Volatility trading

fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= Volatility Trading EUAN SINCLAIR John Wiley & Sons, Inc iii fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= vi fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= Volatility Trading i fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= Founded in 1807, John Wiley & Sons is the oldest independent publishing company in the United States With offices in North America, Europe, Australia and Asia, Wiley is globally committed to developing and marketing print and electronic products and services for our customers’ professional and personal knowledge and understanding The Wiley Trading series features books by traders who have survived the market’s ever changing temperament and have prospered—some by reinventing systems, others by getting back to basics Whether a novice trader, professional or somewhere in-between, these books will provide the advice and strategies needed to prosper today and well into the future For a list of available titles, visit our Web site at www.WileyFinance.com ii fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= Volatility Trading EUAN SINCLAIR John Wiley & Sons, Inc iii fm JWBK128-Sinclair Copyright C April 5, 2008 12:45 Char Count= 2008 by Euan Sinclair All rights reserved Published by John Wiley & Sons, Inc., Hoboken, New Jersey Published simultaneously in Canada 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, scanning, or otherwise, except as permitted under Section 107 or 108 of the 1976 United States Copyright Act, without either the prior written permission of the Publisher, or authorization through payment of the appropriate per-copy fee to the Copyright Clearance Center, Inc., 222 Rosewood Drive, Danvers, MA 01923, (978) 750-8400, fax (978) 750-4470, or on the web at www.copyright.com Requests to the Publisher for permission should be addressed to the Permissions Department, John Wiley & Sons, Inc., 111 River Street, Hoboken, NJ 07030, (201) 748-6011, fax (201) 7486008, or online at http://www.wiley.com/go/permissions Limit of Liability/Disclaimer of Warranty: While the publisher and author have used their best efforts in preparing this book, they make no representations or warranties with respect to the accuracy or completeness of the contents of this book and specifically disclaim any implied warranties of merchantability or fitness for a particular purpose No warranty may be created or extended by sales representatives or written sales materials The advice and strategies contained herein may not be suitable for your situation You should consult with a professional where appropriate Neither the publisher nor author shall be liable for any loss of profit or any other commercial damages, including but not limited to special, incidental, consequential, or other damages Designations used by companies to distinguish their products are often claimed as trademarks In all instances where John Wiley & Sons, Inc is aware of a claim, the product names appear in initial capital or all capital letters Readers, however, should contact the appropriate companies for more complete information regarding trademarks and registration For general information on our other products and services or for technical support, please contact our Customer Care Department within the United States at (800) 762-2974, outside the United States at (317) 572-3993 or fax (317) 572-4002 Wiley also publishes its books in a variety of electronic formats Some content that appears in print may not be available in electronic books For more information about Wiley products, visit our web site at www.wiley.com Library of Congress Cataloging-in-Publication Data: Sinclair, Euan, 1969– Volatility trading + CD-ROM / Euan Sinclair p cm – (Wiley trading series) Includes bibliographical references and index ISBN 978-0-470-18199-7 (cloth/cd-rom) Options (Finance) Hedging (Finance) Futures I Title II Title: Volatility trading HG6024.A3S5623 2008 Financial futures 332.64 5–dc22 2007052403 Printed in the United States of America 10 iv fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= To Ann— Sometimes a trader wins much more than he deserves v fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= vi fm JWBK128-Sinclair April 5, 2008 12:45 Char Count= Contents Introduction The Trading Process CHAPTER Option Pricing The Black-Scholes-Merton Model Summary CHAPTER 14 Volatility Measurement and Forecasting 15 Defining and Measuring Volatility 15 Definition of Volatility 16 Alternative Volatility Estimators 22 Close-to-Close