DERIVATIVES MARKETS Derivatives Markets is a thorough and well-presented textbook that offers readers an introduction to derivatives instruments, with a gentle introduction to mathematical finance, and provides a working knowledge of derivatives to a wide spectrum of market participants. This new and accessible book provides a lucid, down-to-earth, theoretically rigorous but applied introduction to derivatives. Many insights have been discovered since the seminal work in the 1970s and the text provides a bridge to these insights, and incorporates them. It develops the skill sets needed to both understand and intelligently use derivatives. These skill sets are developed, in part, by using concept checks that test the reader’s understanding of the material as it is presented. The text discusses some fairly sophisticated topics not usually discussed in introductory derivatives texts; for example, real-world electronic market trading platforms such as CME’s Globex. On the theory side, there is a much- needed and detailed discussion of what risk-neutral valuation really means in the context of the dynamics of the hedge portfolio. The text is a balanced, logical presentation of the major derivatives classes including forward and futures contracts in Part 1, swaps in Part 2, and options in Part 3. The material is unified by providing a modern conceptual framework and exploiting the no-arbitrage relationships between the different derivatives classes. Some of the elements explained in detail in the text are: • Hedging, Basis Risk, Spreading, and Spread Basis Risk. • Financial Futures Contracts, their Underlying Instruments, Hedging and Speculating. • OTC Markets and Swaps. • Option Strategies: Hedging and Speculating. • Risk-Neutral Valuation and the Binomial Option Pricing Model. • Equivalent Martingale Measures: A Modern Approach to Option Pricing. • Option Pricing in Continuous Time: From Bachelier to Black-Scholes and Beyond. Professor Goldenberg’s clear and concise explanations, running concept checks, and end-of-chapter problems guide the reader through the derivatives markets, developing the reader’s skill sets needed in order to incorporate and manage derivatives in a corporate or risk management setting. This textbook is for students, both undergraduate and postgraduate, as well as for those with an interest in how and why these markets work and thrive. David H. Goldenberg is an independent researcher in New York, USA. DERIVATIVES MARKETS David H. Goldenberg First published 2016 by Routledge 2 Park Square, Milton Park, Abingdon, Oxon OX14 4RN by Routledge 711 Third Avenue, New York, NY 10017 Routledge is an imprint of the Taylor & Francis Group, an informa business © 2016 David H. Goldenberg The right of David H. Goldenberg to be identified as author of this work has been asserted by him in accordance with the Copyright, Designs and Patent Act 1988. All rights reserved. No part of this book may be reprinted or reproduced or utilised in any form or by any electronic, mechanical, or other means, now known or hereafter invented, including photocopying and recording, or in any information storage or retrieval system, without permission in writing from the publishers. Every effort has been made to contact copyright holders for their permission to reprint material in this book. The publishers would be grateful to hear from any copyright holder who is not here acknowledged and will undertake to rectify any errors or omissions in future editions of this book. Trademark notice: Product or corporate names may be trademarks or registered trademarks, and are used only for identification and explanation without intent to infringe. British Library Cataloguing in Publication Data A catalogue record for this book is available from the British Library Library of Congress Cataloging in Publication Data Goldenberg, David Harold, 1949– Derivatives markets / David H. Goldenberg. 