FX Option Performance E-Book

Jessica James

• Herausgeber: John Wiley & Sons
• Kategorie: Fachliteratur
• Serie: Wiley Finance Series
• Sprache: Englisch

Seitenzahl: 381

Veröffentlichungsjahr: 2015

Beschreibung

Get the little known – yet crucial – facts about FX options

Daily turnover in FX options is an estimated U.S. $ 207 billion, but many fundamental facts about this huge and liquid market are generally unknown. FX Option Performance provides the information practitioners need to be more effective in the market, with detailed, specific guidance.

This book is a unique and practical guide to option trading, with the courage to report how much these contracts have really made or lost. Breaking free from the typical focus on theories and generalities, this book gets specific – travelling back in history to show exactly how options performed in different markets and thereby helping investors and hedgers alike make more informed decisions. Not overly technical, the rigorous approach remains accessible to anyone with an interest in the area, showing investors where to look for value and helping corporations hedge their FX exposures. FX Option Performance begins with a quick and practical introduction to the FX option market, then provides specific advice toward structures, performance, rate fluctuation, and trading strategies.

• Examine the historical payoffs to the most popular and liquidly traded options
• Learn which options are overvalued and which are undervalued
• Discover surprising, generally unpublished facts about emerging markets
• Examine systemic option trading strategies to find what works and what doesn't

On average, do options result in profit, loss, or breaking even? How can corporations more cost-effectively hedge their exposure to emerging markets? Are cheap out-of-the-money options worth it?

Leseprobe

For other titles in the Wiley Finance series please see www.wiley.com/finance

FX Option Performance

An Analysis of the Value Delivered by FX Options Since the Start of the Market

JESSICA JAMES JONATHAN FULLWOOD PETER BILLINGTON

This edition first published 2015 © 2015 Jessica James, Jonathan Fullwood and Peter Billington

Registered officeJohn Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom

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Library of Congress Cataloging-in-Publication Data

James, Jessica, 1968–    FX option performance : an analysis of the value delivered by FX options since the start of the market / Jessica James, Jonathan Fullwood, Peter Billington.          pages cm. – (The wiley finance series)    Includes index.       ISBN 978-1-118-79328-2 (hardback)   1. Options (Finance)   I. Fullwood, Jonathan, 1976–    II. Billington, Peter, 1948–   III. Title.    HG6024.A3J355 2015    332.64′53–dc23

2015001988

A catalogue record for this book is available from the British Library.

ISBN 978-1-118-79328-2 (hbk) ISBN 978-1-118-79326-8 (ebk) ISBN 978-1-118-79327-5 (ebk) ISBN 978-1-118-79325-1 (ebk)

Cover Design: Wiley Top Image: ©iStock.com/Maxiphoto Bottom Image: Gears ©iStock.com/Marilyn Nieves Business Graph: ©iStock.com/kickimages

