Equity Derivatives Neil C Schofield Equity Derivatives Corporate and Institutional Applications Neil C Schofield Verwood, Dorset, United Kingdom ISBN 978-0-230-39106-2 ISBN 978-0-230-39107-9 (eBook) DOI 10.1057/978-0-230-39107-9 Library of Congress Control Number: 2016958283 © The Editor(s) (if applicable) and The Author(s) 2017 The author(s) has/have asserted their right(s) to be identified as the author(s) of this work in accordance with the Copyright, Designs and Patents Act 1988. This work is subject to copyright. All rights are solely and exclusively licensed by the Publisher, whether the whole or part of the material is concerned, specifically the rights of translation, reprinting, reuse of illustrations, recitation, broadcasting, reproduction on microfilms or in any other physical way, and transmission or informa- tion storage and retrieval, electronic adaptation, computer software, or by similar or dissimilar methodology now known or hereafter developed. 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The registered company address is: The Campus, 4 Crinan Street, London, N1 9XW, United Kingdom Acknowledgements Like the vast majority of authors, I have been able to benefit from the insights of many people while writing this book. First and foremost, I must thank my friend and fellow trainer, David Oakes of Dauphin Financial Training. On more occasions than he cares to remem- ber David has kindly answered my queries in his normal cheerful manner. If you ever have a question on finance, I can assure you that David will know the answer! I must also thank Yolanda Clatworthy who spent a significant amount of time reviewing chapter three. Her insights have added enormous value to the chapter. Stuart Urquhart arranged for me to have access to Barclays Live and the quality of the data and screenshots has added significant value to the text. Over the years that I have known Stuart he has been a great supporter of all my writing and training activities often when the benefit to himself is marginal. A true gentleman. Many thanks to Doug Christensen who gave permission for the Barclays Live data to be used. Aaron Brask and Frans DeWeert both critiqued the original text proposal and made a number of useful pointers as to how the scope could be improved. Although I had to drop some of the suggestions due to time and space con- straints, their contributions were significant and gladly received. Also thanks to Matt Deakin of Morgan Stanley who helped clarify some equity swap set- tlement conventions. Troy Bowler was an invaluable sounding board in rela- tion to a number of topics. Thanks also go to the many participants who have attended my classroom sessions over the years. The immediacy of the feedback that participants pro- vide is invaluable in helping me deepen my understanding of a topic. v vi Acknowledgements Finally, a word of thanks to my family who have always been supportive of everything that I have done. A special word of thanks to Nicki who never complains even when I work late. “V”. Although many people helped to shape the book any mistakes are entirely my responsibility. I would always be interested to hear any comments about the text and so please feel free to contact me at neil.schofield@fmarketstrain- ing.com or via my website www.fmarketstraining.com. PS. Alan and Roger—once again, two slices of white toast and a cuppa for me! Contents 1 Equity Derivatives: The Fundamentals 1 2 Corporate Actions 35 3 Equity Valuation 45 4 Valuation of Equity Derivatives 73 5 Risk Management of Vanilla Equity Options 105 6 Volatility and Correlation 139 7 Barrier and Binary Options 203 8 Correlation-Dependent Exotic Options 247 9 Equity Forwards and Futures 271 10 Equity Swaps 287 11 Investor Applications of Equity Options 315 vii viii Contents 12 Structured Equity Products 347 13 Traded Dividends 385 14 Trading Volatility 417 15 Trading Correlation 461 Bibliography 479 Index 481 List of Figures Fig. 1.1 Movements of securities and collateral: non-cash securities lending trade 13 Fig. 1.2 Movements of securities and collateral: cash securities lending trade 14 Fig. 1.3 Example