1. Derivative securities. I. Title. HG6024.A3G645 2015 332.64′57—dc23 2015000492 ISBN: 978-0-415-59901-6 (hbk) ISBN: 978-1-315-68924–1 (ebk) Typeset in Bembo and Univers by Florence Production Ltd, Stoodleigh, Devon, UK Additional materials are available on the companion website at www.routledge.com/products/9780415599016 CONTENTS List of figures xxiii List of tables xxvii Preface xxxi Acknowledgments xxxvii PART 1 Forward Contracts and Futures Contracts 1 1. SPOT, FORWARD, AND FUTURES CONTRACTING 3 2. HEDGING WITH FORWARD CONTRACTS 33 3. VALUATION OF FORWARD CONTRACTS ON ASSETS WITHOUT A DIVIDEND YIELD 65 4. VALUATION OF FORWARD CONTRACTS ON ASSETS WITH A DIVIDEND YIELD 87 5. FUTURES CONTRACTS: MARKET ORGANIZATION 121 6. HEDGING WITH FUTURES CONTRACTS, BASIS RISK, AND SPREADING 139 7. INTRODUCTION TO FINANCIAL FUTURES CONTRACTS 211 PART 2 Trading Structures Based on Forward Contracts 271 8. STRUCTURED PRODUCTS, INTEREST-RATE SWAPS 273 vi CONTENTS PART 3 Options 321 9. INTRODUCTION TO OPTIONS MARKETS 323 10. OPTION TRADING STRATEGIES, PART 1 345 11. RATIONAL OPTION PRICING 369 12. OPTION TRADING STRATEGIES, PART 2 415 13. MODEL-BASED OPTION PRICING IN DISCRETE TIME, PART 1: THE BINOMIAL OPTION PRICING MODEL (BOPM, N=1) 435 14. OPTION PRICING IN DISCRETE TIME, PART 2: DYNAMIC HEDGING AND THE MULTI-PERIOD BINOMIAL OPTION PRICING MODEL, N>1 473 15. EQUIVALENT MARTINGALE MEASURES: A MODERN APPROACH TO OPTION PRICING 507 16. OPTION PRICING IN CONTINUOUS TIME 539 17. RISK-NEUTRAL VALUATION, EMMS, THE BOPM, AND BLACK–SCHOLES 595 Index 637 DETAILED CONTENTS List of figures xxiii List of tables xxvii Preface xxxi Acknowledgments xxxvii PART 1 Forward Contracts and Futures Contracts 1 CHAPTER 1 SPOT, FORWARD, AND FUTURES CONTRACTING 3 1.1 Three Ways to Buy and Sell Commodities 5 1.2 Spot Market Contracting (Motivation and Examples) 5 1.3 Forward Market Contracting (Motivation and Examples) 7 1.4 Problems with Forward Markets 11 1.5 Futures Contracts as a Solution to Forward Market Problems (Motivation and Examples) 13 1.6 Futures Market Contracting 17 1.7 Mapping Out Spot, Forward, and Futures Prices 20 1.7.1 Present and Future Spot Prices 20 1.7.2 Forward Prices 24 1.7.3 Futures Prices 25 CHAPTER 2 HEDGING WITH FORWARD CONTRACTS 33 2.1 Motivation for Hedging 33 2.2 Payoff to a Long Forward Position 37 2.3 Payoff to a Short Forward Position 39 viii DETAILED CONTENTS 2.4 Hedging with Forward Contracts 43 2.5 Profits to a Naked (Unhedged) Long Spot Position 45 2.6 Profits to a Fully Hedged Current Long Spot Position 47 2.7 Adding Profit Tables to Determine Profits from a Fully Hedged Position 50 2.8 Combining Charts to See Profits from the Hedged Position 54 CHAPTER 3 VALUATION OF FORWARD CONTRACTS ON ASSETS WITHOUT A DIVIDEND YIELD 65 3.1 Comparing the Payoffs from a Naked Long Spot Position to the Payoffs from a Naked Long Forward Position 66 3.2 Pricing Zero-Coupon, Unit Discount Bonds in Continuous Time 69 3.2.1 Continuous Compounding and Continuous Discounting 69 3.2.2 Pricing Zero-Coupon Bonds 71 3.3 Price vs. Value for Forward Contracts 73 3.4 Valuing a Forward Contract at Expiration 74 3.5 Valuing a Forward Contract at Initiation 75 3.6 Interpreting Forward Contracts via Synthetic Forward Contracts 78 CHAPTER 4 VALUATION OF FORWARD CONTRACTS ON ASSETS WITH A DIVIDEND YIELD 87 4.1 Stock Forwards when the Stock Pays Dividends 88 4.2 Modeling Continuous Yields: An Introduction to Non-Stochastic Differential Equations 90 4.2.1 Modeling Zero-Coupon Bond Yields 90 4.2.2 Modeling Continuous Dividend Yields for Stocks 93 DETAILED CONTENTS ix 4.3 How Dividend Payments Affect Stock Prices 94 4.4 How Capital Gains Affect Stock Prices 98 4.5 Pricing Forward Contracts on Stocks with a Dividend Yield Using the Net Interest Model 99 4.6 Pricing a Forward Contract on a Dividend-Paying Stock Using No-Arbitrage 100 4.6.1 Arbitrage Definitions 100 4.6.2 Forward Pricing Using No-Arbitrage 102 4.7 Currency Spot and Currency Forwards 103 4.7.1 Price Quotes in the FX Market 103 4.7.2 Pricing Currency Forwards 105 4.7.3 Pricing FX Forward Contracts Using No-Arbitrage 106 4.7.4 An Example of Pricing FX Forward Contracts 107 4.8 Appendix: Modeling Stock Returns with and without Dividends 109 CHAPTER 5 FUTURES CONTRACTS: MARKET ORGANIZATION 121 5.1 Futures Market Participants 122 5.2 Three Phases of Futures Trading 125 5.3 ‘Buying’ and ‘Selling’ Futures Contracts 126 5.4 Alternative Types of Orders: Market, Market with Protection, Limit 127 5.4.1 Market Orders and Market Orders with Protection 127 5.4.2 Limit Orders 129 5.4.3 The Limit Order Book (LOB) 130 5.4.4 Depth in the LOB 131 5.5 Globex and the Globex LOB 134 5.6 Pit Trading and the Order Flow Process 136