Brazilian Derivatives and Securities

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Brazilian Derivatives andSecuritiesPricing and Risk Management of FXand Interest-Rate Portfolios for Local andGlobal Markets

Marcos C. S. CarreiraQuantitative Finance Practitioner, Brazil

Richard J. BrostowiczExecutive Director and Head of Brazil Quants, Banco Morgan Stanley, Brazil

© Marcos C. S. Carreira and Richard J. Brostowicz 2016Foreword © Peter Carr 2016

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First published 2016 byPALGRAVE MACMILLAN

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Library of Congress Cataloging-in-Publication DataBrostowicz, Richard J., author.

Brazilian derivatives and securities : pricing and risk management of FX andinterest-rate portfolios for local and global markets / Richard J.Brostowicz, Marcos Carreira.

pages cm

1. Foreign exchange market–Brazil. 2. Derivative securities–Brazil.3. Investments–Brazil. 4. Finance–Brazil. I. Carreira, Marcos, author. II. Title.

HG3933.B76 2015332.64’570981–dc23 2015033263

ISBN 978-1-137-47726-2 ISBN 978-1-137-47727-9 (eBook)10.1057/9781137477279DOI

Contents

List of Figures xiv

List of Tables xvii

Foreword xviiiPeter Carr

Preface xx

Acknowledgments xxi

1 Financial Archeology 11.1 Interest rates and inflation 1

1.1.1 Record levels (the old days of overnight rates of 2% perday and the Real Plan); desperate times call fordesperate measures 1

1.1.2 COPOM (the Brazilian FOMC): behavior, language,influence, targets and bands 9

1.1.3 The Brazilian Payment System (SPB): the end of thedual cash regime; CDI and Selic 16

1.1.4 A new era? What has changed under Tombini?Coordination and communication, or more subtlechanges? 22

1.2 Foreign exchange 241.2.1 Testing the waters 241.2.2 Pegs and multiple currencies 261.2.3 Indexing of local instruments 281.2.4 Floating, ballast and hot air (on the different

mechanisms to manage a floating currency) 281.2.5 Paganism (on how to avoid conversion, and the

history of offshore x onshore spreads) 341.2.6 A bit of a fit (on the 2008 crisis) 37

2 We Mean Business 402.1 Calendars 40

2.1.1 Banking calendars and fixings 402.1.2 Trading and listed contracts 412.1.3 New York, Rio, São Paulo – the FX combined calendar 41

v

vi Contents

2.1.4 Notation used for moving forward or backwardbusiness days in a specified calendar 42

2.2 Interest rate fixings 422.2.1 Selic target 422.2.2 Selic 432.2.3 CDI 452.2.4 TJLP 462.2.5 TR 47

2.3 Inflation fixings 482.3.1 IPCA 482.3.2 IGP-M 52

2.4 Foreign exchange fixings 552.4.1 PTAX 552.4.2 EMTA 562.4.3 WMR 562.4.4 Observability for barriers 57

2.5 The 3 Ts in FX option pricing: a more precise version of theBlack Formula 57

3 Interesting BRL Interest Rates 603.1 3 months in the life of an IR Swap 603.2 3 months in the life of a DI Future 683.3 Explaining it all 693.4 A simple swap 723.5 A promising future – The DI1 Future 723.6 My first numéraire – a more mathematical framework for DI

Futures (DI1) 753.7 The still promising Future -> The Selic Futures (OC1) 783.8 Pricing BRL interest rate futures 79

3.8.1 DI Future (DI1) pricing 793.8.2 BRL onshore CDI curve construction 803.8.3 Selic Future (OC1) pricing 823.8.4 BRL onshore Selic spread curve construction 82

3.9 Giving 110% 833.10 The CDI+Spread is a multiplicative spread 843.11 How to price the 3 possible BRL Fixed X Float payoffs? 84