Estimator 26 Parkinson Estimator Garman-Klass Estimator Rogers-Satchell Estimator 26 27 27 Yang-Zhang Estimator 27 Using Higher-Frequency Data 27 Forecasting Volatility 31 Maximum Likelihood Estimation 36 Forecasting the Volatility Distribution 39 Summary 43 CHAPTER Implied Volatility Dynamics Volatility Level Dynamics 45 48 Informal Definition 50 More Formal Definition A Traders’ Definition 50 50 vii ref JWBK128-Sinclair 200 April 5, 2008 11:14 Char Count= REFERENCES Zakamouline, V 2005 Dynamic Hedging of Complex Option Positions with Transaction Costs Working paper, Bodo Graduate School of Business, Norway Zakamouline, V 2006a Optimal Hedging of Option Portfolios with Transaction Costs Working paper, Faculty of Economics, Agder University College, Norway Zakamouline, V 2006b Efficient Analytic Approximation of the Optimal Hedging Strategy for a European Call Option with Transaction Costs Quantitative Finance 6:435–445 Zakamouline, V 2006c European Option Pricing and Hedging with both Fixed and Proportional Transaction Costs Journal of Economic Dynamics and Control 30:1–25 aboutthe JWBK128-Sinclair March 13, 2008 22:17 Char Count= About the CD-ROM INTRODUCTION This appendix provides you with information on the contents of the CD that accompanies this book For the latest and greatest information, please refer to the ReadMe file located at the root of the CD SYSTEM REQUIREMENTS r A CD-ROM drive r Microsoft Excel USING THE CD WITH WINDOWS To install the items from the CD to your hard drive, follow these steps: Insert the CD into your computer’s CD-ROM drive The CD-ROM interface will appear The interface provides a simple point-and-click way to explore the contents of the CD If the opening screen of the CD-ROM does not appear automatically, follow these steps to access the CD: Click the Start button on the left end of the taskbar and then choose Run from the menu that pops up In the dialog box that appears, type d:\start.exe (If your CD-ROM drive is not drive d, fill in the appropriate letter in place of d.) This brings up the CD Interface described in the preceding set of steps 201 aboutthe JWBK128-Sinclair March 13, 2008 202 22:17 Char Count= ABOUT THE CD-ROM WHAT’S ON THE CD The following sections provide a summary of the software and other materials you’ll find on the CD Content Appendix B contains material about the CD The spreadsheets provided on the CD are of two types Garch.xls, Volatility Cones.xls, Skew and Kurtosis Cones.xls and Corrado Su.xls are directly useful as trading tools They are designed to assist a trader forecast and evaluate volatility and compare this to the current option market Trade Evaluation.xls is a template for monitoring the progress of trades The second type of sheet contains simulation engines Daily Option Hedging Simulation.xls, Trade Goals.xls and Mean Reversion Simulator.xls can help traders develop intuition and gain a deeper understanding of the effects of randomness on option positions and general trading strategies Shareware programs are fully functional, trial versions of copyrighted programs If you like particular programs, register with their authors for a nominal fee and receive licenses, enhanced versions, and technical support Freeware programs are copyrighted games, applications, and utilities that are free for personal use Unlike shareware, these programs not require a fee or provide technical support GNU software is governed by its own license, which is included inside the folder of the GNU product See the GNU license for more details Trial, demo, or evaluation versions are usually limited either by time or functionality (such as being unable to save projects) Some trial versions are very sensitive to system date changes If you alter your computer’s date, the programs will “time out” and no longer be functional Customer Care If you have trouble with the CD-ROM, please call the Wiley Product Technical Support phone number at (800) 762-2974 Outside the United States, call 1(317) 572–3994 You can also contact Wiley Product Technical Support at http://support.wiley.com John Wiley & Sons will provide technical support only for installation and other general quality control items For technical support on the applications themselves, consult the program’s vendor or author To place additional orders or to request information about other Wiley products, please call (877) 762-2974 ind JWBK128-Sinclair March 13, 2008 22:53 Char Count= Index ADRs See American depositary receipts (ADRs) Aggregation of options: on different underlyings, 83–85 underlying drift, in