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• With more than 800 copies sold throught the world, this book is a wonderful opportunity to gain knowledge and insight in the area of FX Risk.

The original book (hardcover), edited by Jügen Hakala and Uwe Wystup, came out in 2002 as a Risk Publication. Currently it is not printed anymore, but it can still be ordered through Uwe Wystup at a price of 195 EUR plus postage. Please contact us (there are only 5 left in stock).

In 2008, the new softcover reprint was issued and can now be ordered directly here.

• Foreign Exchange Risk
Uwe Wystup
ISBN: 1-899-33237-5
Softcover
355 pages
October 2001
Current price: €195.00

## Reviews

##### Salih N. Neftci, Graduate School, CUNY, New York, and Head FAME Certificate, Switzerland

Treasures don’t come cheap…

This book is an excellent manual on tools related to four broad areas. The first are the basic tools that are broadly applicable in all financial markets and that form a gateway to more advanced topics. The second major category is the tools associated in pricing, hedging and risk management of exotic options. Here there are two subcomponents; namely, earlier exotics, such as various barriers, and their more recent relatives. The third class is the set of techniques associated with complex volatility dynamics and the modeling of volatility smile.

The final set of topics is made of numerical methods of modern financial engineering. The subcomponents here are, Monte Carlo and quasi Monte Carlo methods and their applications to pricing and hedging. Fourier transform methods in numerical analysis. PDE methods and their applications to forward and backward Kolmogorov equations, and, a somewhat limited discussion of tree methods.

These topics are discussed within the context of concise, FX –related pricing, hedging and risk-management problems.

The extent of the tools provided in the book is astonishingly broad and up to date. In fact, the only other (broadly used) major tools that are not present are perhaps (1) A more in-depth discussion of measure change technology, (2) Characteristic functions and Fourier transform methods other than numerical applications and (3) The relevance of BGM type models for long term FX options. There is of course the set of tools associated with credit analysis and derivatives that are not here, but that is in fact appropriate. (In spite of the well known analogy between credit default and the devaluation probability.)

Proper risk management of options books, volatility exposures and especially hedging and risk management of exotic options portfolios will require many of the state of the art techniques discussed in this volume. Obviously, pricing problems encountered in dealing with these products will also be much better understood and dealt with, by using the tools discussed here.

The audience. This book will be very useful especially for two types of potential readers. The first are market participants with a good technical background. Experienced traders/dealers, structurers and financial researchers, and book runners in all instruments will find it a very useful manual to be consulted regularly. And this is true not only in the FX sector but for interest rate, equity and commodities as well. The only broad category that one may exclude is perhaps credit.

The second category of readers who will find this book useful and even unique in some ways are students of Masters and beginning Ph.D. level classes in the academia. The book will be an excellent text in technical Financial Engineering courses, or it can be a supplement to well known textbooks such as Hull’s, in intermediate level derivatives and risk management courses.

It must be emphasized that, although the book deals with “Foreign Exchange” as the underlying risk, almost all the tools and motivating examples in the book apply to interest rate and equity risk as well. In fact, Foreign Exchange is a very simple, homogenous and liquid underlying. It does not contain any implicit options, makes well-defined and easy-to-model “payouts” (i.e. foreign interest rates) that are simpler to handle than dividends. Also, Foreign Exchange is not affected by corporate actions—although Central Bank intervention could be unique in some ways-- and most FX related instruments have relatively short expiration periods, so that the effect of stochastic interest rates can be ignored to the first approximation.

This way FX forms an excellent medium for discussing advanced financial engineering tools and methods. Once these tools are understood within the context of FX, they can be extended to other more complex underlyings such as yield curve and equity. Thus, even for those readers whose interest is ultimately in products other than foreign exchange, the “correct” starting point to learning advanced financial engineering methods may very well be seeing them within the context of FX markets.