3.11.1 100% CDI case 843.11.2 CDI+Spread case 853.11.3 Percentage of CDI case 86

4 BRL Interest Rate Market and Credit Risk 874.1 Historical spreads 874.2 The term structure of volatility 89

Contents vii

4.2.1 Slope 894.2.2 Covariance 954.2.3 Principal components 95

4.3 Potential exposures 974.4 Zero curve: and the winner is ... 98

4.4.1 Linear Interpolation (LI) 1004.4.2 Flat Forward (FF) 1014.4.3 Cubic Spline (CS) 1024.4.4 Which is better? 102

4.5 Smooth operator 1024.6 Sensitivities 105

4.6.1 Zero 1054.6.2 Forward 106

4.7 A framework for risk 1074.7.1 Minimal description 1074.7.2 The envelope and liquidity risk 1084.7.3 The first, the last and the ugly 108

4.8 Trading forwards 1084.9 Risk and P&L attribution 109

5 A Man with Two Clocks ... Foreign Exchange in Brazil 1105.1 FX Spot 110

5.1.1 Who can trade it 1105.1.2 How, when and where to trade it 1105.1.3 Observability 111

5.2 DOL 1115.2.1 Contract details 1115.2.2 Liquidity 1115.2.3 DR1 and the roll 1125.2.4 Payoff of DOL contract 1125.2.5 Pricing a DOL contract based FRC, DI’s, nearest

maturity FXFUT and CASADO quotes 1135.2.6 Apples and oranges 1135.2.7 Convexity corrections 114

5.3 Forward points strategies 1155.3.1 FRP 1155.3.2 “Casado” 116

5.4 FX Future crosses 1165.4.1 Payoff 1175.4.2 Pricing and hedging 1175.4.3 Convexity corrections 119

viii Contents

6 And the Even More Interesting USD Onshore InterestRates . . . 1206.1 3 months in the life of a FX Swap 1206.2 3 months in the life of a DDI Future 1206.3 Explaining it all 1206.4 The DDI Futures (DDI) -> Why they were designed this way? 1216.5 The mathematical derivation of a DDI contract price 125

6.5.1 DDI Future pricing 1276.6 It takes two (DDI contracts) to (con)tango -> The FRA de

CUPOM strategy (FRC) 1316.6.1 FRC Future pricing 1326.6.2 Handling a FRC trade before BVMF publication of the

first DDI closing price 1336.7 Calibration of the cupom curve 134

6.7.1 Calibration of the cupom curve on the short end 1346.7.2 Calibration of the cupom curve on the long end 135

6.8 How to compute cupom interest rate risk? 1376.9 Interpolation choices for the cupom curve 139

6.9.1 Log-linear interpolation of cupom curve forwarddiscount factors curve in business days 139

6.9.2 Log-linear interpolation of cupom curve forwarddiscount factors curve in calendar days 140

6.9.3 Log-linear interpolation of cupom curve in FX forwardprices 140

6.10 The SCC contract 1416.11 The mathematical derivation and pricing of a SCC

contract price 1426.12 The SCS contract – a modern, but exotic, cousin 1436.13 The mathematical derivation of a SCS contract price 1436.14 SCS Future pricing 1456.15 Forward starting SCS contracts 1506.16 A much simpler alternative to FRC contracts 1506.17 A BRL Float or Fixed X USD onshore Fixed swap 152

6.17.1 Coupon payoff specification 1526.17.2 Coupon pricing 153

7 Too Many Options? 1547.1 IDI options 156

7.1.1 IDI options available indices and compoundingmethodology 156

7.1.2 IDI options payoff and other contractual information 1577.1.3 IDI options common trading strategies 158

Contents ix

7.1.4 A simple Black pricing formula for an IDI optionassuming the IDI index as its main underlying 159

7.1.5 How to fit a volatility smile for an IDI option assumingthe IDI index as its main underlying 161

7.1.6 A simple Black pricing formula assuming the IDI indexequivalent realized interest rate as the underlying 161

7.1.7 Is the IDI option smiling at you now? 1637.1.8 Or is it smirking? 1647.1.9 A discrete tree model that could fit the smirk volatility

