Table of Contents

About the Authors xi

Data Set xii

CHAPTER 1 Introduction 1

1.1 Why Read This Book? 1

1.2 This Book 3

1.3 What Is an FX Option? 3

1.4 Market Participants 5

1.4.1 How Hedgers Can Use This Information 6

1.4.2 How Investors Can Use This Information 7

1.5 History and Size of the FX Option Market 9

1.6 The FX Option Trading Day 14

1.7 Summary 14

References 14

CHAPTER 2 The FX Option Market: How Options Are Traded and What That Implies for Option Value 17

2.1 Introduction 17

2.2 The Basics of Option Pricing 18

2.2.1 The Black-Scholes-Merton Model 18

2.2.2 The Impact of Volatility 20

2.2.3 The Impact of Rate Differentials 21

2.3 How Options Are Traded 22

2.3.1 Two Views of Volatility 23

2.3.2 Static Trading 24

2.3.3 Dynamic Trading 24

2.4 A More Detailed Discussion of Option Trading 26

2.4.1 The Greeks 26

2.5 Summary 31

References 31

CHAPTER 3 It Is All About the Data 33

3.1 Introduction 33

3.2 The Goal: To Price Lots of Options! 34

3.3 Defining a Universe of Currencies 34

3.4 The Data 37

3.4.1 Pricing Model Data Requirements 38

3.4.2 Sourcing the Data 39

3.4.3 Calculation Frequency 40

3.4.4 Currency of Option Notional Amount 41

3.4.5 Spot Market Value 42

3.5 Limitations 43

3.6 Summary 45

References 45

CHAPTER 4 At-the-Money-Forward (ATMF) Options 47

4.1 What Are ATMF Options? 47

4.1.1 How Are ATMF Options Used and Traded? 47

4.1.2 What Is the ‘Fair’ Price for an ATMF Option? 48

4.2 How Might Mispricings Arise? 50

4.2.1 Can the Forward Rate Be on Average Wrong? 51

4.2.2 Can the Implied Volatility Be on Average Wrong? 52

4.2.3 Simple Example with USDJPY 53

4.3 Results for Straddles for All Currency Pairs 55

4.3.1 Discussion of Results for Straddles 57

4.3.2 A Breakdown of the Results by Currency Pair 62

4.3.3 Drilling Down to Different Time Periods 62

4.3.4 Comparison of Put and Call Options 64

4.4 Have We Found a Trading Strategy? 75

4.5 Summary of Results 76

References 76

CHAPTER 5 Out-of-the-Money (OTM) Options: Do Supposedly ‘Cheap’ OTM Options Offer Good Value? 77

5.1 Introduction 77

5.2 Price versus Value 78

5.3 The Implied Volatility Surface 79

5.4 Why Do Volatility Surfaces Look Like They Do? 80

5.4.1 Equity Indices 80

5.4.2 Foreign Exchange Markets 83

5.5 Parameterising the Volatility Smile 84

5.6 Measuring Relative Value in ATMF and OTM Foreign Exchange Options 88

5.6.1 The Analysis 89

5.6.2 Option Premium 90

5.6.3 Option Payoff 90

5.6.4 Payoff-to-Premium Ratios 90

5.6.5 Discussion 95

5.6.6 Alternative Measures of OTM Option Worth 96

5.7 Summary 97

Reference 97

CHAPTER 6 G10 vs EM Currency Pairs 99

6.1 Why Consider EM and G10 Options Separately? 99

6.2 How Would EM FX Options Be Used? 99

6.3 Straddle Results 100

6.3.1 Comparison of ATMF Put and Call Options 103

6.3.2 Comparison of OTM Put and Call Options 106

6.3.3 The Effect of Tenor 111

6.4 Hedging with Forwards vs Hedging with Options 113

6.5 Summary of Results 120

CHAPTER 7 Trading Strategies 123

7.1 Introduction 123

7.2 History of the Carry Trade 123

7.3 Theory 124

7.4 G10 Carry Trade Results 125

7.5 EM Carry Trade Results 130

7.6 What Is Going On? 131

7.7 Option Trading Strategies – Buying Puts 132

7.8 Option Trading Strategies – Selling Calls 136

7.9 Option Trading Strategies – Trading Carry with Options 140

7.9.1 Premium and Payoff vs MTM Calculations 144

7.10 Summary of Results 146

References 147

CHAPTER 8 Summary 149

8.1 A Call to Arms 149

8.2 Summary of Results from This Book 150

8.3 Building up a Picture 151

8.3.1 What Does This Mean in Practice? 155

8.4 Final Word 156

Appendix 157

Glossary 241

Index 247

About the Author

Jessica James, PhD, is a Managing Director and Head of FX Quantitative Solutions at Commerzbank AG in London. She has previously held positions in foreign exchange at Citigroup and Bank One. Before her career in finance, James lectured in physics at Trinity College, Oxford. Her significant publications include the Handbook of Foreign Exchange, Interest Rate Modelling and Currency Management. She is also Managing Editor for the Journal of Quantitative Finance, and is a Visiting Professor both at UCL and at Cass Business School. She is a Fellow of the Institute of Physics and has been a member of their governing body and of their
Industry and Business Board.

Jonathan Fullwood began his career in finance in 2002 and has since held positions in research, sales and trading at Commerzbank AG in London. He was awarded a CFA charter in 2007 and remains a member of the CFA Institute. Before his career in finance he graduated with first class honours in physics from the  University of Manchester, where he also worked as a mathematics tutor. Jonathan completed his particle physics doctoral thesis in 2001, on work carried out at the Stanford Linear Accelerator Centre.

Peter Billington is Global Head of FX Exotic Options at UniCredit in London. Since 1993 he has worked in FX option trading roles for Standard Chartered Bank and BNP Paribas and has traded metals for Dresdner Kleinwort Wasserstein. He has also worked at Commerzbank AG in several positions, including that of Global Head of FX Trading. Prior to his career in finance, Peter read mathematics and then mathematical modelling and numerical analysis at the University of Oxford.