Brazilian Derivatives and Securities (eBook)

Marcos Carreira is responsible for Traded Risk at HSBC Brazil. Previously he was first the Derivative Products Officer and later the Technical Modeling Officer at BM&FBovespa, with contributions on risk management, derivatives pricing, exchange fees, microstructure and HFT. At Credit Suisse Brazil, he was a Managing Director in charge of the FX and IR Options desk, after being the Risk Manager responsible for Market, Counterparty and Liquidity Risks. He started his career in Finance/Product Control at Banco de Investimentos Garantia. Mr Carreira holds an engineering degree from Instituto Tecnológico de Aeronáutica (ITA), is part of the 2016 class of the Professional Masters in Economics at Insper. He has more than 20 years of experience in the Brazilian Capital Markets. Marcos lectures for the MECAI Professional Masters course in Mathematical Finance at ICMC-USP.Richard Brostowicz is an Executive Director and Head of Brazil Quants at Banco Morgan Stanley, Brazil. He has 8 years of experience as a quant in global markets, having worked previously at Credit Suisse, and 11 years in the Brazilian market. He studied at the University of Sao Paulo (USP) and is a lecturer for a MECAI Professional Masters course in Mathematical Finance at ICMC-USP.

Cover 1
Half-Title 2
Title 4
Copyright 5
Contents 6
List of Figures 15
List of Tables 18
Foreword 19
Preface 21
Acknowledgments 22
Disclaimer 23
1 Financial Archeology 26
1.1 Interest rates and inflation 26
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
1.1.2 COPOM (the Brazilian FOMC): behavior, language, influence, targets and bands 34
1.1.3 The Brazilian Payment System (SPB): the end of the dual cash regime CDI and Selic
1.1.4 A new era? What has changed under Tombini? Coordination and communication, or more subtle changes? 47
1.2 Foreign exchange 49
1.2.1 Testing the waters 49
1.2.2 Pegs and multiple currencies 51
1.2.3 Indexing of local instruments 53
1.2.4 Floating, ballast and hot air (on the different mechanisms to manage a floating currency) 53
1.2.5 Paganism (on how to avoid conversion, and the history of offshore x onshore spreads) 59
1.2.6 A bit of a fit (on the 2008 crisis) 62
2 We Mean Business 65
2.1 Calendars 65
2.1.1 Banking calendars and fixings 65
2.1.2 Trading and listed contracts 66
2.1.3 New York, Rio, São Paulo – the FX combined calendar 66
2.1.4 Notation used for moving forward or backward business days in a specified calendar 67
2.2 Interest rate fixings 67
2.2.1 Selic target 67
2.2.2 Selic 68
2.2.3 CDI 70
2.2.4 TJLP 71
2.2.5 TR 72
2.3 Inflation fixings 73
2.3.1 IPCA 73
2.3.2 IGP-M 77
2.4 Foreign exchange fixings 80
2.4.1 PTAX 80
2.4.2 EMTA 81
2.4.3 WMR 81
2.4.4 Observability for barriers 82
2.5 The 3 Ts in FX option pricing: a more precise version of the Black Formula 82
3 Interesting BRL Interest Rates 85
3.1 3 months in the life of an IR Swap 85
3.2 3 months in the life of a DI Future 93
3.3 Explaining it all 94
3.4 A simple swap 97
3.5 A promising future – The DI1 Future 97
3.6 My first numéraire – a more mathematical framework for DI Futures (DI1) 100
3.7 The still promising Future -> The Selic Futures (OC1)
3.8 Pricing BRL interest rate futures 104
3.8.1 DI Future (DI1) pricing 104
3.8.2 BRL onshore CDI curve construction 105
3.8.3 Selic Future (OC1) pricing 107
3.8.4 BRL onshore Selic spread curve construction 107
3.9 Giving 110% 108
3.10 The CDI+Spread is a multiplicative spread 109
3.11 How to price the 3 possible BRL Fixed X Float payoffs? 109
3.11.1 100% CDI case 109
3.11.2 CDI+Spread case 110
3.11.3 Percentage of CDI case 111
4 BRL Interest Rate Market and Credit Risk 112
4.1 Historical spreads 112
4.2 The term structure of volatility 114
4.2.1 Slope 114
4.2.2 Covariance 120
4.2.3 Principal components 120
4.3 Potential exposures 122
4.4 Zero curve: and the winner is ... 123
4.4.1 Linear Interpolation (LI) 125
4.4.2 Flat Forward (FF) 126
4.4.3 Cubic Spline (CS) 127
4.4.4 Which is better? 127