Certain figures and tables compiled from raw data sourced from Bloomberg

JJ: To my sister Alice

JF: To Lucy

PB: To Gemma, Jamie, Felix and Orson

Contents

About the Authors

Chapter 1 Introduction

1.1 WHY READ THIS BOOK?

1.2 THIS BOOK

1.3 WHAT IS AN FX OPTION?

1.4 MARKET PARTICIPANTS

1.5 HISTORY AND SIZE OF THE FX OPTION MARKET

1.6 THE FX OPTION TRADING DAY

1.7 SUMMARY

NOTES

REFERENCES

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

2.1 INTRODUCTION

2.2 THE BASICS OF OPTION PRICING

2.3 HOW OPTIONS ARE TRADED

2.4 A MORE DETAILED DISCUSSION OF OPTION TRADING

2.5 SUMMARY

NOTES

REFERENCES

Chapter 3 It Is All About the Data

3.1 INTRODUCTION

3.2 THE GOAL: TO PRICE LOTS OF OPTIONS!

3.3 DEFINING A UNIVERSE OF CURRENCIES

3.4 THE DATA

3.5 LIMITATIONS

3.6 SUMMARY

NOTES

REFERENCES

Chapter 4 At-the-Money-Forward (ATMF) Options

4.1 WHAT ARE ATMF OPTIONS?

4.2 HOW MIGHT MISPRICINGS ARISE?

4.3 RESULTS FOR STRADDLES FOR ALL CURRENCY PAIRS

4.4 HAVE WE FOUND A TRADING STRATEGY?

4.5 SUMMARY OF RESULTS

NOTES

REFERENCES

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

5.1 INTRODUCTION

5.2 PRICE VERSUS VALUE

5.3 THE IMPLIED VOLATILITY SURFACE

5.4 WHY DO VOLATILITY SURFACES LOOK LIKE THEY DO?

5.5 PARAMETERISING THE VOLATILITY SMILE

5.6 MEASURING RELATIVE VALUE IN ATMF AND OTM FOREIGN EXCHANGE OPTIONS

5.7 SUMMARY

NOTES

REFERENCE

Chapter 6 G10 vs EM Currency Pairs

6.1 WHY CONSIDER EM AND G10 OPTIONS SEPARATELY?

6.2 HOW WOULD EM FX OPTIONS BE USED?

6.3 STRADDLE RESULTS

6.4 HEDGING WITH FORWARDS VS HEDGING WITH OPTIONS

6.5 SUMMARY OF RESULTS

Chapter 7 Trading Strategies

7.1 INTRODUCTION

7.2 HISTORY OF THE CARRY TRADE

7.3 THEORY

7.4 G10 CARRY TRADE RESULTS

7.5 EM CARRY TRADE RESULTS

7.6 WHAT IS GOING ON?

7.7 OPTION TRADING STRATEGIES – BUYING PUTS

7.8 OPTION TRADING STRATEGIES – SELLING CALLS

7.9 OPTION TRADING STRATEGIES – TRADING CARRY WITH OPTIONS

7.10 SUMMARY OF RESULTS

NOTES

REFERENCES

Chapter 8 Summary

8.1 A CALL TO ARMS

8.2 SUMMARY OF RESULTS FROM THIS BOOK

8.3 BUILDING UP A PICTURE

8.4 FINAL WORD

Appendix

CHAPTER 1

CHAPTER 2

CHAPTER 4

CHAPTER 5

CHAPTER 6

NOTE

Glossary

Index

EULA

List of Tables

Chapter 1

TABLE 1.1

Chapter 2

TABLE 2.1

Chapter 3

TABLE 3.1

TABLE 3.2

TABLE 3.3

TABLE 3.4

Chapter 4

TABLE 4.1

TABLE 4.2

TABLE 4.3

TABLE 4.4

TABLE 4.5

TABLE 4.6

TABLE 4.7

TABLE 4.8

TABLE 4.9

TABLE 4.10

TABLE 4.11

Chapter 6

TABLE 6.1

TABLE 6.2

TABLE 6.3

TABLE 6.4

TABLE 6.5

TABLE 6.6

TABLE 6.7

TABLE 6.8

TABLE 6.9

TABLE 6.10

TABLE 6.11

TABLE 6.12

Chapter 7

TABLE 7.1

TABLE 7.2

TABLE 7.3

TABLE 7.4

TABLE 7.5

Appendix

TABLE A.1

TABLE A.2

TABLE A.3

TABLE A.4

TABLE A.5

TABLE A.6

TABLE A.7

TABLE A.8

TABLE A.9

TABLE A.10

TABLE A.11

TABLE A.12

TABLE A.13

TABLE A.14

TABLE A.15

TABLE A.16

TABLE A.17

TABLE A.18

TABLE A.19

TABLE A.20

TABLE A.21

TABLE A.22

TABLE A.23

TABLE A.24

TABLE A.25

TABLE A.26

TABLE A.27

TABLE A.28

TABLE A.29

TABLE A.30

TABLE A.31

TABLE A.32

TABLE A.33

TABLE A.34

TABLE A.35

TABLE A.36

TABLE A.37

TABLE A.38

TABLE A.39

TABLE A.40

TABLE A.41

TABLE A.42

TABLE A.43

TABLE A.44

TABLE A.45

TABLE A.46

TABLE A.47

TABLE A.48

TABLE A.49

TABLE A.50

TABLE A.51

TABLE A.52

TABLE A.53

TABLE A.54

TABLE A.55

TABLE A.56

TABLE A.57

TABLE A.58

TABLE A.59

TABLE A.60

TABLE A.61

TABLE A.62

TABLE A.63

TABLE A.64

TABLE A.65

TABLE A.66

TABLE A.67

TABLE A.68

TABLE A.69

TABLE A.70

TABLE A.71

TABLE A.72

TABLE A.73

TABLE A.74

TABLE A.75

TABLE A.76

TABLE A.77

TABLE A.78

TABLE A.79

TABLE A.80

TABLE A.81

TABLE A.82

TABLE A.83

TABLE A.84

TABLE A.85

TABLE A.86

TABLE A.87

TABLE A.88

TABLE A.89

List of Illustrations

Chapter 1

FIGURE 1.1

Payoff profile at expiry for a call option

FIGURE 1.2

Cumulative returns in percent of notional to a 1W short put strategy in EURCHF

FIGURE 1.3

Daily FX option flow (notional) from 2013 BIS triennial survey

FIGURE 1.4

Hourly flow for EURUSD options, for 7 July 2014, from Commerzbank AG

Chapter 2

FIGURE 2.1

Annualised daily 1M EURCHF implied volatility and subsequent 1M realised volatility

