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

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 5 1.3.1 Understanding Option Premiums 6 1.3.2 Relation between Premium and Breakeven 7 1.4 Strike Conventions 8 1.5 What is Volatility? 9 1.5.1 Implied Volatility, simplied 9 1.5.2 Probabilities and Breakevens 13 1.5.3 Implied Volatility and Realised Volatility 13 1.5.4 Realised Volatility,

srealised 14 1.6 Trader s Summary 17 2 Understanding OptionsWithout a Model 19 2.1 Vanilla Options 19 2.1.1 Option Payoffs 20 2.2 Making Assumptions 21 2.3 Understanding Vt with Economic Assumptions 21 2.4 Delta and Delta Hedging 23 2.5 The Value Function 24 2.6 Defining Delta 25 2.7 Understanding Delta 26 2.8 Delta as the Probability of an In-The-Money Expiry 29 2.9 Applying Delta as the Probability of an ITM Expiry in Practical Trading 33 2.10 Constructing Vt 34 2.10.1 Jensen s Inequality 35 2.10.2 Trading Intuition Behind Jensen s Inequality 36 2.10.3 American Options 37 2.10.4 Gradient of Vt 37 2.10.5 Drawing Vt 37 2.11 Option Deltas 39 2.12 A Note on Forwards 39 2.13 Put-Call Parity 41 2.14 Trader s Summary 43 3 The Basic Greeks: Theta 45 3.1 Theta,

76 4.10 Trader s Summary 76 5 The Basic Greeks: Vega 79 5.1 Vega 80 5.2 Understanding Vega via the PDF 81 5.3 Understanding Vega via Gamma Trading 81 5.4 Vega of an ATMS Option across Tenors 82 5.5 Vega and Spot 82 5.6 Dependence of Vega on Implied Volatility 85 5.7 Vega Profiles Applied in Practical Options Trading 85 5.8 Vega and PnL Explain 87 5.9 Trader s Summary 87 6 Implied Volatility and Term Structure 89 6.1 Implied Volatility, simplied 90 6.2 Term Structure 94 6.3 Flat Vega and Weighted Vega Greeks 94 6.3.1 Flat Vega 94 6.3.2 Weighted Vega 95 6.3.3 Beta Weighted Vega 97 6.4 Forward Volatility,

Forward Variance and Term Volatility 97 6.4.1 Calculating Implied Forward Volatility 99 6.5 Building a Term Structure Model using Daily Forward Volatility 100 6.6 Setting Base Volatility Using a 3 Parameter GARCH Model 102 6.6.1 Applying the 3 Parameter Model 104 6.6.2 Limitations of GARCH 105 6.6.3 Risk Management Using the 3 Parameter Model 106 6.6.4 Empirical GARCH estimation 106 6.7 Volatility Carry and Forward Volatility Agreements 107 6.7.1 Volatility Carry in the GARCH model 108 6.7.2 Common Pitfalls in Volatility Carry Trading 108 6.8 Trader s Summary 109 7 Vanna, Risk Reversal and Skewness 111 7.1 Risk Reversal 112 7.2 Skewness 114 7.3 Delta Space 116 7.4 Smile in Delta Space 117 7.5 Smile Vega 119 7.5.1 Smile Vega Notionals 121 7.6 Smile Delta 122 7.6.1 Considerations Relating to Smile Delta 123 7.7 Traders Summary 124 8 Volgamma,

Butterfly and Kurtosis 125 8.1 The Butterfly Strategy 126 8.2 Volgamma and Butterfly 127 8.3 Kurtosis 128 8.4 Smile 129 8.5 Butterflies and Smile Vega 130 8.6 Trader.

Q 46 3.1.1 Overnight Theta for an ATM option 47 3.1.2 Dependence of q(St ; t;si) on St 48 3.1.3 Dependence of q(St ; t;si) on t 56 3.2 Trader s Summary 60 4 The Basic Greeks: Gamma 61 4.1 Gamma, G 62 4.2 Gamma and Time Decay 63 4.3 Traders Gamma, Gtrader 64 4.4 Gamma-Time Decay Trade-offs In More Detail 64 4.5 PnL Explain 66 4.5.1 Example: Gamma, Time Decay and PnL Explain for a 1 week Option 66 4.6 Delta Hedging and PnL Variance 69 4.7 Transaction Costs 71 4.8 Daily PnL Explain 71 4.9 The Gamma Profile 73 4.9.1 Gamma and Spot 73 4.9.2 Gamma and Implied Volatility 74 4.9.3 Gamma and Time 75 4.9.4 Total Gamma.