An excellent example to this is the treatment and modeling of volatility smile in the book. FX traders trade the smile routinely as vanilla products using Risk Reversals and Butterflies. At the end, the models dealing with the volatility smile is much easier to understand and test empirically within the Foreign Exchange context. Although stylized facts, terminology and some of the notation used in the case of FX are sometimes different than their counterparts in interest rates or equity, FX may still be the “best” way of approaching modeling and calibrating issues in volatility smile. In this sense the sequence of Chapters 2,4 and then 22 to 25 in the text form a rather complete and up to date discussion of the volatility smile and smile dynamics.

This is an example to another important characteristic of this text. The book is ultimately a collection of state of the art tools and techniques to be utilized in intermediate to advanced financial engineering tasks. Yet, this is done from a market participant’s point of view and the reader is exposed to (1) Best market practices, (2) Market conventions and (3) The market terminology as well. To their credit, the authors have added several real life examples, which motivate the complex set of tools.

A few words on the prerequisites for reading this book… It turns out that most of the preliminary material a typical reader would need is discussed in the first 8 Chapters. However, an un-initiated reader may require a bit more background than what is provided there. In fact, as a prerequisite it may be best if the reader has some familiarity with most of the material in Hull’s book, and with some basics of stochastic calculus. In particular, some earlier introduction to Ito’s Lemma, Girsanov Theorem and Stochastic Differential Equations is something really needed. So is some understanding of PDE methods.

In a book that attempts to discuss state of the art techniques of modern financial engineering it is natural that there will be some missing topics. There are also some typos, but the ones that I discovered were minor and could easily be detected by the reader. Also given the very broad coverage of techniques and instruments, albeit in the FX sector, advanced practitioners in each area may possibly find some specialized aspects of the discussion on advanced techniques lacking in detail. But, the present coverage and depth of the book is already at a surprisingly high level.

This book will be a very useful manual for technically advanced traders, risk managers and structurers. It is as useful for a completely different audience as well. Intermediate and Advanced Financial Engineering classes in universities all around the world will find it as an excellent source for learning modern tools as well as market practices and conventions. The book also contains several real life examples and comments. A small treasure chest... at the end.

##### Glyn Holton, Contingency Analysis

The literature on derivatives pricing has long been dominated by academics, but we are now starting to see full-length books written by practitioners. Examples are Brockhaus and James and Weber. To date, results have been outstanding. Practitioners write with the same technical sophistication as academics, but offer practical techniques and insights that could only be gleaned from working on a trading floor. The writing tends to be breezy and light; skips the basics and goes straight to results. For readers who are comfortable with the occasional stochastic integral, these practitioner books are a goldmine.

This edited collection on foreign exchange financial engineering fits the same mold. Editors Hakala and Wystup both work for Commerzbank. They have compiled 27 outstanding chapters by 23 authors. They have contributed significant content themselves and have done an excellent job promoting a uniform style of writing across all chapters. The book offers easy reading with results that flow one after another. Sources are cited or maybe a summary is given for how a proof might be written, and then it is off to another result or perhaps a discussion of how some instrument is really hedged.

The book is divided into three parts. The first contains12 chapters with practical insights on techniques used day-to-day to manage an FX derivatives book. One chapter covers the impact of non-trading days on derivatives pricing. Another covers components of FX volatility—smile, skew, butterfly and reversal. There are chapters on pricing of first- and second-generation exotics, and an entire chapter focuses on quantos. Another chapter covers put-call parity and hedging of compound options. A chapter explains "forward" and "backward" partial differential equations. All are sophisticated and cutting-edge.

The second part has two chapters on using and calculating the Greeks for exotics. Much of the focus is on efficient computation based upon homogeneity and related techniques.

The third part contains chapters on advanced pricing models and computational techniques. There are chapters on finite differences, variance reduction, fast Fourier transforms, quasi-Monte Carlo methods and binomial trees. For the most part these assume basic familiarity and delve more deeply into the respective topics. Chapters on models cover such things as local volatility surfaces, jump-diffusion models, models for long-dated options and other instruments, Heston's volatility model, etc.

