Second Edition DE RI VAT IV ES PRINCIPLES and PRACTICE R a n g a r a j a n K S u n d a m Sanjiv R Das Derivatives: Principles and Practice The McGraw-Hill/Irwin Series in Finance, Insurance, and Real Estate Stephen A Ross Franco Modigliani Professor of Finance and Economics Sloan School of Management Massachusetts Institute of Technology Consulting Editor FINANCIAL MANAGEMENT Block, Hirt, and Danielsen Foundations of Financial Management Fifteenth Edition Brealey, Myers, and Allen Principles of Corporate Finance Eleventh Edition Brealey, Myers, and Allen Principles of Corporate Finance, Concise Second Edition Brealey, Myers, and Marcus Fundamentals of Corporate Finance Eighth Edition Brooks FinGame Online 5.0 Bruner Case Studies in Finance: Managing for Corporate Value Creation Seventh Edition Cornett, Adair, and Nofsinger Finance: Applications and Theory Third Edition Cornett, Adair, and Nofsinger M: Finance Third Edition DeMello Cases in Finance Second Edition Grinblatt (editor) 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Management and Insurance Second Edition Kapoor, Dlabay, and Hughes Focus on Personal Finance: An active approach to help you achieve financial literacy Fifth Edition Kapoor, Dlabay, and Hughes Personal Finance Eleventh Edition Walker and Walker Personal Finance: Building Your Future First Edition Derivatives: Principles and Practice Second Edition Rangarajan K Sundaram Stern School of Business New York University New York, NY 10012 Sanjiv R Das Leavey School of Business Santa Clara University Santa Clara, CA 95053 DERIVATIVES: PRINCIPLES AND PRACTICE, SECOND EDITION Published by McGraw-Hill Education, Penn Plaza, New York, NY 10121 Copyright © 2016 by McGraw-Hill Education All rights reserved Printed in the United States of America Previous edition © 2011 No part of this publication may be reproduced or distributed in any form or by any means, or stored in a database or retrieval system, without the prior written consent of McGraw-Hill Education, including, but not limited to, in any network or other electronic storage or transmission, or broadcast for distance learning Some ancillaries, including electronic and print components, may not be available to customers outside the United States This book is printed on acid-free paper QVS/QVS ISBN 978-0-07-803473-2 MHID 0-07-803473-6 Senior Vice President, Products & Markets: Kurt L Strand Vice President, General Manager, Products & Markets: Marty Lange Vice President, Content Design & Delivery: Kimberly Meriwether David Managing Director: Doug Reiner Brand Manager: Charles Synovec Product Developer: Jennifer Lohn Digital Product Developer: Meg Maloney Director, Content Design & Delivery: Linda Avenarius Executive Program Manager: Faye M Herrig Content Project Managers: Mary Jane Lampe, Sandra Schnee Buyer: Jennifer Pickel Cover Design: Studio Montage Content Licensing Specialists: Beth Thole Cover Image Credit: © Brand X Pictures/PunchStock Compositor: MPS Limited Typeface: 10/12 Times New Roman Printer: Quad/Graphics All credits appearing on page or at the end of the book are considered to be an extension of the copyright page Library of Congress Cataloging-in-Publication Data Sundaram, Rangarajan K Derivatives : principles and practice / Rangarajan K Sundaram, Sanjiv R Das – Second edition pages cm ISBN 978-0-07-803473-2 (alk paper) Derivative securities I Das, Sanjiv R (Sanjiv Ranjan) II Title HG6024.A3S873 2016 332.64’57—dc23 2014037947 The Internet addresses listed in the text were accurate at the time of