TRADING VOLATILITY

1 VOLATILITYT rading VOLATILITY , Correlation, Term Structure and SkewTRADINGVOLATILITYC olin Bennett VOLATILITYTRADINGC olin Bennett is a Managing Director and Head of Quantitative and Derivative Strategy at Banco Santander. Previously he was Head of Delta 1 Research at Barclays Capital, and Head of Convertible and Derivative Research at Dresdner started his career in Convertible Bond Research at Merrill Lynch, after studying Mathematics and Electrical Engineering at Cambridge University. In the 1993 National Mathematics Contest Colin came 16th in the UK. He has also worked in Equity Derivative Sales, and as a Desk Analyst for the equity derivative TRADING desk. Colin is a regular speaker at CBOE, Eurex, Marcus Evans, Futures and Option World, Risk Magazine and Bloomberg THE AUTHOR A master piece to learn in a nutshell all the essentials about VOLATILITY with a practical and lively approach.

2 A must read! Carole Bernard, Equity Derivatives Specialist at Bloomberg This book could be seen as the VOLATILITY bible ! Markus-Alexander Flesch, Head of Sales & Marketing at Eurex I highly recommend this book both for those new to the equity derivatives business, and for more advanced readers. The balance between theory and practice is struck At-The-Money Paul Stephens, Head of Institutional Marketing at CBOE One of the best resources out there for the VOLATILITY community Paul Britton, CEO and Founder of Capstone Investment Advisors Colin has managed to convey often complex derivative and VOLATILITY concepts with an admirable simplicity, a welcome change from the all-too-dense tomes one usually finds on the subject Edmund Shing PhD, former Proprietary Trader at BNP Paribas In a crowded space, Colin has supplied a useful and concise guide Gary Delany, Director Europe at the Options Industry CouncilAny questions regarding the content of this book can be emailed to TRADING VOLATILITY TRADING VOLATILITY , Correlation, Term Structure and Skew Colin Bennett Copyright 2014 Colin Bennett All rights reserved.

3 No part of this publication may be reproduced, stored in a retrieval system, or transmitted in any form or by any means electronic, mechanical, photocopying, recording or otherwise without written permission of the publisher or author. TRADING VOLATILITY : TRADING VOLATILITY , Correlation, Term Structure and Skew ISBN-13: 978-1499206074 Cover Design by Gareth Allen ACKNOWLEDGEMENTS I would like to thank James Peattie for persuading me to work at Merrill Lynch, and starting my career within research which I still enjoy to this very day. Iain Clamp aka The Guru deserves special recognition, for explaining the intricacies of VOLATILITY TRADING . I will always be grateful to Tom Dauterman and Irene Ferrero for their many months of effort proofing this publication. I would also like to thank Mariano Colmenar, without whose support this book would never have been published. And finally, and most importantly, I would like to thank my wife Claire for her endless patience and understanding with me while I researched and wrote this book over the past 5 years.

4 NOTE ON CONTENTS While there are many different aspects to VOLATILITY TRADING , not all of them are suitable for all investors. In order to allow easy navigation, the sections are combined into seven chapters that are likely to appeal to different parts of the equity derivatives client base. The earlier chapters are most suited to equity investors, while later chapters are aimed at hedge funds and proprietary TRADING desks. The Appendix contains reference material and mathematical detail that has been removed from earlier chapters to enhance readability. CONTENTS PREFACE .. i CHAPTER 1 OPTIONS .. 1 : Option basics .. 2 : Option TRADING in practice .. 4 : Maintenance of option positions .. 11 : Call overwriting .. 15 : Protection strategies using options .. 23 : Option structures TRADING .. 31 CHAPTER 2 VOLATILITY TRADING .. 35 : VOLATILITY TRADING using options.

5 36 : Variance is the key, not VOLATILITY .. 49 : VOLATILITY , variance and gamma swaps .. 52 : Options on variance .. 68 CHAPTER 3 WHY EVERYTHING YOU THINK YOU KNOW ABOUT VOLATILITY IS WRONG .. 73 : Implied VOLATILITY should be above realized VOLATILITY .. 74 : Long VOLATILITY is a poor hedge .. 77 : Variable annuity hedging lifts long-term vol .. 81 : Structured products vicious circle .. 83 : Stretching black-scholes assumptions .. 89 CHAPTER 4 FORWARD STARTING PRODUCTS AND VOLATILITY INDICES .. 99 : Forward starting products .. 100 : VOLATILITY indices .. 109 : Futures on VOLATILITY indices .. 115 : VOLATILITY future ETN/ETF .. 122 : Options on VOLATILITY futures .. 129 CHAPTER 5 LIGHT EXOTICS .. 133 : Barrier options .. 134 : Worst-of/best-of 140 : Outperformance options .. 143 : Look-back options .. 146 : Contingent premium options .. 148 : Composite and quanto options .. 149 CHAPTER 6 RELATIVE VALUE AND CORRELATION TRADING .

