VolatilityPractical Options Theory
Wiley Finance 1. Aufl.
Gain a deep, intuitive and technical understanding of practical options theory The main challenges in successful options trading are conceptual, not mathematical. Volatility: Practical Options Theory provides financial professionals, academics, students and others with an intuitive as well as technical understanding of both the basic and advanced ideas in options theory to a level that facilitates practical options trading. The approach taken in this book will prove particularly valuable to options traders and other practitioners tasked with making pricing and risk management decisions in an environment where time constraints mean that simplicity and intuition are of greater value than mathematical formalism. The most important areas of options theory, namely implied volatility, delta hedging, time value and the so-called options greeks are explored based on intuitive economic arguments alone before turning to formal models such as the seminal Black-Scholes-Merton model. The reader will understand how the model free approach and mathematical models are related to each other, their underlying theoretical assumptions and their implications to level that facilitates practical implementation. There are several excellent mathematical descriptions of options theory, but few focus on a translational approach to convert the theory into practice. This book emphasizes the translational aspect, while first building an intuitive, technical understanding that allows market makers, portfolio managers, investment managers, risk managers, and other traders to work more effectively within—and beyond—the bounds of everyday practice. Gain a deeper understanding of the assumptions underlying options theory Translate theoretical ideas into practice Develop a more accurate intuition for better time-constrained decision making This book allows its readers to gain more than a superficial understanding of the mechanisms at work in options markets. Volatility gives its readers the edge by providing a true bedrock foundation upon which practical knowledge becomes stronger.
Preface xiii Acknowledgments xv About the Author xvii CHAPTER 1 Volatility and Options 1 1.1 What Is an Option? 1 1.2 Options Are Bets on Volatility 3 1.3 Option Premiums and Breakevens 6 1.3.1 Understanding Option Premiums 6 1.3.2 Relation Between Premium and Breakeven 7 1.4 Strike Conventions 9 1.5 What Is Volatility? 10 1.5.1 Implied Volatility, ?implied 11 1.5.2 Probabilities and Breakevens 15 1.5.3 Implied Volatility and Realized Volatility 15 1.5.4 Realized Volatility, ?realized 16 1.6 Trader’s Summary 19 CHAPTER 2 Understanding Options Without a Model 21 2.1 Vanilla Options 21 2.1.1 Option Payoffs 22 2.2 Making Assumptions 23 2.3 Understanding Vt with Economic Assumptions 24 2.4 Delta and Delta Hedging 25 2.5 The Value Function 26 2.6 Defining Delta 27 2.7 Understanding Delta 30 2.8 Delta as the Probability of an In-the-Money Expiry 32 2.9 Applying Delta as the Probability of an ITM Expiry in Practical Trading 37 2.10 Constructing Vt 38 2.10.1 Jensen’s Inequality: Vt = V(St, t, ?i) ? max(St ? K, 0) 40 2.10.2 Trading Intuition Behind Jensen’s Inequality 40 2.10.3 American Options 41 2.10.4 Gradient of Vt 42 2.10.5 Drawing Vt 42 2.11 Option Deltas 44 2.12 A Note on Forwards 45 2.13 Put–Call Parity 46 2.14 Trader’s Summary 48 CHAPTER 3 The Basic Greeks: Theta 49 3.1 Theta, ?? 50 3.1.1 Overnight Theta for an ATM Option 51 3.1.2 Dependence of ??(St, t, ?i) on St 52 3.1.3 Dependence of ??(St, t, ?i) on t 60 3.2 Trader’s Summary 65 CHAPTER 4 The Basic Greeks: Gamma 67 4.1 Gamma, ?? 