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Brazilian Derivatives and Securities Brazilian Derivatives and Securities This page intentionally left blank Brazilian Derivatives and Securities Pricing and Risk Management of FX and Interest-Rate Portfolios for Local and Global Markets Marcos C. S. Carreira Quantitative Finance Practitioner, Brazil Richard J. Brostowicz Executive Director and Head of Brazil Quants, Banco Morgan Stanley, Brazil © Marcos C. S. Carreira and Richard J. Brostowicz 2016 Foreword © Peter Carr 2016 All rights reserved. No reproduction, copy or transmission of this publication may be made without written permission. No portion of this publication may be reproduced, copied or transmitted save with written permission or in accordance with the provisions of the Copyright, Designs and Patents Act 1988, or under the terms of any licence permitting limited copying issued by the Copyright Licensing Agency, Saffron House, 6–10 Kirby Street, London EC1N 8TS. Any person who does any unauthorized act in relation to this publication may be liable to criminal prosecution and civil claims for damages. The authors have asserted their rights to be identified as the authors of this work in accordance with the Copyright, Designs and Patents Act 1988. First published 2016 by PALGRAVE MACMILLAN Palgrave Macmillan in the UK is an imprint of Macmillan Publishers Limited, registered in England, company number 785998, of Houndmills, Basingstoke, Hampshire RG21 6XS. Palgrave Macmillan in the US is a division of St Martins Press LLC, 175 Fifth Avenue, New York, NY 10010. Palgrave Macmillan is the global academic imprint of the above companies and has companies and representatives throughout the world. Palgrave® and Macmillan® are registered trademarks in the United States, the United Kingdom, Europe and other countries ISBN 978-1-137-47726-2 ISBN 978-1-137-47727-9 (eBook) DOI 10.1057/9781137477279 This book is printed on paper suitable for recycling and made from fully managed and sustained forest sources. Logging, pulping and manufacturing processes are expected to conform to the environmental regulations of the country of origin. A catalogue record for this book is available from the British Library. Library of Congress Cataloging-in-Publication Data Brostowicz, Richard J., author. Brazilian derivatives and securities : pricing and risk management of FX and interest-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 2015 332.64’570981–dc23 2015033263 Contents List of Figures xiv List of Tables xvii Foreword xviii Peter Carr Preface xx Acknowledgments xxi 1 Financial Archeology 1 1.1 Interest rates and inflation 1 1.1.1 Record levels (the old days of overnight rates of 2% per day and the Real Plan); desperate times call for desperate 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 the dual cash regime; CDI and Selic 16 1.1.4 A new era? What has changed under Tombini? Coordination and communication, or more subtle changes? 22 1.2 Foreign exchange 24 1.2.1 Testing the waters 24 1.2.2 Pegs and multiple currencies 26 1.2.3 Indexing of local instruments 28 1.2.4 Floating, ballast and hot air (on the different mechanisms to manage a floating currency) 28 1.2.5 Paganism (on how to avoid conversion, and the history of offshore x onshore spreads) 34 1.2.6 A bit of a fit (on the 2008 crisis) 37 2 We Mean Business 40 2.1 Calendars 40 2.1.1 Banking calendars and fixings 40 2.1.2 Trading and listed contracts 41 2.1.3 New York, Rio, São Paulo – the FX combined calendar 41 v vi Contents 2.1.4 Notation used for moving forward or backward business days in a specified calendar 42 2.2 Interest rate fixings 42 2.2.1 Selic target 42 2.2.2 Selic 43 2.2.3 CDI 45 2.2.4 TJLP 46 2.2.5 TR 47 2.3 Inflation fixings 48 2.3.1 IPCA 48 2.3.2 IGP-M 52 2.4 Foreign exchange fixings 55 2.4.1 PTAX 55 2.4.2 EMTA 56 2.4.3 WMR 56 2.4.4 Observability for barriers 57 2.5 The 3 Ts in FX option pricing: a more precise version of the Black Formula 57 3 Interesting BRL Interest Rates 60 3.1 3 months in the life of an IR Swap 60 3.2 3 months in the life of a DI Future 68 3.3 Explaining it all 69 3.4 A simple swap 72 3.5 A promising future – The DI1 Future 72 3.6 My first numéraire – a more mathematical framework for DI Futures (DI1) 75 3.7 The still promising Future -> The Selic Futures (OC1) 78 3.8 Pricing BRL interest rate futures 79 3.8.1 DI Future (DI1) pricing 79 3.8.2 BRL onshore CDI curve construction 80 3.8.3 Selic Future (OC1) pricing 82 3.8.4 BRL onshore Selic spread curve construction 82 3.9 Giving 110% 83 3.10 The CDI+Spread is a multiplicative spread 84 3.11 How to price the 3 possible BRL Fixed X Float payoffs? 