4.5 Smooth operator 127
4.6 Sensitivities 130
4.6.1 Zero 130
4.6.2 Forward 131
4.7 A framework for risk 132
4.7.1 Minimal description 132
4.7.2 The envelope and liquidity risk 133
4.7.3 The first, the last and the ugly 133
4.8 Trading forwards 133
4.9 Risk and P& L attribution
5 A Man with Two Clocks ... Foreign Exchange in Brazil 135
5.1 FX Spot 135
5.1.1 Who can trade it 135
5.1.2 How, when and where to trade it 135
5.1.3 Observability 136
5.2 DOL 136
5.2.1 Contract details 136
5.2.2 Liquidity 136
5.2.3 DR1 and the roll 137
5.2.4 Payoff of DOL contract 137
5.2.5 Pricing a DOL contract based FRC, DI’s, nearest maturity FXFUT and CASADO quotes 138
5.2.6 Apples and oranges 138
5.2.7 Convexity corrections 139
5.3 Forward points strategies 140
5.3.1 FRP 140
5.3.2 “Casado” 141
5.4 FX Future crosses 141
5.4.1 Payoff 142
5.4.2 Pricing and hedging 142
5.4.3 Convexity corrections 144
6 And the Even More Interesting USD Onshore Interest Rates . . . 145
6.1 3 months in the life of a FX Swap 145
6.2 3 months in the life of a DDI Future 145
6.3 Explaining it all 145
6.4 The DDI Futures (DDI) -> Why they were designed this way?
6.5 The mathematical derivation of a DDI contract price 150
6.5.1 DDI Future pricing 152
6.6 It takes two (DDI contracts) to (con)tango -> The FRA de CUPOM strategy (FRC)
6.6.1 FRC Future pricing 157
6.6.2 Handling a FRC trade before BVMF publication of the first DDI closing price 158
6.7 Calibration of the cupom curve 159
6.7.1 Calibration of the cupom curve on the short end 159
6.7.2 Calibration of the cupom curve on the long end 160
6.8 How to compute cupom interest rate risk? 162
6.9 Interpolation choices for the cupom curve 164
6.9.1 Log-linear interpolation of cupom curve forward discount factors curve in business days 164
6.9.2 Log-linear interpolation of cupom curve forward discount factors curve in calendar days 165
6.9.3 Log-linear interpolation of cupom curve in FX forward prices 165
6.10 The SCC contract 166
6.11 The mathematical derivation and pricing of a SCC contract price 167
6.12 The SCS contract – a modern, but exotic, cousin 168
6.13 The mathematical derivation of a SCS contract price 168
6.14 SCS Future pricing 170
6.15 Forward starting SCS contracts 175
6.16 A much simpler alternative to FRC contracts 175
6.17 A BRL Float or Fixed X USD onshore Fixed swap 177
6.17.1 Coupon payoff specification 177
6.17.2 Coupon pricing 178
7 Too Many Options? 179
7.1 IDI options 181
7.1.1 IDI options available indices and compounding methodology 181
7.1.2 IDI options payoff and other contractual information 182
7.1.3 IDI options common trading strategies 183
7.1.4 A simple Black pricing formula for an IDI option assuming the IDI index as its main underlying 184
7.1.5 How to fit a volatility smile for an IDI option assuming the IDI index as its main underlying 186
7.1.6 A simple Black pricing formula assuming the IDI index equivalent realized interest rate as the underlying 186
7.1.7 Is the IDI option smiling at you now? 188
7.1.8 Or is it smirking? 189
7.1.9 A discrete tree model that could fit the smirk volatility surface shape for IDI options 190
7.1.10 Delta hedging IDI options under the discrete tree model 192
7.1.11 Delta hedging IDI options under the SABR model 193
7.1.12 IDI options pricing under HJM model 194
7.1.13 IDI options historical volatility computation – how to price an IDI option if only the DI Futures market was liquid? 199
7.1.14 IDI digital options – limitations and applicability 201
7.1.15 OTC IDI options at Cetip 202
7.2 DI Future options 202
7.2.1 Basic trading information and definition of the contract codes 203
7.2.2 DI Future options payoff – smells like swaption? 203
7.2.3 DI Future options most common trading strategies 205
7.2.4 A simple Black pricing formula for DI Future options 205
7.2.5 Can DI Future options smile with the SABR model? 206
7.2.6 DI Future options pricing under HJM model – where’s the smile? 207
7.2.7 What about DI Future options under the BGM a.k.a Libor Market Model? 209