68 4.2 Gamma and Time Decay 70 4.3 Traders’ Gamma, ??trader 70 4.4 Gamma–Time Decay Trade-offs in More Detail 71 4.5 PnL Explain 73 4.5.1 Example: Gamma, Time Decay, and PnL Explain for a 1-Week Option 73 4.6 Delta Hedging and PnL Variance 76 4.7 Transaction Costs 78 4.8 Daily PnL Explain 79 4.9 The Gamma Profile 81 4.9.1 Gamma and Spot 81 4.9.2 Gamma and Implied Volatility 82 4.9.3 Gamma and Time 83 4.9.4 Total Gamma 84 4.10 Trader’s Summary 84 CHAPTER 5 The Basic Greeks: Vega 87 5.1 Vega 88 5.2 Understanding Vega via the PDF 89 5.3 Understanding Vega via Gamma Trading 89 5.4 Vega of an ATMS Option Across Tenors 90 5.5 Vega and Spot 91 5.6 Dependence of Vega on Implied Volatility 94 5.7 Vega Profiles Applied in Practical Options Trading 95 5.8 Vega and PnL Explain 96 5.9 Trader’s Summary 97 CHAPTER 6 Implied Volatility and Term Structure 99 6.1 Implied Volatility, ?implied 100 6.2 Term Structure 104 6.3 Flat Vega and Weighted Vega Greeks 104 6.3.1 Flat Vega 105 6.3.2 Weighted Vega 106 6.3.3 Beta-Weighted Vega 108 6.4 Forward Volatility, Forward Variance, and Term Volatility 108 6.4.1 Calculating Implied Forward Volatility 110 6.5 Building a Term Structure Model Using Daily Forward Volatility 111 6.6 Setting Base Volatility Using a Three-Parameter GARCH Model 114 6.6.1 Applying the Three-Parameter Model 116 6.6.2 Limitations of GARCH 117 6.6.3 Risk Management Using the Three-Parameter Model 118 6.6.4 Empirical GARCH Estimation 118 6.7 Volatility Carry and Forward Volatility Agreements 119 6.7.1 Volatility Carry in the GARCH Model 120 6.7.2 Common Pitfalls in Volatility Carry Trading 121 6.8 Trader’s Summary 121 CHAPTER 7 Vanna, Risk Reversal, and Skewness 123 7.1 Risk Reversal 125 7.2 Skewness 127 7.3 Delta Space 129 7.4 Smile in Delta Space 130 7.5 Smile Vega 132 7.5.1 Smile Vega Notionals 134 7.6 Smile Delta 135 7.6.1 Considerations Relating to Smile Delta 136 7.7 Trader’s Summary 137 CHAPTER 8 Volgamma, Butterfly, and Kurtosis 139 8.1 The Butterfly Strategy 140 8.2 Volgamma and Butterfly 141 8.3 Kurtosis 142 8.4 Smile 143 8.5 Butterflies and Smile Vega 144 8.6 Trader’s Summary 145 CHAPTER 9 Black-Scholes-Merton Model 147 9.1 The Log-normal Diffusion Model 148 9.2 The BSM Partial Differential Equation (PDE) 148 9.3 Feynman-Kac 152 9.4 Risk-Neutral Probabilities 153 9.5 Probability of Exceeding the Breakeven in the BSM Model 154 9.6 Trader’s Summary 155 CHAPTER 10 The Black-Scholes Greeks 157 10.1 Spot Delta, Dual Delta, and Forward Delta 157 10.1.1 Spot Delta 157 10.1.2 The ATM Strike and the Delta-Neutral Straddle 159 10.1.3 Dual Delta 160 10.1.4 Forward Delta 161 10.2 Theta 161 10.3 Gamma 163 10.4 Vega 164 10.5 Vanna 164 10.6 Volgamma 165 10.7 Trader’s Summary 165 CHAPTER 11 Predictability and Mean Reversion 167 11.1 The Past and the Future 167 11.2 Empirical Analysis 168 APPENDIX A Probability 173 A.1 Probability Density Functions (PDFs) 173 A.1.1 Discrete Random Variables and PMFs 173 A.1.2 Continuous Random Variables and PDFs 174 A.1.3 Normal and Log-normal Distributions 176 APPENDIX B Calculus 179 Glossary 181 References 183 Index 185 Implied Volatility, ?implied
ADAM S. IQBAL is a Managing Director and Global Head of FX Exotics and Correlation at Goldman Sachs, where he has also served as EMEA Head of G10 FX Options Trading. He has worked as an FX Volatility Portfolio Manager at Pimco, and as an FX options trader at Barclays Investment Bank. He holds a PhD in financial mathematics and financial economics from Imperial College London, an MSc in applied mathematics from Oxford University and an MSci and BA in theoretical physics from Cambridge University.
