Options on Foreign Exchange (eBook)

DAVID F. DeROSA is the founder and President of DeRosa Research. He is also an Adjunct Associate Professor of Finance at the Fu Foundation School of Engineering and Applied Science at Columbia University where he teaches courses in derivatives pricing models and foreign exchange. His bachelor's and PhD (finance and economics) are from the University of Chicago. Dr. DeRosa has worked at a variety of Wall Street investment firms, banks, and hedge funds. He sits on the boards of directors of six major hedge fund groups.

Preface xi

What's New to This Edition xii

Before You Begin xii

Acknowledgments xiii

CHAPTER 1: Foreign Exchange Basics 1

The Foreign Exchange Market 1

The International Monetary System 6

Spot Foreign Exchange and Market Conventions 11

Foreign Exchange Dealing 14

Interest Parity and Forward Foreign Exchange 21

Departures from Covered Interest Parity in 2007-2008
26

CHAPTER 2: Trading Currency Options 29

The Interbank Currency Option Market 29

Option Basics 31

Listed Options on Actual Foreign Currency 38

Currency Futures Contracts 40

Listed Currency Futures Options 44

CHAPTER 3: Valuation of European Currency Options 47

Arbitrage Theorems 48

Put-Call Parity for European Currency Options 50

The Black-Scholes-Merton Model 52

How Currency Options Trade in the Interbank Market 60

Reflections on the Contribution of Black, Scholes, and Merton
62

CHAPTER 4: European Currency Option Analytics 65

Base-Case Analysis 65

The "Greeks" 66

Special Properties of At-the-Money Forward Options 77

Directional Trading with Currency Options 79

Hedging with Currency Options 86

Appendix 4.1 Derivation of the BSM Deltas 88

CHAPTER 5: Volatility 91

Alternative Meanings of Volatility 91

Some Volatility History 99

Construction of the Volatility Surface 113

The Vanna-Volga Method 115

The Sticky Delta Rule 118

Risk-Neutral Densities 118

Dealing in Currency Options 119

Trading Volatility 121

Mixing Directional and Volatility Trading 124

Appendix 5.1 Vanna-Volga Approximations 125

CHAPTER 6: American Exercise Currency Options 127

Arbitrage Conditions 127

Put-Call Parity for American Currency Options 128

The General Theory of American Currency Option Pricing 131

The Economics of Early Exercise 132

The Binomial Model 136

The Binomial Model for European Currency Options 143

American Currency Options by Approximation 144

Finite Differences Methods 149

CHAPTER 7: Currency Futures Options 159

Currency Futures and Their Relationship to Spot and Forward
Exchange Rates 159

Arbitrage and Parity Theorems for Currency Futures Options
167

Black's Model for European Currency Futures Options 174

The Valuation of American Currency Futures Options 178

The Quadratic Approximation Model for Futures Options 180

CHAPTER 8: Barrier and Binary Currency Options 183

Single Barrier Currency Options 185

Double Barrier Knock-Out Currency Options 193

Binary Currency Options 197

Contingent Premium Currency Options 203

Applying Vanna-Volga to Barrier and Binary Options 204

What the Formulas Don't Reveal 205

CHAPTER 9: Advanced Option Models 207

Stochastic Volatility Models 208

The Mixed Jump-Diffusion Process Model 211

Local Volatility Models 213

Stochastic Local Volatility 214

Static Replication of Barrier Options 215

Appendix 9.1: Equations for the Heston Model 231

CHAPTER 10: Non-Barrier Exotic Currency Options 233

Average Rate Currency Options 233

Compound Currency Options 237

Basket Options 241

Quantos Options 242

Comments on Hedging with Non-Barrier Currency Options 250

Appendix 10.1 Monte Carlo Simulation for Arithmetic Mean Average
Options 250

Bibliography 253

Index 263