FIGURE 2.2

A simple example of delta hedging. With the spot rate finishing below the option breakeven rate the seller makes a profit. Spot rate volatility means that the option buyer could have realised a profit too

Chapter 3

FIGURE 3.1

Downloaded series USDMYR 1M implied volatility. Pricing was unresponsive in the early years, making the first part of the history unsuitable for inclusion in the analysis

FIGURE 3.2

Downloaded series for EURCZK 1W forward points shows bad data points for 2006

Chapter 4

FIGURE 4.1

Payoff profile for call option

FIGURE 4.2

Difference between premium and payoff over time (% notional). Different series, same average value

FIGURE 4.3

Payoff/premium ratio for USDJPY straddles

FIGURE 4.4

Result of continuously selling USDJPY 1W straddles

FIGURE 4.5

Result of continuously buying USDJPY 2Y straddles

FIGURE 4.6

Payoff/premium ratio – averaged over 34 pairs

FIGURE 4.7

Payoff/premium ratio for straddles for different currency pairs

FIGURE 4.8

Payoff/premium ratio – averaged over 34 currency pairs for separate time periods

FIGURE 4.9

Payoff/premium ratio for ATMF calls – averaged over 34 pairs

FIGURE 4.10

Payoff/premium ratio for ATMF puts – averaged over 34 pairs

FIGURE 4.11

Payoff/premium ratio for ATMF calls for different currency pairs

FIGURE 4.12

Payoff/premium ratio for ATMF puts for different currency pairs

FIGURE 4.13

Spot at inception versus forward, with likely historical range of spot at expiry

FIGURE 4.14

Implied versus historical rate distributions at expiry

FIGURE 4.15

Option payoffs with implied and historical rate distributions

FIGURE 4.16

Option and forward payoffs with implied versus historical distributions

Chapter 5

FIGURE 5.1

The implied volatility surface

FIGURE 5.2

European equity index – sharp moves lower are more likely than sharp moves higher

FIGURE 5.3

The implied volatility smile

FIGURE 5.4

Schematic implied volatility skew for an equity index

FIGURE 5.5

Volatility smiles for USDMXN and EURGBP as at 28 June 2013

FIGURE 5.6

Measures of skewness for the volatility smile

FIGURE 5.7

A butterfly spread can be used to gauge the steepness of the volatility smile

FIGURE 5.8

Average premiums for ATMF, 25-delta and 10-delta straddles/strangles in percent of notional amount for 2004–2013 inclusive

FIGURE 5.9

Average payoffs for ATMF, 25-delta and 10-delta straddles/strangles in percent of notional amount for 2004–2013 inclusive

FIGURE 5.10

Average straddle/strangle payoff/premium ratios for 2004–2013 inclusive

FIGURE 5.11

Average straddle/strangle payoff/premium ratios by tenor for 2004–2013 inclusive

FIGURE 5.12

Average straddle/strangle payoff/premium ratios by tenor for 2004–2013 inclusive. In this instance calculations are performed at mid-market rates in order to exclude the bid-ask spread

FIGURE 5.13

Average payoff-to-premium ratios by tenor for 2004–2013 inclusive

Chapter 6

FIGURE 6.1

Forward and option payoffs for high interest rate differentials

FIGURE 6.2

Payoff/premium ratio for ATMF G10 straddles – average over 14 pairs

FIGURE 6.3

Payoff/premium ratio for ATMF EM straddles – average over 20 pairs

FIGURE 6.4

Payoff/premium ratio for ATMF G10 straddles

FIGURE 6.5

Payoff/premium ratio for ATMF EM straddles

FIGURE 6.6

Payoff/premium ratio for ATMF puts

FIGURE 6.7

Payoff/premium ratio for ATMF calls

FIGURE 6.8

Payoff diagram for large and small interest rate differentials for calls

FIGURE 6.9

Payoff diagram for large and small interest rate differentials for puts

FIGURE 6.10

Payoff/premium ratio for G10 puts

FIGURE 6.11

Payoff/premium ratio for EM puts

FIGURE 6.12

Payoff/premium ratio for 25-delta puts

FIGURE 6.13

Payoff/premium ratio for 10-delta puts

FIGURE 6.14

Payoff/premium ratio for G10 calls

FIGURE 6.15

Payoff/premium ratio for EM calls

FIGURE 6.16

Payoff/premium ratio for 25-delta calls

FIGURE 6.17

Payoff/premium ratio for 10-delta calls

FIGURE 6.18

Payoff diagram for ATMF vs OTM calls

FIGURE 6.19

Payoff diagram for ATMF vs OTM puts

FIGURE 6.20

Payoff diagram for the case of small interest rate differentials

FIGURE 6.21

Payoffs for forwards, ATMF calls and OTM calls for the case of high interest rate differentials