6 153 : Relative value TRADING .. 154 : Relative value VOLATILITY TRADING .. 158 : Correlation TRADING .. 161 : TRADING earnings announcements/jumps .. 178 CHAPTER 7 SKEW AND TERM STRUCTURE TRADING .. 183 : Skew and term structure are linked .. 184 : Square root of time rule can compare term structures and 193 : Term structure TRADING .. 198 : How to measure skew and smile .. 201 : Skew TRADING .. 210 APPENDIX : Local VOLATILITY .. 230 : Measuring historical VOLATILITY .. 232 : Proof implied jump formula .. 245 : Proof var swaps can be hedged by log contract (=1/k2) .. 248 : Proof variance swap notional = vega/2 .. 250 : Modelling VOLATILITY 251 : Black-scholes formula .. 255 : Greeks and their meaning .. 257 : Advanced (practical or shadow) greeks .. 262 : Shorting stock by borrowing shares .. 266 : Sortino ratio .. 269 : Capital structure arbitrage .. 270 INDEX .. 286 PREFACE One of the main reasons I decided to write this book, was due to the lack of other publications that deal with the practical issues of using derivatives.

7 This publication aims to fill the void between books providing an introduction to derivatives, and advanced books whose target audience are members of quantitative modelling community. In order to appeal to the widest audience, this publication tries to assume the least amount of prior knowledge. The content quickly moves onto more advanced subjects in order to concentrate on more practical and advanced topics. CHAPTER 1 OPTIONS This chapter is focused on real life uses of options for directional investors, for example using options to replace a long position in the underlying, to enhance the yield of a position through call overwriting, or to provide protection from declines. In addition to explaining these strategies, a methodology to choose an appropriate strike and expiry is shown. Answers to the most common questions are given, such as when an investor should convert an option before maturity, and the difference between delta and the probability that an option expires in the money.

8 2 CHAPTER 1: OPTIONS : OPTION BASICS This section introduces options and the history of options TRADING . The definition of call and put options, and how they can be used to gain long or short equity exposure, is explained. Key definitions and terminology are given, including strike, expiry, intrinsic value, time value, ATM, OTM and ITM. HISTORY OF VOLATILITY TRADING While standardised exchange traded options only started TRADING in 1973 when the CBOE (Chicago Board Options Exchange) opened, options were first traded in London from 1690. Pricing was made easier by the Black-Scholes-Merton formula (usually shortened to Black-Scholes), which was invented in 1970 by Fischer Black, Myron Scholes and Robert Merton. Option TRADING exploded in the 1990s The derivatives explosion in the 1990s was partly due to the increasing popularity of hedge funds, which led to VOLATILITY becoming an asset class in its own right.

9 New VOLATILITY products such as VOLATILITY swaps and variance swaps were created, and a decade later futures on VOLATILITY indices gave investors listed instruments to trade VOLATILITY . In this chapter we shall concentrate on option TRADING . CALL OPTIONS GIVE RIGHT TO BUY, PUTS RIGHT TO SELL A European call is a contract that gives the investor the right (but not the obligation) to buy a security at a certain strike price on a certain expiry date (American options can be exercised before expiry). A put is identical except it is the right to sell the security. Call option gives long exposure, put options give short exposure A call option profits when markets rise (as exercising the call means the investor can buy the underlying security cheaper than it is TRADING , and then sell it at a profit). A put option profits when markets fall (as you can buy the underlying security for less, exercise the put and sell the security for a profit).

10 Options therefore allow investors to put on long (profit when prices rise) or short (profit when prices fall) strategies. : Option Basics 3 SELLING OPTIONS GIVES OPPOSITE EXPOSURE As a call option gives long exposure to the underlying security, s elling a call option results in short exposure to the underlying security. Similarly while a put option is a bearish (profits from decline in the underlying) strategy, selling a put option is a bullish strategy (profits from a rise in the underlying). While the direction of the underlying is the primary driver of profits and losses from buying or selling options, the VOLATILITY of the underlying is also a driver. OPTIONS TRADING GIVES VOLATILITY EXPOSURE If the VOLATILITY of an underlying is zero, then the price will not move and an option s payout. is equal to the intrinsic value. Intrinsic value is the greater of zero and the spot strike price for a call and is the greater of zero and strike price spot for a put.