surface shape for IDI options 1657.1.10 Delta hedging IDI options under the discrete tree

model 1677.1.11 Delta hedging IDI options under the SABR model 1687.1.12 IDI options pricing under HJM model 1697.1.13 IDI options historical volatility computation – how to

price an IDI option if only the DI Futures market wasliquid? 174

7.1.14 IDI digital options – limitations and applicability 1767.1.15 OTC IDI options at Cetip 177

7.2 DI Future options 1777.2.1 Basic trading information and definition of the

contract codes 1787.2.2 DI Future options payoff – smells like swaption? 1787.2.3 DI Future options most common trading strategies 1807.2.4 A simple Black pricing formula for DI Future options 1807.2.5 Can DI Future options smile with the SABR model? 1817.2.6 DI Future options pricing under HJM model – where’s

the smile? 1827.2.7 What about DI Future options under the BGM a.k.a

Libor Market Model? 1847.2.8 DI Future options historical volatility

computation – how to price a DI Future option if onlythe DI Futures market was liquid 185

7.3 IR option strategies – VTF and VID 1887.3.1 VTF 1887.3.2 DI Future delta hedge computation by BVMF 1897.3.3 VID 1907.3.4 DI Future delta hedge computation by BVMF 191

7.4 Jabuticabas: risk management of options on interest rates 1917.4.1 IDI options 191

7.5 BRLUSD Listed FX options 192

7.5.1 Contract details 193

x Contents

7.5.2 BRLUSD Listed FX options payoff 193

7.5.3 A simple Black pricing formula for BRLUSD Listed

FX options 1947.5.4 Volatility surface based on SABR model 1947.5.5 Volatility surface based on polynomial on FX delta 195

7.6 BRLUSD Listed FX options with daily margining 196

7.7 BRLUSD FX options: strategies 196

7.7.1 VTC 1967.7.2 FX Future delta hedge computation by BVMF 1977.7.3 Do you believe you are delta hedged? 197

7.8 OTC IR and FX options 198

8 The Mountain Goes to . . . Foreign Exchange ContractsOffshore 2008.1 CME BRL

USD FX Futures 2018.1.1 Contract details 2018.1.2 Payoff 2018.1.3 Pricing 202

8.2 OTC – NDFs 2028.2.1 BRL

USD offshore NDFs – payoff and differences for theequivalent onshore NDF contract 202

8.2.2 A quick detour for pricing collateralized derivatives 2068.2.3 Pricing a collateralized NDF contract offshore 2088.2.4 How offshore NDFs are usually traded in the

interbank market? 2108.2.5 Revisiting the cupom curve construction based on

NDF spread strategies 2118.2.6 The mythical offshore BRL discounting curve 211

8.3 OTC – BRL/USD options 212

9 Start from Where? Constructing Markets for FX Forwards, Futures,Onshore USD Interest Rates and OffshoreInstruments 2179.1 Observability of contracts 217

9.1.1 Spot x DOL 2179.1.2 FRC x Forward x DOL 2179.1.3 NDFs and forward points 218

9.2 Structures 2189.2.1 Dates 2189.2.2 Events (breaks, fixings, market points) 2189.2.3 “The Triangle” 219

9.3 Curve construction 2209.3.1 Cupom Cambial 220

Contents xi

9.3.2 Forwards 2209.4 The offshore x onshore spread 220

9.4.1 Changing standards 2209.4.2 Convertibility, demand and taxes 221

9.5 The mythical offshore BRL discounting curve 221

10 Offshore IR Products Based on CDI Fixings 22210.1 Offshore BRL Fixed-Float swaps 222

10.1.1 Offshore BRL Fixed-Float swaps payoff 22310.1.2 Foreign market participants appetite for offshore BRL

Fixed-Float swaps 22310.1.3 Which discounting curve to use for offshore BRL

Fixed-Float swaps pricing? 22410.1.4 Is this a quanto swap? Let’s analyze it from a hedging

perspective 22410.1.5 Now let’s analyze it from a mathematical perspective 22510.1.6 BRL Fixed-Float offshore breakeven historical swap rate 22910.1.7 Calibrating an offshore BRL Fixed-Float swap basis

curve 23010.2 Offshore BRL Fixed-Float swaptions 230

10.2.1 BRL Fixed-Float offshore swaption payoff andspecification 231

11 The Dual Case – US Libor Onshore Swaps 23411.1 Payoff of US Libor onshore swaps 23411.2 Pricing of US Libor onshore swaps 234