Who is this book for? First of all, it is essential reading for anyone who prices or trades FX derivatives. Second, it is essential reading for researchers. This one book, in a nutshell, defines the state of the art. For the same reason, I recommend it to financial engineers working in any of the capital markets. Finally, it will be valuable for students who understand the theory of financial engineering, but need to learn how it is used in practice.

##### Pierre Lequeux, Head of Currency Management, ABN AMRO Asset Management Ltd

Foreign exchange is without any doubt the world largest financial markets with an estimated US$1.2 trillion turnover in transaction per day. Its size by far outstrip equity and bonds markets. Features such as high liquidity, low transaction cost and readily access to leverage make foreign exchange markets a very flexible environment for active managers. Currency markets provides a large range of strategies and instruments to the investor and corporate that seek to extract better value from their international risk exposures. Amongst these instruments options have taken an increasing share of the volume transacted throughout the last ten years. At the last triennial survey conducted by the BIS they represented an estimated daily turnover of US$ 60 Bn against US\$ 41 bn in 1995. A significant increase of more than 38 % over the past 6 years. The main factors behind this significant increase in turnover are without any doubt an increased sophistication of risk reporting system and better understanding of currency issues by the international investor. However there remains much skepticism about the use of options and the risk attached to them due to events that have shaken financial markets and attracted much press attention in the past. However it is also true that many of these events are often dwarfed by other corporate failures where option risk had not any part to play. Options are arguably not always the most cost efficient vehicles to implement active strategies in the currency markets, however they provide the investor with a far greater degree of flexibility whilst addressing some of the most complex hedging scenarios. They therefore should be considered in their own right when addressing currency risk.

This book intends to give the reader a broad view on the present developments and research of option pricing theory. The editors Jürgen Hakala and Uwe Wystup have managed to give the reader much more than a concise review of the option literature by compiling works of their own and also from an impressive list of contributors. They cover practical issues that are paramount to the market practitioner.

The first section of the book (re-) introduces the reader to the basics of options theory: Black & Scholes equation, Greeks, volatility and term structure issues. The editors then provide ample materials on existing products, starting from the relatively plain vanilla barrier options to more complex structures such as forward start and ratchet options.

The second part of the book concentrates on risk management issues and takes the reader through the computation of option price sensitivities using homogeneity properties of financial markets. This provides a robust answer to the use of differentiations methods that are reputably time consuming. The authors present correlation-hedging techniques to tackle efficiently a well-known risk feature of quanto and basket options.

The final part takes us through the most advanced pricing techniques in option pricing theory. It looks amongst others at the use of quasi-random number generators and Monte-Carlo approaches to value look backs and baskets options. The authors have good credit in reviewing in high detail the main algorithms that may be used in the sequence generation process and also elaborating on their convergence ability. This is surely of great help for the market practitioner. They also address extensively two very important topics: Pricing options accounting for the volatility smile implied by market data and valuing notoriously difficult to hedge Digital options. The editors have managed to produce a book that will be of great use to traders, financial engineers and risk managers.

The book is written in a refreshingly fluid and accurate style, which is an achievement in itself as applied option theory is often a difficult topic to address. The twenty-seven chapters of this book will contribute toward a finer knowledge of this very specialized field as well as giving some orientation in terms of future research to the reader. This book should be an asset to the market practitioner that have or intend to have dealing with the foreign exchange derivatives markets.