Black-Scholes-Merton (BSM) example, 10 Ahmad, R., 94, 97 Ait-Sahalia, Y., 28 Alexander, C., 46–47 Algorithms, genetic, 39 American depositary receipts (ADRs), 26, 29 Analysis See also Historical data analysis; Trade evaluation of market impact, 80 neglect of base rate in, 159–160 neglect of sample size in, 160 post-trade (example), 171–173 pretrade (example), 165–167 principal component (PCA), 45–48 rescaled range (R/S analysis), 144–145 Anchoring and adjusting bias, 162 Annualization: estimates from daily returns, 22 factor, 16, 93–94 higher-frequency data, 29 historical data, 16 and Parkinson estimator, 22–23 price paths (examples), 93–94 Sharpe ratio (risk measurement), 135–140 time series, 16 Apple computer (AAPL) (example), 165–173 APT (commercial factor model), 85 Assets, tradable, 12 Asymptotic solution See Whalley-Wilmott (WW) asymptotic solution At-the-money (ATM) volatility versus Corrado-Su model, 60 first day and right before expiration jumps, 88–90 versus out-of-the-money, 98 principal component analysis, 46–48 regularities in, as basis of trade, 52 straddle position, 92 VIX index (CBOE), 48–51 AtherGenics (AGIX) (examples), 153–154 Availability heuristic (rule of thumb), 155–156 Back-testing with fixed trade size, 103 Backward adjustment, 17 Backward-looking historical volatilities, 43 Baird, A J., 78 BARRA (commercial factor model), 85 Barton, D., 61 Base rate, neglecting, in analysis, 159–160 Behavioral psychology, 149–163 Beta estimating and forecasting, 84 Betting: coin flipping (examples), 101–103, 106–107 fixed versus proportional, 103–104 Kelly strategy, 103–113, 120–122 Oscar’s system, 114–115 positive and negative progressions, 114–115 Bias: anchoring and adjusting, 162 availability heuristic (rule of thumb), 155–156 Black-Scholes-Merton (BSM), 41–42 cognitive, 150–162 confirmation, 160–161 conservatism and representativenenss, 158–160 correcting for, 16–31 emotional, 150–151, 157–158, 160–161 feel (intuition) in trade sizing, 102–103 getevenitis, 157 hindsight, 161–162 in measuring samples, 19, 23–24 loss aversion, 157–158 overconfidence, 151–155 overreaction and underreaction, 160 203 ind JWBK128-Sinclair March 13, 2008 22:53 204 Bias (Continued) selective memory, 127 self-attribution, 151–152 short gamma positions, 157 short-term thinking, 156–157 types of, in trading, 150 Bid/ask spread: in hedging, 78 interest rates, 12 in trading implied/realized spread, 47 Whalley-Wilmott (WW) asymptotic solution, 73 Black-Scholes-Merton (BSM) model: analysis of equation, 7–14 bias of, 42 extended to incorporate skewness and kurtosis, 55–62 hedging, 63–64 option pricing model (example), 3–5 as pricing method, 13 Bollinger band, 51–52, 125 Brandt and Kinlay studies of estimators, 25 Brandt, M W., 25 Braun, Julian, 114–115 Browne strategy, 115–118 Browne, S., 113–118 BSM See Black-Scholes-Merton (BSM) model Burghart, G., 39 Butterfly spread, 77–78 Calmar ratio, 138 Carr, P., 78, 94 Certainty equivalent, 66 Chapman, S., 110 Checklist for record keeping, 129–130 Chicago Board Options Exchange Volatility Index, 42 Close-to-close estimator backward-looking historical volatilities, 43 compared to Garman-Klass estimator, 24 efficiency, 22–23 higher-frequency data, 29 good and bad points, 26 stock moves related to volatility, 21 30-day, 42–43 Close-to-open volatility, 24–25 Cognitive bias, 150–162 Coin flipping (example of trade sizing), 101–103, 106–107 Commercial factor models, 85 Concentration, 177 Cone See Volatility, cone Confidence interval in sampling, 20–21 Confirmation bias, 160–161 Char Count= INDEX Consecutive successes of independent events (example), 159 Conservatism and representativenenss bias, 158–160 Corrado, C., 58 Corrado-Su model, 58–62 CPR See Cross product ratio Crop reports, 53 Cross product ratio (CPR) test, 143–144 Daily returns: delta hedges as majority of, 130 estimating annualized returns, 22 versus higher-frequency data, 28 parameters for daily change in volatility surface, 46 Dark liquidity, 80 Data: Brandt and Kinlay studies of estimators, 25 daily, 28 GARCH models, 37–38 higher-frequency, 22, 27–31 versus model, 37–38 opening jump–adjusted, high-frequency volatility estimator, 29–31 seasonality and higher-frequency data, 29 Defensive hedging, 94 Definitions: cognitive dissonance, 158 getevenitis, 157 good trader, 157 hedging, 63, 78 jump, 54 luck versus skill, 142–143 skewness and kurtosis, 54, 57 smile dynamics, 13 standard deviation, 21–22 time series, 50–52 variance (equation), 84 volatility, 16–22, 49 Delta: aggregation of options on different underlyings, 84 band, edge