12 FX Trading (Interest Rate and Fixing) Market and Credit Risk 23712.1 Fixing 23712.2 The term structure of the Cupom Cambial 238

12.2.1 Slope 23812.2.2 Casado 238

12.3 Potential exposures 23812.4 Interpolation and sensitivities 24012.5 A framework for risk 24112.6 Trading forwards 24112.7 Risk and P&L attribution 24212.8 DOL convexity correction to a FX forward price 243

13 A Skewed Perspective of the World: FX Options 24613.1 Starting from the end (market standards for offshore

FX options) 24613.1.1 Weightlifting 24613.1.2 Reversal of fortune 248

xii Contents

13.1.3 The locals are friendly 25313.1.4 Thin tails wagging the dogs 25413.1.5 The couple, decoupled 255

13.2 Back to the beginning (What is different in onshoreFX options?) 25613.2.1 Uncertain smile 25613.2.2 Fixing the averaging 25613.2.3 I’d risk everything 25713.2.4 Look in the mirror 258

13.3 Risk management 26613.4 Risk and P&L attribution 268

14 Some Cash Is Better Than Nothing – What You Need to Know aboutCash Products 27014.1 Local government bonds 270

14.1.1 Floating to the top – LFTs 27014.1.2 The name of the game – LTNs and NTN-Fs 27014.1.3 Making it real – NTN-Bs 27114.1.4 Living fossils – NTN-As 27114.1.5 Reading the fine print 271

14.2 Local corporate bonds 27214.3 Local funding practices 27214.4 Offshore government and corporate bonds 27214.5 Liquidity (or lack thereof) 27214.6 The Brazilian repo market (Compromissadas) 273

15 Index of Choice . . . Inflation-Linked Products and Curves 27615.1 Government inflation-linked bonds 27615.2 Inflation-linked swaps 278

15.2.1 IGPM and IPCA publication 27815.2.2 IGPM and IPCA swaps payoff 27915.2.3 Dirty and clean rates . . . again 27915.2.4 Trading conventions for IGPM and IPCA swaps. Are

they liquid? 27915.2.5 IPCA swaps pricing – the market approach 28115.2.6 IPCA swaps pricing – the foreign currency analogy

approach and why it’s complicated 28115.2.7 IPCA swaps pricing – the IPCA forwards calibration

approach 28315.2.8 IPCA index forwards interpolation without

seasonality 28415.2.9 Adding seasonality 285

Contents xiii

15.2.10 Joint calibration of IPCA curve with NTN-B bondquotes (reduced by asset-swap spread) and IPCA swaprate quotes 285

15.2.11 The IGPM market 28715.3 Exchange traded inflation-linked Futures 288

16 Microstructure of the Listed Derivatives 28916.1 Microstructure: concepts 28916.2 Can durations be estimated? 29016.3 What happens in practice? 29116.4 What is the importance of the tick size? 29216.5 The model with uncertainty zones (Robert and Rosenbaum) 294

16.5.1 Description of the model 29416.5.2 What can we do with this model? 295

16.6 DOL 29616.7 DI 296

17 Unlucky End: On the Obsolescence of Products and Books 297

References 298

Index 300

List of Figures

1 Selic target 52 Selic since 1986 53 Selic (log scale) 64 CDI (daily rate) 75 Change in overnight rates with the Real Plan (Jul-1994) 76 Overnight rates after the Real Plan (1994) 87 Overnight rates from Jul-1994 to Jul-1999 88 Effective Selic rate 129 CDI standards in 1986 13