Volatility: Practical Options Theory dissects options—the financial contracts that provide exposure to volatility risk—to help readers marry foundational knowledge with practical application. While textbook treatments of the mathematical theory of options are abundant, this book is unique in its emphasis on developing an intuitive understanding of both the basic and advanced ideas in options theory. The discussion examines options theory concepts both with and without mathematical models, and then further develops this approach with insightful guidance on merging the two perspectives to serve practical implementation. This translational approach may prove particularly valuable to options traders and other practitioners tasked with making pricing or risk management decisions in an environment where time constraints mean that simplicity and intuition is of more value than mathematical formalism. Develop a deeper understanding of option greeks, delta hedging, implied volatility, and other major concepts based on intuitive economic arguments before applying a mathematical model. Translate theoretical ideas into practice. Delve into the Black-Scholes-Merton model and its underlying theoretical assumptions—and their implications—in a way that facilitates real-world implementation. Refresh calculus and advanced statistical skills using helpful appendices that provide important formulae and functions. Author Adam S. Iqbal argues that option trading's main challenges are conceptual rather than mathematical; by tackling these challenges head-on and providing a clear link between theoretical and practical, this book offers traders, portfolio managers, investment managers, risk managers, and other market practitioners an invaluable source of insight designed to facilitate more effective volatility strategy. Comprehensive in scope and depth, Volatility: Practical Options Theory provides a much-needed reference for practitioners seeking a more effective grasp of options and volatility.
"Adam's presentation of this book - with emphasis on intuition and practical rules of thumb - makes it extremely useful not only as a compulsory read for aspiring derivatives traders but also as a handbook for seasoned practitioners of the trade. As many who have been on the job know, it is often quick intuitive judgment that is the only recourse to a trader in a highly volatile moving market, and this book does an excellent job of training one's mind for it." —Manikandan Natarajan, Partner, Managing Director and Global Head of FX Options at Goldman Sachs (Retired) "How much can you say about financial options before you even specify a model? This outstanding book by a leading industry expert reveals the rich nature of these securities, blending theory and practical insights in a remarkable fashion. Anyone seeking to understand options should read this book." —Professor William Perraudin, Director, Risk Control Limited THE CRITICAL LINK BETWEEN OPTIONS THEORY AND REAL-WORLD PRACTICE Volatility: Practical Options Theory is an essential resource for those tasked with making pricing or risk management decisions in time-constrained environments. When simplicity and intuition are more valuable than mathematical formalism, practitioners must have a deep, reflexive grasp of both theoretical concepts and technical mechanisms. This level of knowledge goes much deeper than a textbook and is the product of true understanding brought about by real exploration of fundamental principles. The ideas in this book apply to equity, bond, commodity, and other options. However, this book focuses on the FX options OTC market which, given the high liquidity and low constraints, provides a good "training ground" for implementation of ideas being discussed. Major concepts are explored at length on an intuitive level before introducing the Black-Scholes-Merton model, and although some background in calculus, probability, and statistics is helpful, it is by no means required to realize practical benefit. Practitioners, students, and academics alike will find value in this unique approach to volatility and options, and the informal style coupled with clear explanations and deep insight will make this book a permanent part of any practitioner's library.
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