erosion due to cumulative hedging, 71 band, S-shaped modified, 71 daily returns, 130 hedging, 65 “letting their deltas run,” 94 neutral position, 64 Dennis, K., 61 Dependency: path, 87–93 volatility, 93–99 ind JWBK128-Sinclair March 13, 2008 22:53 Char Count= 205 Index Derivatives, standard for Black-Scholes-Merton (BSM) method, 7–8 Derman, E., 46 Distribution: Corrado-Su model, 58–62 discrete, of volatility, 37 effect of frequency of hedging, 90–93 excess kurtosis, 57 expected, of winning and losing days, 159 KURT function (Microsoft Excel), 57 leptokurtic (kurtosis greater than 3), 57 platykurtic (kurtosis smaller than 3), 57 of profit/loss as function of entry level, 124–126 Poisson (example), 80–81 price, 57–58 probability distribution function (PDF), 110–111 return, 58–62 skewness and kurtosis, 57 win/loss, 159 Dividends: assumptions of, 12 effect of stocks going ex-dividend, 16–17 Double asymptotic method (Zakamouline), 74–78 Drawdown: as critical performance measure, 130 Calmar ratio, 138 Sortino ratio, 138 Drift (mean returns): estimators with drift term, 24–25 post-earnings announcement, 158–160 Rogers-Satchell estimator, 24 trading of, by equity trader, 93 of underlying, in Black-Scholes-Merton (BSM) example, 10 versus variance, 17–20, 24 Yang-Zhang estimator, 24–27 Dunning, D., 155 Dupire, B., 97 Dynamics, implied, of volatility: level, 48–54 skewness and kurtosis, 54–62 smile dynamics, 46–48, 54–62 strike and term structure, 45–47 surface, example of, 45–46 Econometric methods, 39 Edge See also Trade evaluation bid/ask spread, 78 erosion of, in hedging, 71 finding, by forecasting volatility, 3–5 implied/realized spread of index, 41, 45, 47–48 loss of, 146 psychology of traders, 149 statistical, 175 Edgeworth expansion, 62 Efficiency, close-to-close estimator and range-based estimator, 22–23 Emotional bias, 150–151, 157–158, 160–161 Engle, R F., 38 Entry-level distribution of profit/loss, 124–126 Error: large, in sampling, 22 learning from, 151 psychological biases, 151–162 versus sampling error, 21 Estimators: Brandt and Kinlay studies, 25 close-to-close estimator, 21–26 efficiency, 22–23 Garman-Klass estimator, 23–27 good and bad points, 26–27 inefficient, 19–20 maximum likelihood (MLE), 36–38 opening jump–adjusted, high-frequency volatility, 29–31 Parkinson, 22–23 range-based, 22–23 Rogers-Satchell estimator, 24–27 volatility measurement and forecasting, 15–43 Yang-Zhang estimator, 24–27 ETF See Exchange-traded fund Ethier, S., 114 European options, Corrado-Su model, 62 Evaluation See Trade evaluation EWMA See Exponentially weighted moving average Exchange-traded fund (ETF), 83 Execution ability, 176–177 Exit, reasons for, 173 Expectations, positive, 115 Expected wealth versus typical wealth, 105 Exponentially weighted moving average (EWMA), 33–34 Fair value, 119 Feel (intuition): and overconfidence bias, 153–155 logic-based versus intuitive trading, trade sizing, 102–103 Fixed fraction system, 103 Fixed trade size system, 103 ind JWBK128-Sinclair March 13, 2008 22:53 206 Forecasting: beta versus volatility, 84 Black-Scholes-Merton (BSM) bias, 41–42 GARCH models, 34–39 mean-reverting process of volatility, 34 moving window method, 32–33 outliers, 33 rolling windows, 41 term structure for volatility, 35 volatility, 31–38 volatility distribution, 38–43 See also Volatility, cone Forward adjustment of prices, 17 Fundamental aspects of trades, Gambling See Betting Gamma: aggregation of options on different underlyings, 84 bias for short position, 157 changing, and long butterfly spread, 77–78 different deltas, 64 long and short positions, 97 and mental arithmetic, 19–20 near strike at expiration, 97 relationship with vega function, 12 short and long gamma in hedging, 94 volatile and path dependent, 12 GARCH models: maximum likelihood function, 37 parameters, 36–37 versions of, 38 Garman, M B., 23 Garman-Klass estimator: bias of, 25 compared to Parkinson estimator, 24 of volatility, 23–27 Gaussian distribution and extreme risk, 13 GBM See Geometric Brownian motion Generalized auto-regressive conditional heteroskedasticity (GARCH) models See GARCH models Genetic algorithms, 39 Geometric Brownian motion (GBM): Parkinson estimator, 22–23, 27 Browne strategy, 116–118 stock path (example), 90–91 Getevenitis, 157 Glaser, M., 154 Goals: setting, 140–142 mispriced options, mispriced volatility, capturing, 176 tradinggoals.xls spreadsheet, 140 Char Count= INDEX Google earnings announcements (example), 156 Gram-Charlier expansion, 58, 61, 62 Greenberg, Ace, 157 Haircut: versus bankroll, 113 collateral for