10 CDI standards in 1990 1311 Words of each COPOM statement (not counting the votes tally)

since 2003 2312 PTAX since 1986 2513 Log10(PTAX) since 1986 2514 PTAX (adjusted) since 1986 2615 USDBRL % returns (rolling mean over 21 bd) 2716 DOL x PTAX in Jan-1999 2917 Contracts traded in DOL futures (expiries Feb. and Mar.) in Jan-1999 3018 DOL prices (Feb-1999 expiry) 3019 Reserves (liquidity) in USD billions 3120 Interventions of the BCB on the FX Spot market by quarter, in USD

billions 3221 PTAX from 2011 to 2013 3522 Gamma profile of hedged forward options 3823 Daily changes in SETA 4424 Spread SETA-Selic 4425 Daily changes in Selic 4526 Spread between Selic and CDI 4627 Daily changes in CDI 4628 TJLP (monthly) 4729 TJLP and SETA (monthly average) 4830 TR since 1991 4931 TR since 2000 4932 TR in 2012 and 2013 5033 IPCA yoy since 1980 5134 IPCA yoy after the Real Plan 52

xiv

List of Figures xv

35 IPCA mom since 2000 5336 IPCA mom since 2010 5337 IGP-M mom compared with IPCA 5438 IGP-M components 5439 DI1 futures 01-Aug-2011 6140 First DI1 futures 01-Aug-2011 6141 Weighted DI1s 01-Aug-2011 6242 3 DIs maturing in our 3m window 6543 CDI for the 2nd half of 2011 6644 Realized accrual for the 3m window 6645 f (τ ,τ ,T) for the 3m window 6746 PV for the 3m IR Swap 6847 Daily cashflows for the DI 6948 DI1 Open interest as of 19th May of 2014 7049 Selic futures OC1 contract open interest on 19th of May 2014 7050 DI1 Closing prices at 19th of May 2014 7451 Annualized 3m “average” rates 8852 Annualized 3m “average” rates for the second half of 2011 8853 Annualized 3m “average” rates for the first half of 2012 8954 Annualized 3m “average” rates for the second half of 2012 8955 Annualized 3m “average” rates for the first half of 2013 9056 Spreads between the realized 3m accruals of SETA, Selic and CDI 9057 DI curve before and after the 1st round of the 2014 presidential

elections 9158 Absolute changes for the DI curve after the 1st round of the 2014

presidential elections 9159 Relative changes for the DI curve after the 1st round of the 2014

presidential elections 9260 DI curve in Jun-2013 9361 Changes in curve after the 31 August 2011 surprise 9362 Changes in curve after the 17 March 2010 surprise 9463 Interpolating short rates 10664 Sensitivities for local interpolations 10665 Sensitivities for non-local interpolations 10766 Behavior of the roll DR1 and casado (spread) from 2002 to 2004 11467 DDI Futures contracts open interest on 19 May 2014 12268 NDFOnOff Spread for 3m since 2010 20469 NDFOnOff Spread for 6m since 2010 20470 NDFOnOff Spread for 1y since 2010 20471 NDFOnOff Spread for 2y since 2010 20572 NDFOnOff Spread for 2y from Jul-2008 to Jul-2009 20673 A simple smile using Malz 248

xvi List of Figures

74 Delta forward of an ATMF straddle with implied volatility=16% 25075 Delta forward of an ATMF straddle with implied volatility=30% 25076 RKO, strike 100, barrier 90 25577 Strikes for a 25 delta USD Call 26078 Strikes for a 25 delta USD Put 26079 Interpolation according to Malz; (ATM, RR, ST)=(16, 3, 1)% 26380 Modified Malz interpolation 26381 Strikes for each delta 26482 Implied volatility as a function of strike 26483 Strikes for deltas (onshore and offshore) 26584 Implied volatility (onshore and offshore) 26585 Differences between onshore and offshore implied volatilities 26686 Visualization of vanillas 26787 Vanillas and strikes 267

