Modeling Fixed-Income Securities and Interest Rate Options
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1 jarr_fm.qxd 5/16/02 4:49 PM Page iii Modeling Fixed-Income Securities and Interest Rate Options SECOND EDITION Robert A. Jarrow Stanford Economics and Finance An Imprint of Stanford University Press Stanford, California 2002
2 jarr_fm.qxd 5/16/02 4:49 PM Page iv Stanford University Press Stanford, California 2002 by the Board of Trustees of the Leland Stanford Junior University Printed in the United States of America on acid-free, archival-quality paper ISBN (cloth : alk. paper) Designed by: R. Kharibian & Associates Typeset by: Interactive Composition Corporation in 11/13 Times New Roman Original Printing 2002 Last figure below indicates year of this printing:
3 jarr_fm.qxd 5/16/02 4:49 PM Page ix Preface to the Second Edition xv Prologue 1 Approach 1 Motivation 2 Methodology 6 Overview 8 References 9 PART I Introduction 1 Traded Securities Treasury Securities Treasury Security Markets Repo Markets Treasury Futures Markets Interest Rate Derivatives on Treasuries Eurodollar Spot, Forward, and Futures Markets Interest Rate Derivatives on LIBOR 24 References 24 2 The Classical Approach Motivation Coupon Bonds 25 ix
4 jarr_fm.qxd 5/16/02 4:49 PM Page x x PART II 2.3 Bond s Yield, Duration, Modified Duration, and Convexity Risk Management 34 Reference 38 Theory 3 The Term Structure of Interest Rates The Economy The Traded Securities Interest Rates Forward Contracts Futures Contracts Option Contracts Summary 55 References 56 4 The Evolution of the Term Structure of Interest Rates Motivation The One-Factor Economy The Two-Factor Economy Multiple-Factor Economies Consistency with Equilibrium 83 References 84 5 The Expectations Hypothesis Motivation Present Value Form Unbiased Forward Rate Form Relation Between the Two Versions of the Expectations Hypothesis Empirical Illustration 95 References 98 6 Trading Strategies, Arbitrage Opportunities, and Complete Markets Motivation Trading Strategies Arbitrage Opportunities Complete Markets 112
5 jarr_fm.qxd 5/16/02 4:49 PM Page xi xi 7 Bond Trading Strategies An Example Motivation Method 1: Synthetic Construction Method 2: Risk-Neutral Valuation Bond Trading Strategies Theory Motivation The One-Factor Economy The Two-Factor Economy Multiple-Factor Economies 154 Appendix 154 References Interest Rate Derivatives Valuation Theory Motivation The One-Factor Economy The Two-Factor Economy Multiple-Factor Economies 170 Appendix 171 PART III Applications 10 Coupon Bonds The Coupon Bond as a Portfolio of Zero-Coupon Bonds The Coupon Bond as a Dynamic Trading Strategy Comparison of HJM Hedging Versus Duration Hedging Options on Bonds Distribution-Free Option Theory European Options on Zero-Coupon Bonds American Options on Coupon Bonds Call Provisions on Coupon Bonds 206 References Forwards and Futures Forwards Futures The Relationship Between Forward and Futures Prices 224
6 jarr_fm.qxd 5/16/02 4:49 PM Page xii xii 12.4 Options on Futures Exchange-Traded Treasury Futures Contracts 230 References Swaps, Caps, Floors, and Swaptions Fixed-Rate and Floating-Rate Loans Interest Rate Swaps Interest Rate Caps Interest Rate Floors Swaptions 253 References Interest Rate Exotics Simple Interest Rates Digital Options Range Notes Index-Amortizing Swaps 267 References 272 PART IV Implementations 15 Continuous-Time Limits Motivation The One-Factor Economy The Two-Factor Economy Multiple-Factor Economies Computational Issues 298 References Parameter Estimation Coupon Bond Stripping The Initial Forward Rate Curve Volatility Function Estimation Application to Coupon Bond Data 310 Appendix 321 References 322
7 jarr_fm.qxd 5/16/02 4:49 PM Page xiii xiii PART V Extensions/Other 17 Spot Rate Models Bond Pricing Contingent Claims Valuation Limit Economies 335 References Extensions Foreign-Currency Derivatives Credit Derivatives and Counterparty Risk Commodity Derivatives 339 References 340 Index 341
Modeling Fixed-Income Securities and Interest Rate Options
jarr_fm.qxd 5/16/02 4:49 PM Page iii Modeling Fixed-Income Securities and Interest Rate Options SECOND EDITION Robert A. Jarrow Stanford Economics and Finance An Imprint of Stanford University Press Stanford,
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