FIGURE 6.22

Average cash flow for 3M G10 hedges (positive exposure)

FIGURE 6.23

Average cash flow for 3M EM hedges (positive exposure)

FIGURE 6.24

Hedge cash flow in percent of notional for period of worst depreciation

FIGURE 6.25

Payoffs for forwards, ATMF puts and OTM puts for the case of moderate interest rate differentials

FIGURE 6.26

Payoffs for forwards, ATMF puts and OTM puts for the case of high interest rate differentials

FIGURE 6.27

Average cash flow for 3M G10 hedges (negative exposure)

FIGURE 6.28

Average cash flow for 3M EM hedges (negative exposure)

FIGURE 6.29

Average cash flow in percent of notional for different hedge tenors, averaged over G10 currency pairs

FIGURE 6.30

Average cash flow in percent of notional for different hedge tenors, averaged over EM currency pairs

Chapter 7

FIGURE 7.1

G10 carry trade returns with spot and interest rate components

FIGURE 7.2

USD crosses

FIGURE 7.3

GBP crosses

FIGURE 7.4

EUR (DEM prior to 1999) crosses

FIGURE 7.5

JPY crosses

FIGURE 7.6

CHF crosses

FIGURE 7.7

SEK crosses

FIGURE 7.8

NOK crosses

FIGURE 7.9

DKK crosses

FIGURE 7.10

CAD crosses

FIGURE 7.11

AUD crosses

FIGURE 7.12

EM carry trade returns with spot and interest rate components

FIGURE 7.13

USD crosses

FIGURE 7.14

EUR crosses

FIGURE 7.15

G10 carry trade

FIGURE 7.16

EM carry trade

FIGURE 7.17

Potential profitable payoff when buying put options

FIGURE 7.18

Average cumulative returns for buying ATMF puts

FIGURE 7.19

Cumulative returns of put buying for 1M options

FIGURE 7.20

Cumulative returns of put buying for 12M options

FIGURE 7.21

Potential profitable payoff when selling call options

FIGURE 7.22

Average cumulative returns for selling ATMF calls

FIGURE 7.23

Cumulative returns of call selling for 1M options

FIGURE 7.24

Cumulative returns of call selling for 12M options

FIGURE 7.25

AUDUSD carry trade for 1M options

FIGURE 7.26

AUDUSD carry trade for 12M options

FIGURE 7.27

Carry trade for 1M options – All

FIGURE 7.28

Carry trade for 1M options – G10

FIGURE 7.29

Carry trade for 1M options – EM

FIGURE 7.30

Carry trade for 12M options – All

FIGURE 7.31

Carry trade for 12M options – G10

FIGURE 7.32

Carry trade for 12M options – EM

FIGURE 7.33

Average quarterly option carry trade returns (payoff – premium)

FIGURE 7.34

Average annualised carry trade returns

Chapter 8

FIGURE 8.1

Forward and spot rates with distributions

FIGURE 8.2

Why the carry trade works

FIGURE 8.3

ATMF put and call options

FIGURE 8.4

Hedging quote currency appreciation risk

FIGURE 8.5

Hedging quote currency depreciation risk

FIGURE 8.6

ATMF vs OTM call option

FIGURE 8.7

ATMF vs OTM put option

Guide

Cover

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About the Authors

Prof Jessica James

Jessica James 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.

Jessica is a 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.

Dr Jonathan Fullwood

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

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.

CHAPTER 1Introduction

1.1 WHY READ THIS BOOK?

Let's be honest, there is no shortage of books on Foreign Exchange (FX) options. There are plenty of places, online and on paper, where you can read about how to value FX options and associated derivatives. You can learn about the history of the market and how different valuation models work. Regular surveys will inform you about the size and liquidity of this vast market, and who trades it.

This is not what this book is about. This is about what happens to an option once it is bought or sold. It is about whether the owner of an option had cause to be happy with their purchase. It is about whether FX options deliver value to their buyers.