List of Tables

1 Presidents of Brazil’s Central Bank since 1965 22 Brazil’s Finance Ministers since 1965 33 Brazil’s currencies since 1942 34 Interest rate decisions before the inflation targeting regime 105 Interest rate decisions under Arminio Fraga (1999–2000) 146 Interest rate decisions under Arminio Fraga (2001–2002) 157 Interest rate decisions under Henrique Meirelles (2003–2005) 178 Interest rate decisions under Henrique Meirelles (2006–2010) 199 Interest rate decisions under Alexandre Tombini 21

10 Interest rates before the SPB 2111 Interest rates after the SPB 2212 Holidays (partial) 4113 Holidays (total) 4214 Month codes for listed contracts 7015 Scenarios for potential exposures 9916 FFC algorithm (simple) 10317 FFC algorithm (simple, numeric) 10318 FFC algorithm (complex) 10419 FFC algorithm (fit and curvature) 10420 Limits hit by DOL in October 2008 243

xvii

Foreword

My first encounter with Brazilian derivatives and securities arose when I was adoctoral student in finance at UCLA 32 years ago. I was fortunate enough toshare an office with a gentleman named Eduardo Facó Lemgruber, whose disser-tation covered the valuation of executive stock options (ESOs). In the mid 1980s,a strong theory had developed for pricing exchange-traded options. However,the applicability of this theory for off exchange ESOs was far from immediate.In his UCLA dissertation, my enterprising office-mate showed how to adapt thestandard theory to cover ESOs. Dr. Lemgruber is now a much sought after man-agement consultant, after spending 31 years as a distinguished academic. Wemeet from time to time at international conferences, and reminisce about theglory days, a past time especially appealing to people of our vintage.

Fast forward 32 years and the Brazilian derivatives market has become thelargest in Latin America. BM&FBovespa is the only Latin American exchangeto crack the top ten largest derivatives exchanges in the world. The prominenceof the Brazilian derivatives and securities market tracks larger trends. The Feder-ative Republic of Brazil is the largest country in both South America and in theLatin American region. Brazil is the world’s fifth largest country, both by geo-graphical area and by population. It is the largest Portuguese-speaking countryin the world, with roughly 20 times the population of Portugal. The 2014 FIFAWorld Cup was held in Brazil and the next summer Olympics are scheduled forRio in 2016.

Given these trends, it is only fitting that we have now been blessed with thefirst book to take a serious look at the Brazilian derivatives and securities market.Brazilian financial markets have been criticized in the past for a lack of trans-parency, so it is exciting to see the curtain pulled back by our two esteemedco-authors. It is quite rare to find a pair of practitioners with the requisite energyneeded to share their deep understanding of financial markets in book form,while somehow managing to keep the lights on in their day jobs. It is equallyrare to find a pair of financial institutions willing to stand up to the culture ofclosedness that permeates typical institutional mindsets.

This book adapts the theory of mathematical finance to the realities of theBrazilian financial marketplace. Since its development at MIT in the early 1970s,mathematical finance has led to a deepened understanding of derivatives mar-kets, which in turn has had a profound impact on financial markets as a whole.The pioneers in the field of mathematical finance were compelled to posit sev-eral simplifying assumptions, in order to expose the basic intuition underlying

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Foreword xix

derivatives pricing. While not necessarily relevant to Brazilian financial markets,these assumptions included price transparency and the continuity of asset pricesover time. Price or rate jumps of Poisson type were later added to extend thetheory, but price or rate jumps occurring at known times are not consideredpart of the mainstream. These latter type of jumps have come to be known asevents, which are all too important in Brazilian securities markets. Includedin events are discrete changes in interest rates or jumps in FX rates that arisedue to skipped interest and principal payments on sovereign borrowing. Whilethe Brazilian government’s credit has substantially improved over time, thereremains a vibrant market in hedges against a possible default. About ten yearsago, I co-authored a paper with Liuren Wu that compared the implicit pricingof sovereign default event risk in both credit default swap (CDS) and foreignexchange (FX) markets. Our research led to a Bloomberg function called CDFXthat compares the implied risk-neutral probabilities from the two markets.