publication The inclusion of a website does not indicate an endorsement by the authors or McGraw-Hill Education, and McGraw-Hill Education does not guarantee the accuracy of the information presented at these sites www.mhhe.com To my lovely daughter Aditi and to the memory of my beautiful wife Urmilla RKS To my departed parents and Priya and Shikhar SRD Brief Contents Author Biographies Preface xvi xxi 19 Exotic Options II: Path-Dependent Options 467 20 Value-at-Risk Acknowledgments 18 Exotic Options I: Path-Independent Options 437 xv Introduction 495 21 Convertible Bonds 22 Real Options PART ONE Futures and Forwards Futures Markets PART THREE 21 Swaps Pricing Forwards and Futures II: Building on the Foundations 88 Hedging with Futures and Forwards 104 Interest-Rate Forwards and Futures 126 567 23 Interest Rate Swaps and Floating-Rate Products 569 24 Equity Swaps 614 25 Currency and Commodity Swaps 651 26 The Term Structure of Interest Rates: Concepts 653 155 157 27 Estimating the Yield Curve Options: Payoffs and Trading Strategies 173 29 Factor Models of the Term Structure 10 Early Exercise and Put-Call Parity 216 11 Option Pricing: A First Pass 231 261 13 Implementing Binomial Models 14 The Black-Scholes Model 671 28 Modeling Term-Structure Movements 688 No-Arbitrage Restrictions on Option Prices 199 12 Binomial Option Pricing 697 30 The Heath-Jarrow-Morton and Libor Market Models 714 PART FIVE 290 309 Credit Risk 753 31 Credit Derivative Products 755 15 The Mathematics of Black-Scholes 346 32 Structural Models of Default Risk 16 Options Modeling: Beyond Black-Scholes 359 33 Reduced-Form Models of Default Risk 816 17 Sensitivity Analysis: The Option “Greeks” 401 34 Modeling Correlated Default vi 632 PART FOUR Interest Rate Modeling PART TWO Options Markets 547 19 Pricing Forwards and Futures I: The Basic Theory 63 Options 516 850 789 Brief Contents Bibliography Index B-1 I-1 The following Web chapters are available at www.mhhe.com/sd2e: PART SIX Computation 35 Derivative Pricing with Finite Differencing 36 Derivative Pricing with Monte Carlo Simulation 23 37 Using Octave 45 vii Contents Author Biographies Preface xvi Acknowledgments Chapter Introduction 1.1 1.2 1.3 1.4 1.5 1.6 3.8 Futures Prices 75 3.9 Exercises 77 Appendix 3A Compounding Frequency 82 Appendix 3B Forward and Futures Prices with Constant Interest Rates 84 Appendix 3C Rolling Over Futures Contracts 86 xv xxi Forward and Futures Contracts Options Swaps 10 Using Derivatives: Some Comments The Structure of this Book 16 Exercises 17 Chapter Pricing Forwards and Futures II: Building on the Foundations 88 12 PART ONE Futures and Forwards Chapter Futures Markets 19 21 2.1 Introduction 21 2.2 The Functioning of Futures Exchanges 23 2.3 The Standardization of Futures Contracts 32 2.4 Closing Out Positions 35 2.5 Margin Requirements and Default Risk 37 2.6 Case Studies in Futures Markets 40 2.7 Exercises 55 Appendix 2A Futures Trading and US Regulation: A Brief History 59 Appendix 2B Contango, Backwardation, and Rollover Cash Flows 62 Chapter Pricing Forwards and Futures I: The Basic Theory 63 3.1 3.2 3.3 3.4 Introduction 63 Pricing Forwards by Replication 64 Examples 66 Forward Pricing on Currencies and Related Assets 69 3.5 Forward-Rate Agreements 72 3.6 Concept Check 72 3.7 The Marked-to-Market Value of a Forward Contract 73 viii 4.1 Introduction 88 4.2 From Theory to Reality 88 4.3 The Implied Repo Rate 92 4.4 Transactions Costs 95 4.5 Forward Prices and Future Spot Prices 96 4.6 Index Arbitrage 97 4.7 Exercises 100 Appendix 4A Forward