynamics to Implementation.
BDT Lattice Model.
Hull–White, Black–Karasinski Models.
CHAPTER 9 Bermudan–Style Options.
Bellman′s Equation—Backward Induction.
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.
HJM Framework Typically Leads to Nonrecombining Trees.
CHAPTER 11 Forward–Measure Lens.
Numeraires Are Arbitrary.
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.
Model versus Market: Liquidity and Concentration Risk.
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.
APPENDIX C Girsanov′s Theorem and Change of Numeraire.
Continuous–Time, Instantaneous–Forwards HJM Framework.