In the financial markets, there is huge and detailed effort made to value contracts accurately at the start of their lives. Some decades ago this work was begun in earnest when Black and Scholes published their famous paper [1]. Perhaps indeed we could say it started in 1900 when Bachelier derived a very similar model [2] though this was not followed up on. But, in general, quantitative researchers in the markets and in universities spend long hours to devise ways of correctly valuing complex contingent deals under sets of assumptions which make the mathematics possible.

But are these assumptions right, i.e. over time, do they turn out to have been correct? Bizarrely, they do not have to have been ‘correct’ to continue to be used; later in the book we will give some detailed examples of assumptions that turn out to be manifestly incorrect. For an option, we can say that in an efficient (‘correctly priced’) market, on average, we would expect an option to pay back the money it cost in the first place – less costs, of course.1 In this book we will use terms like ‘mispriced’ or ‘misvalued’ to indicate that the average payoff of the option is significantly different from the average premium paid to own the option.2

That this is not always the case may be surprising. But that options can be systematically ‘cheap’ or ‘expensive’ throughout the history of the market, depending on their precise nature, is even more surprising, and should be of significant interest to many different areas of the finance community.

Why is this not widely known? In part it is simply the focus of the market participants. Most trading desks will operate on a daily mark to market P/L with drawdown and stop-loss limits.3 Another way of putting this is that they will want to make money all or most days, with limited risk. So the timescale and nature of a trading desk dictates that the price of a contract ‘now’ is the focus of the market. Further, depending on the hedging strategy and how the option is traded, different end results can be seen. So pricing the contract ‘now’ is in many ways simpler than trying to model an option's performance. Later, we will discuss in detail how a desk manages its portfolio of options to make money, but we may summarise it now by saying that, ideally, deals are done and hedged so that a small but almost riskless profit is locked in almost immediately. After that, the combination of the deal and its offsetting hedges should be almost immune to market movements – so a systematic tendency for deals to be cheap or expensive over time may well not be noticed on a trading desk, as long as they can be hedged at a profit. The situation is complicated by the fact that a perfect hedge is rarely available, combined with the fact that a trading desk may want to have a ‘position’ – a sensitivity to market movements – when they believe that certain moves are likely to occur.

But the other reason that the long-term mispricing of parts of the FX option markets is not well known is that FX options are a young market! Before one can say that a contract is generally cheap or expensive, one needs to observe it under a variety of circumstances. To say that 12M options bought in 2006, when market confidence was high and volatility low, were cheap because they paid out large sums in 2007, when confidence was greatly shaken and volatilities had begun a very sharp rise, would be to look at a particular case which does not represent the generality of market conditions. It is only really now, with widely available option data available going back to the 1990s, that we can say we have information available for a wide variety of market regimes, and importantly, the transitions between these regimes. We will discuss exactly what data are needed and available in the next chapter, but for now we may say that for most liquid currencies there will be perhaps 20 years of daily data available, with longer time series or higher frequencies available in some cases.

So, we are now in a position to say whether FX options have performed well or badly for their buyers and sellers. We can take a day in the past, collect all the data needed to calculate the cost of the option and look ahead to the payoff of the option at expiry to compare the two. We can tell, on average and for different time periods, whether the options have had the correct price.

If they have not had the correct price – and the fact that there is a book being written on the subject implies that this has been the case at least some of the time! – then the situation becomes much more interesting. Why did the market appear to be inefficient? Was there a good reason? Is it connected to the way options are used, the way they are hedged, differences in demand and supply? We will show that indeed, in different ways, the payoff and the cost of the options have differed significantly throughout the history of the market, and moreover these differences have been systematic, repeated in different currency pairs and market regimes.4

1.2 THIS BOOK

The book is laid out in increasing order of complexity. We give a brief history of the market and describe how options are valued – this will cover simple widely used valuation techniques; it is not our intention to go deeply into the details of exotic option pricing. Then we set the scene by introducing the available dataset and discussing the way that the market operates. We next introduce the first set of comparisons, looking at payoff vs cost or premium for options of different tenors.5 We then move on to look at different types of option: puts, calls, options which pay out at different levels or strikes, and options on emerging market currencies, which present particular features and may have less data available. Finally we examine whether some of the anomalies we see are predictable and whether it is possible to use some market indicators to buy and sell options in a dynamic fashion to improve the protection they provide or to deliver value.