Prices with Convenience Yields 103 Chapter Hedging with Futures and Forwards 104 5.1 5.2 5.3 5.4 5.5 5.6 5.7 5.8 5.9 5.10 Introduction 104 A Guide to the Main Results 106 The Cash Flow from a Hedged Position 107 The Case of No Basis Risk 108 The Minimum-Variance Hedge Ratio 109 Examples 112 Implementation 114 Further Issues in Implementation 115 Index Futures and Changing Equity Risk 117 Fixed-Income Futures and Duration-Based Hedging 118 5.11 Exercises 119 Appendix 5A Derivation of the Optimal Tailed Hedge Ratio h ∗∗ 124 Chapter Interest-Rate Forwards and Futures 6.1 6.2 6.3 6.4 6.5 Introduction 126 Eurodollars and Libor Rates 126 Forward-Rate Agreements 127 Eurodollar Futures 133 Treasury Bond Futures 140 126 Contents 6.6 Treasury Note Futures 144 6.7 Treasury Bill Futures 144 6.8 Duration-Based Hedging 144 6.9 Exercises 147 Appendix 6A PVBP-Based Hedging Using Eurodollar Futures 151 Appendix 6B Calculating the Conversion Factor 152 Appendix 6C Duration as a Sensitivity Measure 153 Appendix 6D The Duration of a Futures Contract 154 PART TWO Options 155 Chapter Options Markets 157 7.1 7.2 7.3 7.4 7.5 Introduction 157 Definitions and Terminology 157 Options as Financial Insurance 158 Naked Option Positions 160 Options as Views on Market Direction and Volatility 164 7.6 Exercises 167 Appendix 7A Options Markets 169 Chapter Options: Payoffs and Trading Strategies 173 8.1 Introduction 173 8.2 Trading Strategies I: Covered Calls and Protective Puts 173 8.3 Trading Strategies II: Spreads 177 8.4 Trading Strategies III: Combinations 185 8.5 Trading Strategies IV: Other Strategies 188 8.6 Which Strategies Are the Most Widely Used? 191 8.7 The Barings Case 192 8.8 Exercises 195 Appendix 8A Asymmetric Butterfly Spreads 198 Chapter No-Arbitrage Restrictions on Option Prices 199 9.1 Introduction 199 9.2 9.3 9.4 9.5 9.6 9.7 9.8 Motivating Examples 199 Notation and Other Preliminaries 201 Maximum and Minimum Prices for Options 202 The Insurance Value of an Option 207 Option Prices and Contract Parameters 208 Numerical Examples 211 Exercises 213 Chapter 10 Early Exercise and Put-Call Parity 10.1 10.2 10.3 10.4 10.5 216 Introduction 216 A Decomposition of Option Prices 216 The Optimality of Early Exercise 219 Put-Call Parity 223 Exercises 229 Chapter 11 Option Pricing: A First Pass 231 11.1 Overview 231 11.2 The Binomial Model 232 11.3 Pricing by Replication in a One-Period Binomial Model 234 11.4 Comments 238 11.5 Riskless Hedge Portfolios 240 11.6 Pricing Using Risk-Neutral Probabilities 240 11.7 The One-Period Model in General Notation 244 11.8 The Delta of an Option 245 11.9 An Application: Portfolio Insurance 249 11.10 Exercises 251 Appendix 11A Riskless Hedge Portfolios and Option Pricing 255 Appendix 11B Risk-Neutral Probabilities and Arrow Security Prices 256 Appendix 11C The Risk-Neutral Probability, No-Arbitrage, and Market Completeness 257 Appendix 11D Equivalent Martingale Measures 260 ix ... Fifth Edition Kapoor, Dlabay, and Hughes Personal Finance Eleventh Edition Walker and Walker Personal Finance: Building Your Future First Edition Derivatives: Principles and Practice Second Edition. .. Eighth Edition Brooks FinGame Online 5.0 Bruner Case Studies in Finance: Managing for Corporate Value Creation Seventh Edition Cornett, Adair, and Nofsinger Finance: Applications and Theory Third Edition. .. Edition DeMello Cases in Finance Second Edition Grinblatt (editor) Stephen A Ross, Mentor: Influence through Generations Grinblatt and Titman Financial Markets and Corporate Strategy Second Edition