The interest in applying mathematical finance to Brazilian financial marketsis stronger than ever. My former Bloomberg colleague Bruno Dupire studiedin Brazil for three years and has for the last nine years co-organized a highlyregarded annual conference called Research in Options (RIO!) at IMPA with JorgeZubelli. It is just a matter of time before specialized journals emerge to cover thisgrowing field. The contents of this book reflect almost half a century of com-bined experience of the two co-authors. I truly hope that the current generationof traders and risk managers will take the lessons of the ensuing pages to heart.Our shared financial future depends on it.

Peter Carr, PhD,Managing Director at Morgan Stanley, Global Head of Market Modeling, and

Executive Director of NYU Courant’s Masters in Mathematical Finance.

Preface

Brazil is not a simple country; one could say that for any other country, butBrazilians seem to utter this evocation with a quite peculiar sort of resignation, asif giving up hope that the country will ever change to become more standardized.Anyone who sees the electrical plugs mandated by law will understand that.

And yet it is a fascinating country, where you could find double-digit interestrates and an investment grade (maybe not for long). The history and productsof this financial market are quite unique, and we are glad to help the readerunderstand this corner of the world a bit better.

This book will refer to other books that already explain concepts like managingoption risks and stochastic calculus instead of repeating them, but once we delveinto the details of the products we will provide the mathematical backgroundand the heuristics for these, in a level somewhat beyond an undergraduatecourse. In fact, we used the draft of this book as the reference for a Masters’course.

Chapter 1 introduces the history of the markets over the past 20–30 years, andsome definitions and concepts will be detailed later. In Chapter 2 we define themain fixings, for which the markets and curves described in Chapters 3 through6, 9 and 15 will provide a framework for trading and hedging.

Chapters 7 and 13 cover IR and FX options, respectively. Much more couldhave been written on FX options, but again we defer to other excellent books onthis subject.

The link between local fixings and offshore markets is discussed in Chapters8 and 10; Chapter 11 covers the opposite case (onshore markets and offshorefixings).

We briefly cover cash products in Chapter 14, mainly worried about marketdynamics rather than trying to exhaust all possible cash instruments available.

The microstructure of the Brazilian markets has been sadly underrepresented inthe literature, and Chapter 16 is a brief introduction to our work in this subject.

The (hopefully satisfied but still curious) reader should finish the book atChapter 17 with the reminder that some of the rules, products and marketsdescribed in the book are subject to sudden and puzzling changes, and we swearthat these are not our fault. In fact, they will provide us with an opportunityto publish further editions of the book, and we will be glad to receive any feed-back that might improve those future versions. The publisher’s website will helpwith that.

xx

Acknowledgments

Richard thanks Dorival Leão for interesting discussions regarding financial topicsand for asking him to be a lecturer on the new MECAI Master’s course in Brazil.He also thanks Stefan Andreev, an outstanding quant who has been very patientwith Stefan since his first days at Morgan Stanley and a very good friend. Aspecial thank you also goes to the triplet, Dolina, Nina and Ruby, who, rock hislife like a free jazz trio. Dolina keeps the rhythm like a steady bass player, Ninais the sax player, with Coltrane-like improvisation, and Ruby is the hard hittingdrum player. Last but not least, a big thank you goes to his tight, warm and smallfamily nucleus: Mama, Baba, Bisna and Brígida [R.I.P.]. You are all great!

Marcos thanks Emanuel Derman for, among other things, showing that mostof quantitative finance is just a way to find the price of fruit salad, and for theencouragement and help with the decision to write this book. He also thanksRobert Almgren for the advice on learning Python, for pointing out MathiasRosenbaum’s work on market microstructure and more useful advice. Specialthanks to Kathya, Gabriel and Gustavo, for understanding the time spent awayfrom family while at the same time making sure I kept the focus on writing thebook, which could not have been written without Kathya’s energy and support.