Perhaps we need to say at this point – before the reader gets too far – that there will be no magical profit-making trading strategy found in these pages. Though the market can consistently show features which seem to indicate that it lacks efficiency, inevitably they are not those which lead to a fast buck and early retirement for those who happen upon them. That is not to say that the information here may not be useful to those looking for trading strategies. At the very least it could prevent them from reinventing the wheel, show them where opportunity may lie and where they may be wasting their time. But the authors confess freely that they have not yet discovered the Holy Grail of risk-free yet profitable trading. And if they do, they may not be publishing it in a book…

1.3 WHAT IS AN FX OPTION?

Before we discuss which market participants can use this information, we should define more precisely what kind of contract we are talking about. Foreign Exchange (FX) options are contracts whose payoff depends upon the values of FX rates, and they are widely used financial instruments.

Let's look at a definition from a popular website…6

A foreign-exchange option is a derivative financial instrument that gives the owner the right but not the obligation to exchange money denominated in one currency into another currency at a pre-agreed exchange rate on a specified future date.

The price or cost of this right is called the premium, by analogy with the insurance market, and it is usually (depending on the tenor and the market at the time) a few percent of the insured amount (notional amount). The specified future date is called the expiry or expiry date.7 The payoff profile at expiry of the simplest type of option is shown schematically in Figure 1.1.

FIGURE 1.1 Payoff profile at expiry for a call option

The figure shows the payoff received by the holder of an at-the-money-forward (ATMF) call option on an FX rate. This means that the strike of the option is the forward rate, and the option is the right to buy the base currency, or, in other words, an option to buy the FX rate.8 In other markets such as commodities and equities it is obvious what the call or put is applied to but in FX more clarity is needed. For instance a call option associated with the currency pair USDJPY could be a call on USD (and thereby a put on JPY) or a call on JPY (and therefore a put on USD). As different currency pairs have different conventions it is always best to clarify the exact details before trading. A put option would be the right to sell the base currency, or FX rate. We will discuss forward rates and their relationship with options more completely in later chapters but in essence the forward rate is the current FX rate adjusted for interest rate effects. If the interest rates for the period of the option were identical in both currencies involved in the FX rate, then the forward rate would be identical to today's FX rate. Because they usually are not the same, the rate which one may lock in an exchange without risk for a future date will be somewhat different from today's rate.

The figure shows the premium cost of the option. At all FX rates at expiry which are less than the forward rate, this will be what the option holder loses, meaning that he or she paid a premium to buy the option and will make no money from it. The net result is the loss of the premium. At the forward rate, the payoff begins to rise, at first reducing the overall cost and then taking the owner of the option into profitable territory for higher FX rates at expiry. We have also shown the payoff from a forward contract, which is simply when the owner of the contract locks in the forward rate at the expiry date. This will lose money when the rate at expiry is less than the forward, and make money when the rate is higher. The forward rate is costless to lock in other than bid-offer costs.

The essential thing to grasp about the payoff to an option contract is that it is asymmetric. There is limited loss (the owner of the option can only lose the premium) but in theory unlimited gain. Conversely, the seller of the option stands to make a limited gain but an unlimited loss. Thus the option payoff looks very much like that of an insurance contract: we expect to pay a fixed premium to cover a variety of different loss types, up to and including very large losses indeed.

The difference between FX options and the more familiar types of insurance such as for a house or car is that, with the latter, we are pretty sure that we are paying more than we really need to. After all, in addition to covering losses, the insurance companies are paying their staff salaries, taxes and business costs. With FX options, we would anticipate that the bid-offer costs or trading activity cover the desk and business costs as a market-making desk makes money from buying and selling options, unlike an insurance company, which can only sell. We would expect the premium to add relatively little to the costs of the option; that the average cost of an option is close to the average payoff for the same option. If it is not (and in many cases we can show that it is not, at least on a historical basis) then there will be a number of interested parties. See the Appendix for more detail on what an option ‘should’ cost.

1.4 MARKET PARTICIPANTS

This information has potential to be of use to a wide variety of market participants. One way of looking at it would be to think of option suppliers (sellers of risk) and option consumers (buyers of risk). The former might be balance sheet holders who can sell a ‘covered option’ – essentially, if they hold the underlying currency, they can make money by selling an option which pays out if the currency rises but not if it falls. If it rises, their holdings will increase in value so they can pay the option holder. If it falls, they do not have to pay but they collect the premium. The option consumers have unwanted currency risk they need to reduce, like an investor with an international portfolio of bonds, or a corporation selling goods in another country. Additional to option suppliers, there are market makers like the option desks of larger banks, which both buy and sell options to make a profit from the bid-offer spread. Also there are purely profit-focused entities, like hedge funds, which take views on direction or inefficiencies in the market to make money. Finally the world's central banks can direct massive FX flow, sometimes using options, to execute policy aims like currency strength or weakness. And each of these has properties of the others; a portfolio manager may wish to protect against currency risk but derive some return, and even a central bank may maintain a trading arm to smooth volatility and influence currency levels.