84 3.11.1 100% CDI case 84 3.11.2 CDI+Spread case 85 3.11.3 Percentage of CDI case 86 4 BRL Interest Rate Market and Credit Risk 87 4.1 Historical spreads 87 4.2 The term structure of volatility 89 Contents vii 4.2.1 Slope 89 4.2.2 Covariance 95 4.2.3 Principal components 95 4.3 Potential exposures 97 4.4 Zero curve: and the winner is ... 98 4.4.1 Linear Interpolation (LI) 100 4.4.2 Flat Forward (FF) 101 4.4.3 Cubic Spline (CS) 102 4.4.4 Which is better? 102 4.5 Smooth operator 102 4.6 Sensitivities 105 4.6.1 Zero 105 4.6.2 Forward 106 4.7 A framework for risk 107 4.7.1 Minimal description 107 4.7.2 The envelope and liquidity risk 108 4.7.3 The first, the last and the ugly 108 4.8 Trading forwards 108 4.9 Risk and P&L attribution 109 5 A Man with Two Clocks ... Foreign Exchange in Brazil 110 5.1 FX Spot 110 5.1.1 Who can trade it 110 5.1.2 How, when and where to trade it 110 5.1.3 Observability 111 5.2 DOL 111 5.2.1 Contract details 111 5.2.2 Liquidity 111 5.2.3 DR1 and the roll 112 5.2.4 Payoff of DOL contract 112 5.2.5 Pricing a DOL contract based FRC, DI’s, nearest maturity FXFUT and CASADO quotes 113 5.2.6 Apples and oranges 113 5.2.7 Convexity corrections 114 5.3 Forward points strategies 115 5.3.1 FRP 115 5.3.2 “Casado” 116 5.4 FX Future crosses 116 5.4.1 Payoff 117 5.4.2 Pricing and hedging 117 5.4.3 Convexity corrections 119 viii Contents 6 And the Even More Interesting USD Onshore Interest Rates . 120 6.1 3 months in the life of a FX Swap 120 6.2 3 months in the life of a DDI Future 120 6.3 Explaining it all 120 6.4 The DDI Futures (DDI) -> Why they were designed this way? 121 6.5 The mathematical derivation of a DDI contract price 125 6.5.1 DDI Future pricing 127 6.6 It takes two (DDI contracts) to (con)tango -> The FRA de CUPOM strategy (FRC) 131 6.6.1 FRC Future pricing 132 6.6.2 Handling a FRC trade before BVMF publication of the first DDI closing price 133 6.7 Calibration of the cupom curve 134 6.7.1 Calibration of the cupom curve on the short end 134 6.7.2 Calibration of the cupom curve on the long end 135 6.8 How to compute cupom interest rate risk? 137 6.9 Interpolation choices for the cupom curve 139 6.9.1 Log-linear interpolation of cupom curve forward discount factors curve in business days 139 6.9.2 Log-linear interpolation of cupom curve forward discount factors curve in calendar days 140 6.9.3 Log-linear interpolation of cupom curve in FX forward prices 140 6.10 The SCC contract 141 6.11 The mathematical derivation and pricing of a SCC contract price 142 6.12 The SCS contract – a modern, but exotic, cousin 143 6.13 The mathematical derivation of a SCS contract price 143 6.14 SCS Future pricing 145 6.15 Forward starting SCS contracts 150 6.16 A much simpler alternative to FRC contracts 150 6.17 A BRL Float or Fixed X USD onshore Fixed swap 152 6.17.1 Coupon payoff specification 152 6.17.2 Coupon pricing 153 7 Too Many Options? 154 7.1 IDI options 156 7.1.1 IDI options available indices and compounding methodology 156 7.1.2 IDI options payoff and other contractual information 157 7.1.3 IDI options common trading strategies 158 Contents ix 7.1.4 A simple Black pricing formula for an IDI option assuming the IDI index as its main underlying 159 7.1.5 How to fit a volatility smile for an IDI option assuming the IDI index as its main underlying 161 7.1.6 A simple Black pricing formula assuming the IDI index equivalent realized interest rate as the underlying 161 7.1.7 Is the IDI option smiling at you now? 163 7.1.8 Or is it smirking? 164 7.1.9 A discrete tree model that could fit the smirk volatility surface shape for IDI options 165 7.1.10 Delta hedging IDI options under the discrete tree model 167 7.1.11 Delta hedging IDI options under the SABR model 168 7.1.12 IDI options pricing under HJM model 169 7.1.13 IDI options historical volatility computation – how to price an IDI option if only the DI Futures market was liquid? 174 7.1.14 IDI digital options – limitations and applicability 176 7.1.15 OTC IDI options at Cetip 177 7.2 DI Future options 177 7.2.1 Basic trading information and definition of the contract codes 178 7.2.2 DI Future options payoff – smells like swaption? 178 7.2.3 DI Future options most common trading strategies 180 7.2.4 A simple Black pricing formula for DI Future options 180 7.2.5 Can DI Future options smile with the SABR model? 181 7.2.6 DI Future options pricing under HJM model – where’s the smile? 182 7.2.7 What about DI Future options under the BGM a.k.a Libor Market Model? 184 7.2.8 DI Future options historical volatility computation – how to price a DI Future option if only the DI Futures market was liquid 185 7.3 IR option strategies – VTF and VID 188 7.3.1 VTF 188 7.3.2 DI Future delta hedge computation
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