clearing firm, 134 record keeping, 129 Haug, E., 62 Hedging: aggregation of options on different underlyings, 83–85 bandwidth (examples), 69–70, 74–77 Black-Scholes-Merton (BSM) method, 63–64 continuous versus discrete, 88 defensive, 94 delta band, 65 delta hedges as majority of daily returns, 130 discrete, and path dependency, 87–93 double asymptotic method of Zakamouline, 74–78 expiring at or near strike, 97 frequency, effect of, 90–93 historical data, 26 Hodges-Neuberger (HN) methodology, 68–69, 71, 73, 77 implied/realized volatility, 93–99 “letting their deltas run,” 94 long butterfly spread, 77–78 mispriced volatility, capturing, 176 Monte Carlo example, 64 option positions, 87–99 purpose of, 78 reduction of costs, 83 regular intervals, 65 residual risk versus single stock risk, 83 risk aversion/seeking, 66–68, 71 semistatic, 13 transaction costs, estimation of, 78–82 underlying price changes, 65–66 utility theory, 66–68 volatility smile, 13 See also Smile dynamics Whalley-Wilmott (WW) asymptotic solution, 71–74, 77 Henrard, M., 94 Hilton, D J., 154 Hindsight bias, 161–162 Historical data analysis See also Analysis; Trade evaluation annualization, 16 annualized terms and daily returns, 22 backward adjustment, 17 backward-looking, 43 ind JWBK128-Sinclair March 13, 2008 22:53 Index close-to-close volatility estimator, 21–26 confidence interval of measured volatility, 20–21 convergence of sample variance to true population variance, 20 correcting for deviations in samples, 18–22 day-to-day changes, 17 versus drift (mean returns), 17–20 forward adjustment, 17 Garman-Klass estimator, 23–27 higher-frequency data, 27–31 Microsoft Excel function (KURT), 57 Microsoft Excel function (VAR), 18 opening jump–adjusted, high-frequency volatility estimator, 29–31 overfitting to past data, 123 Parkinson estimator, 22–23, 26–27 risk measurements, 135–140 Rogers-Satchell volatility estimator, 27 sampling error versus measurement error, 21 of volatility, 26 volatility cones, 39–43 Yang-Zhang estimator, 24–27 Hodges, S., 40, 68 Hodges-Neuberger (HN) model, 68–69, 71, 73 Hua, P., 78 Human element versus mathematical models, Hurst exponent, 144–147 Iceberg order, 80 Implied/realized volatility, 93–99 Indexes: implied/realized spread, 41, 45, 47–48 VIX index (Chicago Board of Exchange), 48–51 volatility surface (example), 45–46 Integrated volatility, 31 Interest rates: bid/ask spread, 12 large economic releases, 53 Interoil Corporation (IOC), 123 Intuition See Feel Inventory reports, 53 James, Bill, 149, 150 Jarrow, R., 57 Jensen’s inequality, 18, 23 Jondeau, E., 61 Judgment calls See Trade evaluation Jump calculating, of underlying (strike) movement, 53–54 Char Count= 207 defined, 54 first day and right before expiration, 88–90 opening, 24–25 opening, adjusted high-frequency volatility estimator, 29–31 underlying (strike) movement, 53–54, 88–90 Yang-Zhang estimator, 24 Kahneman, D., 157, 160 Kamal, M., 46 Kazemi, 138 Kelly strategy: alternatives to, 113–118 anti- and pro-Kelly groups, 112 compared to Browne strategy, 117 gains and losses (equations), 103–113 long run versus short run, 110, 113 mean-reverting process, 120–122 probability distribution function (PDF), 110–111 ratio, 105 Kelly, John, 103–113 Kinlay, J., 25 Klass, M J., 23 Kruger, J., 155 Lane, M., 39 Leptokurtic distribution (kurtosis greater than 3), 57 Level dynamics of volatility: at-the-money implied volatilities, 52–54 mean reversion, definitions, 49–52 model-free volatility, 48–49 Liquidity: dark, 80 underlying options, 12 Lo, A., 136 Logic-based versus intuitive trading, Long-term potential versus short-term profits, 114 Loss aversion: bias, 157–158 models based on, 73 psychology of traders, 157–158 in utility theory, 66–68, 71 Luck versus skill, 142–143, 151 Market: impact analysis, 80 information, current versus historical, 41 overreaction or underreaction, 158 Martinelli, L., 76 ind JWBK128-Sinclair March 13, 2008 22:53 Char Count= 208 Mean Reversion Simulator.xls spreadsheet, 123 Mean reverting process, 119–124 Measurement error versus sampling error, 21 Measures: Calmar ratio, 138 correcting for deviation, 18–22 gamma function in measuring normal distribution, 18 Jensen’s inequality, 18, 23 performance, risk-adjusted, 135–140 population standard deviation, 18–19 risk, 134–140 sample standard deviation, 18–19 Sharpe ratio, 135–140 Sortino ratio, 138–140 Sterling ratio, 138–139 vega, for measuring expected profit, 11 Merrill Lynch, 80 Microsoft Excel: KURT function (excess kurtosis), 57 Mean Reversion Simulator.xls spreadsheet, 123 Trade Sizing.xls