Option Trading: Pricing and Volatility Strategies and Techniques

Preface xi

Professional Trading xii

The Role of Mathematics xiv

The Structure of this Book xvi

Acknowledgments xix

CHAPTER 1 History 1

Summary 6

CHAPTER 2 Introduction to Options 7

Options 9

Specifications for an Option Contract 9

Uses of Options 11

Market Structure 14

Summary 20

CHAPTER 3 Arbitrage Bounds for Option Prices 21

American Options Compared to European Options 25

Absolute Maximum and Minimum Values 25

Summary 39

CHAPTER 4 Pricing Models 41

General Modeling Principles 42

Choice of Dependent Variables 45

The Binomial Model 48

The Black-Scholes-Merton (BSM) Model 55

Summary 61

CHAPTER 5 The Solution of theBlack-Scholes-Merton (BSM) Equation 63

Delta 67

Gamma 72

Theta 76

Vega 80

Summary 88

CHAPTER 6 Option Strategies 89

Forecasting and Strategy Selection 89

The Strategies 93

Summary 116

CHAPTER 7 Volatility Estimation 117

Defining and Measuring Volatility 119

Forecasting Volatility 129

Volatility in Context 132

Summary 136

CHAPTER 8 Implied Volatility 137

The Implied Volatility Curve 138

Parameterizing and Measuring the Implied Volatility Curve 142

The Implied Volatility Curve as a Function of Expiration 145

Implied Volatility Dynamics 146

Summary 151

CHAPTER 9 General Principles of Trading and Hedging 153

Edge 154

Hedging 156

Trade Sizing and Leverage 158

Scalability and Breadth 163

Summary 164

CHAPTER 10 Market Making Techniques 165

Market Structure 166

Market Making 169

Trading Based on Order-Book Information 181

Summary 189

CHAPTER 11 Volatility Trading 191

Hedging 192

Hedging in Practice 193

The P/L Distribution of Hedged Option Positions 203

Summary 213

CHAPTER 12 Expiration Trading 215

Pinning 215

Pin Risk 219

Forward Risk 221

Exercising the Wrong Options 221

Irrelevance of the Greeks 223

Expiring at a Short Strike 224

Summary 225

CHAPTER 13 Risk Management 227

Example of Position Repair 228

Inventory 232

Delta 234

Gamma 234

Vega 238

Correlation 240

Rho 242

Stock Risk: Dividends and Buy-in Risk 242

The Early Exercise of Options 243

Summary 248

Conclusion 249

APPENDIX A Distributions 253

Example 253

Moments and the “Shape” of Distributions 254

APPENDIX B Correlation 263

Glossary 271

Index 285