of an equity swap 20 Fig. 1.4 Profit and loss profiles for the four main option building blocks 22 Fig. 1.5 Example of expiry payoffs for reverse knock in and out options 24 Fig. 1.6 At expiry payoffs for digital calls and puts 25 Fig. 1.7 Overview of equity market interrelationship 32 Fig. 2.1 Techniques applied to equity derivative positions dependent on the type of takeover activity 38 Te asset conversion cycle 49 Fig. 3.1 Fig. 4.1 Structuring and hedging a single name price return swap 82 Fig. 4.2 Diagrammatic representation of possible arbitrage between the equity, money and equity swaps markets 84 Fig. 4.3 Diagrammatic representation of possible arbitrage between the securities lending market and the equity swaps market 85 Fig. 4.4 ATM expiry pay off of a call option overlaid with a stylized normal distribution of underlying prices 92 Fig. 4.5 ITM call option with a strike of $50 where the underlying price has increased to $51 93 Fig. 4.6 Increase in implied volatility for ATM call option 93 Te impact of time on the value of an ATM call option 95 Fig. 4.7 Fig. 4.8 Relationship between option premium and the underlying price for a call option prior to expiry 97 Fig. 5.1 Relationship between an option’s premium and the underlying asset price for a long call option prior to expiry 106 Fig. 5.2 Delta for a range of underlying prices far from expiry for a long-dated, long call option position 106 ix x List of Figures Fig. 5.3 Delta for a range of underlying prices close to expiry for a long call option position 107 Fig. 5.4 Equity call option priced under different implied volatility assumptions 109 Fig. 5.5 Positive gamma exposure for a long call position 112 Fig. 5.6 Expiry profile of delta-neutral short volatility position 114 Fig. 5.7 Initial and expiry payoffs for delta-neutral short position 115 Fig. 5.8 Impact on profit or loss for a 5 % fall in implied volatility on the delta-­neutral short volatility position 115 Fig. 5.9 Sources of profitability for a delta-neutral short volatility trade 118 Fig. 5.10 Theta for a 1-year option over a range of spot prices 121 Fig. 5.11 The theta profile of a 1-month option for a range of spot prices 122 Fig. 5.12 Pre- and expiry payoff values for an option, which displays positive theta for ITM values of the underlying price 123 Fig. 5.13 Vega for a range of spot prices and at two different maturities 127 Fig. 5.14 FX smile for 1-month options on EURUSD at two different points in time 130 Fig. 5.15 Volatility against strike for 3-month options. S&P 500 equity index 131 Fig. 5.16 Implied volatility against maturity for a 100 % strike option (i.e. ATM spot) S&P 500 equity index 132 Fig. 5.17 Volatility surface for S&P 500 as of 25th March 2016 133 Fig. 5.18 Volgamma profile of a long call option for different maturities for a range of spot prices. Strike price = $15.15 135 Fig. 5.19 Vega and vanna exposures for 3-month call option for a range of spot prices. Option is struck ATM forward 136 Fig. 5.20 Vanna profile of a long call and put option for different maturities and different degrees of ‘moneyness’ 137 Fig. 6.1 A stylized normal distribution 140 Fig. 6.2 Upper panel: Movement of Hang Seng (left hand side) and S&P 500 index (right hand side) from March 2013 to March 2016. Lower panel: 30-day rolling correlation coefficient over same period 145 Fig. 6.3 The term structure of single-stock and index volatility indicating the different sources of participant demand and supply 146 Fig. 6.4 Level of the S&P 500 and 3-month implied volatility for a 50 delta option. March 2006–March 2016 151 Fig. 6.5 Implied volatility for 3-month 50 delta index option versus 3-month historical index volatility (upper panel). Implied volatility minus realized volatility (lower panel). March 2006–March 2016 152 Fig. 6.6 Average single-stock implied volatility versus average single-stock realized volatility (upper panel). Implied volatility minus realized volatility (lower panel). March 2006–March 2016 153 List of Figures xi Fig. 6.7 Implied volatility of 3-month 50 delta S&P index option versus average implied volatility of 50 largest constituent stocks.