spreadsheet, 106 Tradinggoals.xls spreadsheet, 140 VAR function, 18 Microstructure: high-frequency data, 31 noise, 28 transaction costs, 74 Miller, William, 112 Mispriced options, Mispriced volatility, capturing, 176 Mispricing, understanding causes of, 151 MLE See Maximum likelihood estimation Model versus data, 37–38 Models See also Betting Black-Scholes-Merton (BSM) sample equation, 7–14 commercial factor models, 85 Corrado-Su, 58–62 Hodges-Neuberger (HN), 68–69, 71, 73 Kelly strategy, 103–113, 120–122 mathematical versus human element, 2–3 Ornstein-Ulenbeck mean-reverting model, 119–124 stochastic volatility model, Money management See also Portfolio management ad hoc schemes, 101–103 aggressive schemes, 122, 125 alternatives to Kelly strategy, 113–118 INDEX Browne strategy, 115–118 Kelly strategy, 103–113, 120–122 mean reverting process, 119–124 Ornstein-Ulenbeck mean-reverting model, 119–124 trade sizing, 118–126 Movement of trades: large implied volatility and tendency to reverse, 52 principal component analysis (PCA), 45–48 Moving window method, 32–33 Neglect: of base rate, 159–160 of sample size, 160 Neuberger, A., 68 Neural networks, 39 Nondirectional strategy, 88 Omega risk measure, 139 Open-to-close volatility, 24–25 Opening jump, 24–25, 29–31, 88–89 Option positions See also Positions aggregating of, across different underlyings, 83–85 delta-hedged (example), 8–14 discrete hedging and path dependency, 87–93 hedging plans, 63–85 monitoring volatility, 43 normalizing of, 84 straddles, 47–48, 53 Options: Black-Scholes-Merton (BSM) sample equation, 7–14 pricing (valuing), 7–14 properties of, short-dated, 12 standard deviation of underlying returns, 11 Ornstein-Ulenbeck mean-reverting model, 119–124 Oscar’s system (betting), 114–115 Out-of-the-money options, 135–140 Overconfidence bias, 151–155 Overfitting to past data, 123 Parameters: daily change in volatility surface, 46 EWMA method, 36 GARCH method, 36, 36–37 of smile dynamics, 55–62 time increments versus price changes, 76 Parkinson estimator: compared to Garman-Klass estimator, 24 ind JWBK128-Sinclair March 13, 2008 22:53 Index good and bad points, 26–27 high-frequency data, 30 versus close-to-close estimator, 22–23 Parkinson, M., 22–23 Path dependency: discrete hedging and, 88 effect of drift of underlying, 93–94, 96–97 geometric Brownian motion (GBM), 90–91 profit/loss (P/L), 130 vega (equation), 87 PCA See Principal component analysis PDF See Probability distribution function Performance: change, identifying cause of, 146–147 loss of, in long-term winning trade, 146 luck versus skill, 142–143 measures, risk-adjusted, 135–140 Persistence: absolute, 144–147 relative, 143–144 Peters, E., 144 P/L See Profit/loss Platykurtic distribution (kurtosis smaller than 3), 57 Poisson distribution, 80–81 Portfolio management See also Money management delta-hedged, used in BSM example, 8–14 long call/short stock, Positions See also Option positions adjusted volatility for long and short, 70–71 long and short gamma positions (HN solution), 73, 97 normalizing of option, 84 straddles, 47–48, 53, 92 strangles or strips versus straddles, 97 Post-earnings announcement drift, 158 Pragmatism, 2–3 Priaulet, P., 76 Price: distribution, 57–58 moves versus time increments, 76 paths, profit/loss evolution (examples), 97–99 options (valuing), 7–14 Price changes: and delta-hedged position, in Black-Scholes-Merton (BSM) example, 10–11 daily versus higher-frequency data, 28 hedging, 65–66 measuring versus risk measuring, 12–13 Principal component analysis (PCA), 45–48 Char Count= 209 Probability distribution function (PDF), 110–111 Product selection, 177 Profit See also Profit/loss (P/L) discrete hedging, 87–93 gamma relationship with vega, 12 long-term potential versus short-term profits, 113–114 selling implied volatility, 42 short-term versus long-term potential, 113–115 typical wealth versus expected wealth, 105 Profit/loss (P/L): implied/realized volatility and hedging, 93–99 mark-to-market, one time step, 96 maximizing profit, 124–126 path dependency, 130 profile, 176 swings, 95 vega, 53, 87 Profitability and planning, 129 Psychology of traders: anchoring and adjustment, 162 availability heuristic, 155–156 availability heuristic (rule of thumb), 155–156 confirmation bias, 160–161 conservatism and representativeness, 158–160 hindsight bias, 161–162 loss aversion, 157–158 overconfidence, 152–155 self-attribution bias, 151–152 short-term thinking, 156–157 versus knowledge and skill, 149 Put buying, Quantity of shares, effect on transaction costs, 79–82 Range-based