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Disclaimer

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The information herein has been prepared solely for informational purposesand is not an offer to buy or sell or a solicitation of an offer to buy or sell any secu-rity or instrument or to participate in any trading strategy. Any such offer wouldbe made only after a prospective participant had completed its own indepen-dent investigation of the securities, instruments or transactions and received allinformation it required to make its own investment decision, including, whereapplicable, a review of any offering, circular or memorandum describing suchsecurity or instrument, which would contain material information not containedherein and to which prospective participants are referred. No representation orwarranty can be given with respect to the accuracy or completeness of the infor-mation herein, or that any future offer of securities, instruments or transactionswill conform to the terms hereof. Morgan Stanley and its affiliates disclaim anyand all liability relating to this information. Morgan Stanley, its affiliates andothers associated with it may have positions in, and may effect transactions in,securities and instruments of issuers mentioned herein and may also perform orseek to perform investment banking services for the issuers of such securities andinstruments.

The information herein may contain general, summary discussions of certaintax, regulatory, accounting and/or legal issues relevant to the proposed transac-tion. Any such discussion is necessarily generic and may not be applicable to, orcomplete for, any particular recipient’s specific facts and circumstances. MorganStanley is not offering and does not purport to offer tax, regulatory, account-ing or legal advice and this information should not be relied upon as such.Prior to entering into any proposed transaction, recipients should determine, inconsultation with their own legal, tax, regulatory and accounting advisors, theeconomic risks and merits, as well as the legal, tax, regulatory and accountingcharacteristics and consequences, of the transaction.

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Disclaimer xxiii

of the securities, instruments or transactions described herein and any fact relat-ing to the structure of the securities, instruments or transactions that may berelevant to understanding such tax treatment, and all materials of any kind(including opinions or other tax analyses) that are provided to such a personrelating to such tax treatment and tax structure, except to the extent confiden-tiality is reasonably necessary to comply with securities laws (including, whereapplicable, confidentiality regarding the identity of an issuer of securities or itsaffiliates, agents and advisors).

The projections or other estimates in these materials (if any), including esti-mates of returns or performance, are forward-looking statements based uponcertain assumptions and are preliminary in nature. Any assumptions used in anysuch projection or estimate that were provided by a recipient are noted herein.Actual results are difficult to predict and may depend upon events outside theissuer’s or Morgan Stanley’s control. Actual events may differ from those assumedand changes to any assumptions may have a material impact on any projec-tions or estimates. Other events not taken into account may occur and maysignificantly affect the analysis. Certain assumptions may have been made formodeling purposes only to simplify the presentation and/or calculation of anyprojections or estimates, and Morgan Stanley does not represent that any suchassumptions will reflect actual future events. Accordingly, there can be no assur-ance that estimated returns or projections will be realized or that actual returns orperformance results will not be materially different than those estimated herein.Any such estimated returns and projections should be viewed as hypotheti-cal. Recipients should conduct their own analysis, using such assumptions asthey deem appropriate, and should fully consider other available information inmaking a decision regarding these securities, instruments or transactions. Pastperformance is not necessarily indicative of future results. Price and availabilityare subject to change without notice.

The offer or sale of securities, instruments or transactions may be restrictedby law. Additionally, transfers of any such securities, instruments or transactionsmay be limited by law or the terms thereof. Unless specifically noted herein,neither Morgan Stanley nor any issuer of securities or instruments has taken orwill take any action in any jurisdiction that would permit a public offering ofsecurities or instruments, or possession or distribution of any offering materialin relation thereto, in any country or jurisdiction where action for such purposeis required. Recipients are required to inform themselves of and comply with anylegal or contractual restrictions on their purchase, holding, sale, exercise of rightsor performance of obligations under any transaction. Morgan Stanley does notundertake or have any responsibility to notify you of any changes to the attachedinformation.

With respect to any recipient in the U.K., the information herein has beenissued by Morgan Stanley & Co. International Limited, regulated by the U.K.

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Financial Services Authority. This communication is directed in the UK to thosepersons who are market counterparties or intermediate customers (as defined inthe UK financial servises authority’s rules).

Additional information is available upon request.