The accounting and regulatory bodies additionally maintain a strong interest in the use of FX options, and could be interested to learn that in some circumstances simple options can be more useful than forward contracts. Thus a wide range of market participants from central banks to hedge funds, investment banks to insurance companies, corporations to pension funds could find much of interest in the data we present.

Perhaps the most useful division of FX option traders is into two broad categories: those who wish to protect against losses due to foreign exchange movements, and those who wish to make money from those same movements. We can call them the hedgers and the investors, while understanding that most trading entities contain both types to some extent.

1.4.1 How Hedgers Can Use This Information

A good example of a hedger would be a European corporate which sells cars to the United States (US). Assuming they have no manufacturing capacity in the US, then their expenses are largely in EUR while a large part of their income will be in USD.9 If the value of the USD falls relative to that of the EUR, their income will drop but their expenses will remain fixed. Thus they would possibly like to insure themselves against this eventuality.

Such insurance will naturally be temporary in nature; one could insure for a period, but eventually it will expire and the company will be left with the new exchange rate to deal with. But what can be covered are sudden price jumps over the period, so that at the end of the year (if the period is a year) the company can take stock and plan the following year with some confidence.

So it will be useful to be able to protect against sudden damaging drops in the value of the USD. But it would be good for the company if sudden rises in the value of the USD, which would be beneficial, could nevertheless be taken advantage of. These two facts are important to the company's decision of whether to hedge the risk.

Clearly an option, with its asymmetric payoff, will be of interest in this situation. If the company could be reasonably confident that the option offered good value for money, then it would be the obvious choice. However, in general, the company will simply not know whether the option is good value. It is often assumed that because options are more complex than forward hedges they must be much more expensive. So if we can show that under some circumstances options have historically not been expensive, the corporates which currently avoid them would be interested to take another look.

Of course payoff is not the only factor to consider when choosing a hedge strategy. A forward hedge will reduce overall volatility, as it is in some ways simply the opposite exposure to the hedged quantity. So if this is important, the forward rate will have an advantage.

Additionally, for a hedger the evolution of the underlying is critical. Many corporate hedgers already effectively have an FX position – our European car manufacturer mentioned above might buy a protective option and never need it, with the money spent on the premium being lost. But, if the USD has appreciated several percent in the period, they will have made money overall. Conversely, a sophisticated hedge programme might sell a few short dated call options on the EURUSD rate, reasoning that if it moves in their favour (decreasing rate in this example) then they will make money and can cover the option payoffs. Their reasoning may be that if the rate moves mildly against them then they will pick up some mitigating profit from the option premiums – but this will not help them much if the rate move is large.

Finally, accounting and tax treatments will play significant roles in the choice of hedge strategy and tend to favour forward contracts. Perhaps if the historical behaviour of options were more widely known it might have an effect in these very different circles.

1.4.2 How Investors Can Use This Information

The word ‘investors’ covers a wide variety of market participants; we list a few below:

Insurance companies

Hedge funds

Pension funds

Mutual funds

High Net Worth individuals.

The investors will want to make money. They are motivated to use money to make more of it. Thus they will buy an option if they have reason to believe that the payoff will be larger than the premium, and sell it if the opposite is the case.

Short10 dated option selling uses the fact that, in some markets, the investor believes that the premium is too large given the risks in the market (more of this later…). A truly classic example of this would be in the aftermath of a high risk period. Shortly after the market shock caused by the Lehman bankruptcy in the autumn of 2008, FX option volatilities remained very high for some months. They were implying that markets in the future would be choppy and very active. Essentially, they were reflecting the views of nervous and shaken market participants that the market was in a state of high risk. In fact, the months following the 2008 crisis were consistently less volatile than implied by the option volatilities; selling options would have been very profitable. In Figure 1.2 we show the cumulative result of selling one-week EURCHF options each week between 1998–2013. We chose EURCHF as an example here to include a currency pair which had periods of very low and very high volatility. It is easily seen that the investor who correctly judged when the market was overestimating the future risks would have made strong returns – but it would have taken nerves of steel. A misjudgement could have seen sharp losses, which would have been almost impossible to avoid as liquidity was at times non-existent during this period.