estimator, 22–23 Record keeping See Trade evaluation Rescaled range analysis (R/S analysis), 144–145 Residual risk versus single stock risk, 83 Returns: distribution, 58–62 historical, and noise, 136 normal distribution, in Black-Scholes-Merton (BSM) method, 17 persistence, 158 ratio of return to volatility, 137–140 ind JWBK128-Sinclair March 13, 2008 22:53 210 Returns (Continued) risk-adjusted, 105 Sharpe ratio, 135–140 variance versus drift (mean returns), 17–20 Risher, B., 74 Risk: -aversion and -seeking, 66–68, 78 due to interest charges (rho), 12 Gaussian distribution moments as misleading, 13 hedging, 78 measuring versus price measuring, 12–13 models based on risk-aversion, 73 overall level of implied volatility, 47–48 replication, in imperfect hedging, 64 residual risk versus single stock risk, 83 Sharpe ratio, 135–140 tail, 13 underlying position utility theory, 66–68 Risk-adjusted performance measures: alternatives to Sharpe ratio, 137–140 Calmar ratio, 138 omega risk measure, 139 Sharpe ratio, 135–137 Sortino ratio, 138–140 Sterling ratio, 138–139 Rockinger, M., 61 Rogers, L., 24 Rogers-Satchell estimator, 24–27 Rolling windows, 41 Rubinstein, M., 61, 62 Rudd, A., 57 Rule of thumb (availability heuristic), 155–156 S-shaped modified delta, 71 Sample size: convergence of sample variance to true population variance, 19–20 correction factor as a function of, 19, 20 efficiency, 22–24 error in, discrete intervals of hedging, 92–93 higher-frequency data, 27–31 law of small numbers, 160 Satchell, S., 24 Scalping, aggressive, 125 Seasonality, 29–30 Sectors, breakdown by, in evaluation, 134 Self-attribution bias, 151–152 Shannon, Claude, 112 Sharpe ratio: alternatives to, 137–140 risk-adjusted performance measures, 135–137 Char Count= INDEX Short-term profit versus long-term potential, 113–115 Short-term thinking: Oscar’s system (betting), 114–115 psychology of traders, 156–157 Skewness and kurtosis, 57 breakeven volatility, 97 excess kurtosis (kurtosis minus 3), 57 leptokurtic (kurtosis greater than 3), 57 platykurtic (kurtosis smaller than 3), 57 smile dynamics, 54–62 Smile dynamics: Corrado-Su model, 58–62 correlation effect, 55 parameterizing, 55–62 reasons for, 54–55 variation of volatility, 46–48 versus level of volatility, 47, 54 Sortino ratio, 138 Spread: bid/ask and transaction costs, 78–79 implied/realized volatility, 41–43, 93–99 long butterfly, 77–78 Spreadsheets: Mean Reversion Simulator.xls, 123 Trade sizing.xls, 106 trading goals.xls, 140 VIX entry test.xls, 125 Steenbarger, Brett, 149–150, 153 Stereotypes (representativeness bias), 158–160 Sterling ratio, 138–139 Stocks: bid/ask spread, 12, 21, 47, 73 calculating jump of underlying (strike) movement, 53–54 close-to-close estimator, 21 effect of going ex-dividend, 16–17 historical price series, 16–17 path, geometric Brownian motion (GBM), 90–91 shorting, 12 Straddle: standard deviation of, 92 versus strangles or strips, 97 Strike, expiring at or near, 97 Su, T., 58 Taleb, N T., 78 Taleb, Nathan, 157 Taylor expansion: aggregation of options on different underlyings, 83–84 second-order, in Black-Scholes-Merton (BSM) example, 9–11 ind JWBK128-Sinclair March 13, 2008 22:53 Index Term structure, 35 Thorpe, Ed, 112 Time decay, 70 Time intervals, 80–84 Time series: annualized terms, 16 day-to-day changes, 17 definitions, 50–52 econometric methods, 39 GARCH methods, 34–39 versus price moves, 76 Tompkins, R., 40 Trade evaluation See also Analysis; Historical data analysis achievement, three levels, 128 Calmar ratio, 138 checklist for record keeping, 129–130 drawdown as performance measure, 130 goal setting, 140–142 historical data analysis, 135–140 judgment calls, tracking results of, 133 margin improvements, 128 omega risk measure, 139 overmanagement, 142 performance measures, 130 persistence of performance, 142–147 planning procedures, 126–134 profitability, 129 record keeping, 176 risk-adjusted performance measures, 134–140 sectors, breakdown by, 134 Sharpe ratio, 135–140 Sortino ratio, 138 Sterling ratio, 138–139 Trade sizing: continuously changing setting, 118–126 evaluation of projected return and risk, 176 fixed fraction system, 103 fixed trade size system, 103 logic-based versus feel (intuition), positive expectations, 115 probability distribution function (PDF), 110–111 Traders, risk-averse and risk-seeking, 66–68 Trading: concentration, 177 execution ability, 176–177 finding profitable trades, 3–6 mispriced options, product selection, 177 strangles or strips versus straddles, 97 time intervals, effect on transaction costs, 80–84 Char Count= 