## Errata

• There are many small typos in Chapter 6 "The Pricing of First Generation Exotics". I have written a new version of the formulas, which you can see here. Detailed typos are listed right below.
• Chapter 6 "The Pricing of First Generation Exotics": Table 6.1 contains a formula for w, however, w is not needed for this section. The parameter m in the formula for w is not needed either. It it is defined as SQRT(my*my+2*sigma*sigma*rd)/(sigma*sigma). It will be used in the form of theta_/sigma in formula (6.88) for omega=0 later on. The variable a is also not used later on.
• Chapter 6 "The Pricing of First Generation Exotics": Equations (6.12) and (6.16) should be exchanged, i.e. (6.16) is the one for the value and (6.12) is the one for the delta.
• Chapter 6 "The Pricing of First Generation Exotics": Page 40, Equation (6.24) end of first line has an extra closing parenthesis ")", which should be removed. Thank you, Jörg Kubitz, for reporting this.
• Chapter 6 "The Pricing of First Generation Exotics": Page 46, equation (6.93), gamma of the one-touch. In the last two lines, the e+and the e-are divided by tau. They should be divided by (2 tau). Thank you, Sven Foulon and Yanhong Zhao, for pointing this out. Yanhong produced a corrected formula in pdf.
• Chapter 6 "The Pricing of First Generation Exotics": Page page 52, variables AK, AH and ALH are defined in equations (6.142)-(6.144). The pricing formulae of the double barrier (6.150)-(6.151) on page 53 make use of these variables and another undefined variable AL. The mistake is made in the definition of AK in (6.142), where the definitions of AK and AL are accidently but wrongly taken together: the right part of the equation is the definition of AL, while for the correct definition of AK one should replace L by K. This has been reported by Randy Brenkers and checked by Alexander Stromilo. Thank you both. Alexander Stromilo produced a corrected version in pdf.
• Chapter 6 "The Pricing of First Generation Exotics": Page 53 right after Equation (6.150) the sentence should read as "Similarly we obtain for the price of the put (\phi=-1)".
• Chapter 6 "The Pricing of First Generation Exotics": Page 53 in Equations (6.150)-(6.151) the function N is the same as the caligraphical N defined in Table 6.1, i.e. the standard normal cdf. Thank you, Jörg Kubitz, for reporting this.
• Chapter 7 "The Pricing of Second Generation Exotics": Page 61 Equations (7.33) and (7.40). There is a minus sign missing in front of the discounting from the premium payment date and the horizon date: it should be -r(T_p-t).
• Chapter 7 "The Pricing of Second Generation Exotics": Page 70 Equation (7.90). Erase the extra “d” in front of the “dW_j”.
• Chapter 7 "The Pricing of Second Generation Exotics": Page 70 Equation (7.92). Erase the extra t after the indicator function inside the expected value.
• Chapter 13 "Efficient Computation of Option Price Sensitivities": Equation (13.79): A=ln(x/S_1(0))-r\tau+.... and similarly Equation (13.82): B=[ln(y/S_2(0))-r\tau+...
• Chapter 13 "Efficient Computation of Option Price Sensitivities": Equation (13.96): in the last line it should be \phi\eta N_2 instead of \phi N_2.
• Chapter 16 "Finite Differences": Equation (16.9) should have a coefficient (1+rd*h). In Equation (16.6) the coefficients in front of H_n^j and H_n^(j+1) should be: (-1-rd*h-e*sigma^2*h_xx) and (-1+e'*simga^2*h_xx). In (16.8) probably +B_l(j+1) and +B_h^(j+1) respectively. If you want to really use these, we advise you to recalculate.
• Chapter 18 "Quasi-Random Numbers and their Application to Pricing Basket and Lookback Options": Equation (18.45): the gamma of the lookback: corrected pdfproduced by Alexander Stromilo. Thank you, Jeroen Devreese, for pointing this out.
• Chapter 21 "Fast Fourier Method for the Valuation of Options": Figure (21.5): The labelling of the curves FFT and Sobol should be exchanged, the best method shown in the figure is FFT.
• Chapter 22 "Local Volatility Surfaces -- Tackling the Smile": Equation (22.11): Seems wrong, rather use 12.6. Equation (22.12) should have a factor c(y,t) along with the rf(t).
• Chapter 23 "Heston's Stochastic Volatility Model Applied to Foreign Exchange Options": Table (23.1): Formula (23.17): replace d by d_j, in the argument of the Ln in the denominator replace 1-exp(...) by 1-g_j. Formula (23.19) LHS in the arguments of the function f replace t by tau.
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