Volatility : Practical Options Theory

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. Cover Title Page Copyright Contents Preface Acknowledgments About the Author Chapter 1 Volatility and Options 1.1 What Is an Option? 1.2 Options Are Bets on Volatility 1.3 Option Premiums and Breakevens 1.3.1 Understanding Option Premiums 1.3.2 Relation Between Premium and Breakeven 1.4 Strike Conventions 1.5 What Is Volatility? 1.5.1 Implied Volatility, σimplied 1.5.2 Probabilities and Breakevens 1.5.3 Implied Volatility and Realized Volatility 1.5.4 Realized Volatility, σrealized 1.6 Trader's Summary Chapter 2 Understanding Options Without a Model 2.1 Vanilla Options 2.1.1 Option Payoffs 2.2 Making Assumptions 2.3 Understanding Vt with Economic Assumptions 2.4 Delta and Delta Hedging 2.5 The Value Function 2.6 Defining Delta 2.7 Understanding Delta 2.8 Delta as the Probability of an In-the-Money Expiry 2.9 Applying Delta as the Probability of an ITM Expiry in Practical Trading 2.10 Constructing Vt 2.10.1 Jensen’s Inequality: Vt = V (St , t, σi ) ≥ max(St −K , 0) 2.10.2 Trading Intuition Behind Jensen's Inequality 2.10.3 American Options 2.10.4 Gradient of Vt 2.10.5 Drawing Vt 2.11 Option Deltas 2.12 A Note on Forwards 2.13 Put–Call Parity 2.14 Trader's Summary Chapter 3 The Basic Greeks: Theta 3.1 Theta, θ 3.1.1 Overnight Theta for an ATM Option 3.1.2 Dependence of θ(St , t, σi ) on St 3.1.3 Dependence of θ(St , t, σi ) on t 3.2 Trader's Summary Chapter 4 The Basic Greeks: Gamma 4.1 Gamma, Γ 4.2 Gamma and Time Decay 4.3 Traders' Gamma, Γtrader 4.4 Gamma–Time Decay Trade-offs in More Detail 4.5 PnL Explain 4.5.1 Example: Gamma, Time Decay, and PnL Explain for a 1-Week Option 4.6 Delta Hedging and PnL Variance 4.7 Transaction Costs 4.8 Daily PnL Explain 4.9 The Gamma Profile 4.9.1 Gamma and Spot 4.9.2 Gamma and Implied Volatility 4.9.3 Gamma and Time 4.9.4 Total Gamma 4.10 Trader's Summary Chapter 5 The Basic Greeks: Vega 5.1 Vega 5.2 Understanding Vega via the PDF 5.3 Understanding Vega via Gamma Trading 5.4 Vega of an ATMS Option Across Tenors 5.5 Vega and Spot 5.6 Dependence of Vega on Implied Volatility 5.7 Vega Profiles Applied in Practical Options Trading 5.8 Vega and PnL Explain 5.9 Trader's Summary Chapter 6 Implied Volatility and Term Structure 6.1 Implied Volatility, σimplied 6.2 Term Structure 6.3 Flat Vega and Weighted Vega Greeks 6.3.1 Flat Vega 6.3.2 Weighted Vega 6.3.3 Beta-Weighted Vega 6.4 Forward Volatility, Forward Variance, and Term Volatility 6.4.1 Calculating Implied Forward Volatility 6.5 Building a Term Structure Model Using Daily Forward Volatility 6.6 Setting Base Volatility Using a Three-Parameter GARCH Model 6.6.1 Applying the Three-Parameter Model 6.6.2 Limitations of GARCH 6.6.3 Risk Management Using the Three-Parameter Model 6.6.4 Empirical GARCH Estimation 6.7 Volatility Carry and Forward Volatility Agreements 6.7.1 Volatility Carry in the GARCH Model 6.7.2 Common Pitfalls in Volatility Carry Trading 6.8 Trader's Summary Chapter 7 Vanna, Risk Reversal, and Skewness 7.1 Risk Reversal 7.2 Skewness 7.3 Delta Space 7.4 Smile in Delta Space 7.5 Smile Vega 7.5.1 Smile Vega Notionals 7.6 Smile Delta 7.6.1 Considerations Relating to Smile Delta 7.7 Trader's Summary Chapter 8 Volgamma, Butterfly, and Kurtosis 8.1 The Butterfly Strategy 8.2 Volgamma and Butterfly 8.3 Kurtosis 8.4 Smile 8.5 Butterflies and Smile Vega 8.6 Trader's Summary Chapter 9 Black-Scholes-Merton Model 9.1 The Log-normal Diffusion Model 9.2 The BSM Partial Differential Equation (PDE) 9.3 Feynman-Kac 9.4 Risk-Neutral Probabilities 9.5 Probability of Exceeding the Breakeven in the BSM Model 9.6 Trader's Summary Chapter 10 The Black-Scholes Greeks 10.1 Spot Delta, Dual Delta, and Forward Delta 10.1.1 Spot Delta 10.1.2 The ATM Strike and the Delta-Neutral Straddle 10.1.3 Dual Delta 10.1.4 Forward Delta 10.2 Theta 10.3 Gamma 10.4 Vega 10.5 Vanna 10.6 Volgamma 10.7 Trader's Summary Chapter 11 Predictability and Mean Reversion 11.1 The Past and the Future 11.2 Empirical Analysis Appendix A Probability A.1 Probability Density Functions (PDFs) A.1.1 Discrete Random Variables and PMFs A.1.2 Continuous Random Variables and PDFs A.1.3 Normal and Log-normal Distributions Appendix B Calculus Glossary References Index EULA **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 theoryTranslate theoretical ideas into practiceDevelop a more accurate intuition for better time-constrained decision makingThis 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.