211 Trading partner, checklist for choosing, 151 Trading strategies: Browne strategy, 115–116 Kelly criterion, 103–113, 120–122 Ornstein-Ulenbeck mean-reverting model, 119–124 Oscar’s progressive betting system, 113–115 Tradinggoals.xls spreadsheet, 140 Transaction costs: discrete hedging, 92–93 due to replication, 64 estimating, 78–82 fixed components, 78 hedging bandwidth, 72–74 incorporating, in models, 70, 74 microstructure issue, 74 modified options prices to allow for, 68 overmanagement, 142 Whalley-Wilmott asymptotic solution, 71–74 Tversky, A., 157, 160 Underlying (strike): aggregation of options on different, 83–85 calculating implied jump, 53–54 close to, at expiration, 97 drift, effect of, 10, 93–94, 96–97 first day and just before expiration jumps, 88–90 hedging plans, 63–85 price paths (examples), 93–94 smile dynamics, 54–62 trading of, 64 Utility theory of hedging, 66–68 Variance: definition (equation), 84 exponentially weighted moving average (EWMA), 33–34 GARCH models, 34–39 rolling windows, 41 Vega: aggregation of options on different underlyings, 84 calculating expected profit, 11–12 defined, 11 and gamma relationship, 12 profit/loss (P/L) (equation), 87 profits, 53 VIX entry test.xls spreadsheet, 125 VIX index (Chicago Board of Exchange), 48–51 ind JWBK128-Sinclair March 13, 2008 22:53 Char Count= 212 Volatility: adjusted for long and short positions, 70–71 at-the-money (ATM), 46–48 beta term, 84 breakeven skews, 97 cone, ranges of volatility, 39–43 cones, for historical measuring, 15, 39–43 correcting for deviations in samples, 18–24 definition of, 16–22 dependency, 93–99 dynamics, of implied, 45–62 earnings releases, 52 effect of stocks going ex-dividend, 16–17 estimators, 16–27 historical measuring, 15–43 implied, and correlation effect, 55 implied/realized spread, 11, 41, 47–48, 93–99 integrated, 31 Kelly strategy, 103–113, 120–122 large, and tendency to reverse, 52 level dynamics, 48–54 mean-reverting process, 34 measurement and forecasting, 15–43 path dependency, 87–93 predicting of average, 54 relationship with volume of shares, 80–84 sampling risk, 93 seasonality, 29–30 INDEX smile dynamics, 46–48, 54–62 spread of implied and realized, 41, 47–48 surface (example), 45–46 transaction costs, 71–74 versus volume of shares, 79–82 Volume of shares: effect on transaction costs, 79–82 relationship with volatility, 80–84 Weston, D., 161 Whalley, A E., 71–74 Whalley-Wilmott asymptotic solution, 71–74, 77 Whipsaw losses, 73 Wilmott, P., 71–74, 77, 78, 94, 97 Wilson, A., 114, 115 Win/loss ratios, 159 Yang, D., 24 Yang-Zhang estimator: bias of, 25 of volatility, good and bad points, 27 opening jumps, 24 Yoon, Y., 24 Zakamouline, V., 74–78 Zhang, Q., 24 ind JWBK128-Sinclair March 13, 2008 22:53 213 Char Count= scrap JWBK128-Sinclair March 13, 2008 22:27 Char Count= CUSTOMER NOTE: IF THIS BOOK IS ACCOMPANIED BY SOFTWARE, PLEASE READ THE FOLLOWING BEFORE OPENING THE PACKAGE This software contains files to help you utilize the models described in the accompanying book By opening the package, you are agreeing to be bound by the following agreement: This software product is protected by copyright and all rights are reserved by the author, John Wiley & Sons, Inc., or their licensors You are licensed to use this software on a single computer Copying the software to another medium or format for use on a single computer does not violate the U.S Copyright Law Copying the software for any other purpose is a violation of the U.S Copyright Law This software product is sold as is without warranty of any kind, either express or implied, including but not limited to the implied warranty of merchantability and fitness for a particular purpose Neither Wiley nor its dealers or distributors assumes any liability for any alleged or actual damages arising from the use of or the inability to use this software (Some states not allow the exclusion of implied warranties, so the exclusion may not apply to you.) 214 ... option trading is in trading our estimate of future volatility against the markets Before we can forecast volatility we need to be able to measure it In Chapter we look at methods of historical volatility. .. volatility measurement including close-to-close volatility, Parkinson volatility, Rogers-Satchell volatility, Garman-Klass volatility, and YangZhang volatility We discuss the efficiency and bias... Higher-Frequency Data 27 Forecasting Volatility 31 Maximum Likelihood Estimation 36 Forecasting the Volatility Distribution 39 Summary 43 CHAPTER Implied Volatility Dynamics Volatility Level Dynamics 45