FIGURE 1.2 Cumulative returns in percent of notional to a 1W short put strategy in EURCHF

Anecdotally, many hedge funds do make money by selling volatility in this way. ATMF options might not be the contracts of choice; they are liquid and have relatively large premiums, but the investor might want to collect a larger premium with a more complex structure, or might want to make a payoff less likely by choosing an out-of-the-money option – see Chapters 5 and 6 on these. But the principle is the same: selling volatility makes money when the market overestimates future risk. However, this route to profit is paved with disasters. Many a hedge fund has seen literally years of steadily accrued profits evaporate in a day or two of crisis-driven market action. We see this in Figure 1.2; though the option selling strategy ends up in profit, the losses or drawdowns can be huge and sudden.11 The data set finishes in 2013, but one can imagine the effect of 2015 events when the currency peg was removed by the central bank.

The other way that investors in general trade option markets is to buy options which they believe are undervalued – the idea behind Naseem Taleb's famous ‘Black Swan’ fund [3]. This type of strategy seeks out markets where risks seem to be underestimated and buys options which will pay out handsomely if this is true. Consider a longer dated option, say for 12M, bought in the spring of 2008 on USDJPY. The investor might have reasoned that problems surfacing in the US housing market would sooner or later cause a sharp depreciation of the USD – and they would have been right. Buying an option with a longer tenor allowed them to make money even though they were uncertain of the precise timescale.

So clearly there is much of interest in systematic differences between premium and payoff for the investor community. However, we said that there is no magical formula for trading strategies within these pages. Why not?

Once one considers how trading strategies would be executed, it becomes possible to understand how inefficiencies are not necessarily pots of gold at the end of financial rainbows. Imagine we identified a strategy which said that selling options of a certain type could result over time in a profit. We know, however, that sold options have unlimited loss potential, so even if the result after a few years was likely to be profitable, the risks in between could be enormous. The investor might have to tolerate a loss of 20% in one year to average a 5% return over several. That's not a very good risk/reward ratio on your investment. Or perhaps one might identify an opportunity to buy options and make money. In this case the risks would at least be limited, but what if the options were long term and only made money near the end of their lives? The investor would have to fund a loss for some time before it was likely he would see profit. Given that the strategies would only be expected to make money over a number of years, with profit and loss in between, there would always be a risk that in any one year they would be unlucky. In short, while we hope this book will inform investors about likely areas for further investigation, as we said before, there is no magical recipe within these pages.

Finally, investors often buy overseas assets which have good return potential. In this case they may wish only to have exposure to the asset itself, and not to accept the FX risk. In this case they turn back into hedgers and may find utility in this book as previously discussed.

1.5 HISTORY AND SIZE OF THE FX OPTION MARKET

During the mid-1980s a confluence of events gave birth to the FX option market as we know it today, namely: a demand for the product, the ability to price the product, a market place to trade and, with the advent of computer power, the ability to manage risk.

To have an option market, first it is necessary to have a liquid market in the underlying rate (usually called just the underlying) upon which the options are based. Before the 1970s, when exchange rates were in general fixed to specific values and adjusted at intervals, there was no possibility of an option in the market. But as different countries gradually abandoned the increasingly unworkable fixed FX rate regime which had been implemented after the post-war Bretton–Woods agreement, risk appeared, and the first to take note and act upon this risk were the corporations of the world. As has been described earlier, companies with income and liabilities in other countries are highly sensitive to exchange rate fluctuations and seek ways to minimise them. Corporate treasurers initially used forward FX contracts to lock in rates but then realised they could sell them if the contracts entered very negative territory, assuming a trending market, and replace them if they became close to positive once more. This crudely replicates the protective properties of an option, though it was a cumbersome and imprecise process. The idea of a product where another company took over this adjustment process was attractive. The very early currency overlay companies did exactly this, calling it option replication. As the markets started to swing wildly during the 1980s the demand for this increased. True options in FX began to be bought and sold, though the correct price for an option was hotly debated.

Equity option traders began to use the Black-Scholes-Merton model shortly after its publication in 1973 [1] but there was at that time little thought of using it for FX contracts. In 1983 Garman and Kohlhagen published the extension to the Black-Scholes-Merton model which enabled FX options to be clearly and simply valued for the first time, as it included dual interest rates [4].

With the demand for the product, and the ability to price it, came the distribution. The first FX option was dealt on the Philadelphia Stock Exchange in November 1982 [5]. At that time they were a small futures exchange who courageously introduced the new instrument when there was no OTC12 market at all, and virtually no other instruments available to use as pricing references. These options, consistent with similar equity products at the time, were, American-style, exercisable by the option purchaser any time up to expiry, which would have made them even more challenging to value. But clearly they showed promise; by the mid-1980s the exchange in Chicago was also actively trading contracts on FX options, and the number of boutique option houses grew.