7.2.8 DI Future options historical volatility computation – how to price a DI Future option if only the DI Futures market was liquid 210
7.3 IR option strategies – VTF and VID 213
7.3.1 VTF 213
7.3.2 DI Future delta hedge computation by BVMF 214
7.3.3 VID 215
7.3.4 DI Future delta hedge computation by BVMF 216
7.4 Jabuticabas: risk management of options on interest rates 216
7.4.1 IDI options 216
7.5 BRL/USD Listed FX options 217
7.5.1 Contract details 218
7.5.2 BRL/USD Listed FX options payoff 218
7.5.3 A simple Black pricing formula for BRL/USD Listed FX options 219
7.5.4 Volatility surface based on SABR model 219
7.5.5 Volatility surface based on polynomial on FX delta 220
7.6 BRL/USD Listed FX options with daily margining 221
7.7 BRL/USD FX options: strategies 221
7.7.1 VTC 221
7.7.2 FX Future delta hedge computation by BVMF 222
7.7.3 Do you believe you are delta hedged? 222
7.8 OTC IR and FX options 223
8 The Mountain Goes to . . . Foreign Exchange Contracts Offshore 225
8.1 CME BRL/USD FX Futures 226
8.1.1 Contract details 226
8.1.2 Payoff 226
8.1.3 Pricing 227
8.2 OTC – NDFs 227
8.2.1 BRL/USD offshore NDFs – payoff and differences for equivalent onshore NDF contract 227
8.2.2 A quick detour for pricing collateralized derivatives 231
8.2.3 Pricing a collateralized NDF contract offshore 233
8.2.4 How offshore NDFs are usually traded in the interbank market? 235
8.2.5 Revisiting the cupom curve construction based NDF spread strategies 236
8.2.6 The mythical offshore BRL discounting curve 236
8.3 OTC – BRL/USD options 237
9 Start from Where? Constructing Markets for FX Forwards, Futures, Onshore USD Interest Rates and Offshore Instruments 242
9.1 Observability of contracts 242
9.1.1 Spot x DOL 242
9.1.2 FRC x Forward x DOL 242
9.1.3 NDFs and forward points 243
9.2 Structures 243
9.2.1 Dates 243
9.2.2 Events (breaks, fixings, market points) 243
9.2.3 “The Triangle” 244
9.3 Curve construction 245
9.3.1 Cupom Cambial 245
9.3.2 Forwards 245
9.4 The offshore x onshore spread 245
9.4.1 Changing standards 245
9.4.2 Convertibility, demand and taxes 246
9.5 The mythical offshore BRL discounting curve 246
10 Offshore IR Products Based on CDI Fixings 247
10.1 Offshore BRL Fixed-Float swaps 247
10.1.1 Offshore BRL Fixed-Float swaps payoff 248
10.1.2 Foreign market participants appetite for Fixed-Float swaps 248
10.1.3 Which discounting curve to use for offshore Fixed-Float swaps pricing? 249
10.1.4 Is this a quanto swap? Let’s analyze it from perspective 249
10.1.5 Now let’s analyze it from a mathematical 250
10.1.6 BRL Fixed-Float offshore breakeven historical 254
10.1.7 Calibrating an offshore BRL Fixed-Float swap curve 255
10.2 Offshore BRL Fixed-Float swaptions 255
10.2.1 BRL Fixed-Float offshore swaption payoff specification 256
11 The Dual Case – US Libor Onshore Swaps 259
11.1 Payoff of US Libor onshore swaps 259
11.2 Pricing of US Libor onshore swaps 259
12 FX Trading (Interest Rate and Fixing) Market and Credit 262
12.1 Fixing 262
12.2 The term structure of the Cupom Cambial 263
12.2.1 Slope 263
12.2.2 Casado 263
12.3 Potential exposures 263
12.4 Interpolation and sensitivities 265
12.5 A framework for risk 266
12.6 Trading forwards 266
12.7 Risk and P& L attribution
12.8 DOL convexity correction to a FX forward price 268
13 A Skewed Perspective of the World: FX Options 271
13.1 Starting from the end (market standards for offshore FX options) 271
13.1.1 Weightlifting 271
13.1.2 Reversal of fortune 273
13.1.3 The locals are friendly 278
13.1.4 Thin tails wagging the dogs 279
13.1.5 The couple, decoupled 280
13.2 Back to the beginning (What is different in onshore FX options?) 281
13.2.1 Uncertain smile 281
13.2.2 Fixing the averaging 281
13.2.3 I’d risk everything 282
13.2.4 Look in the mirror 283
13.3 Risk management 291
13.4 Risk and P& L attribution
14 Some Cash Is Better Than Nothing – What You Need to Know about Cash Products 295
14.1 Local government bonds 295
14.1.1 Floating to the top – LFTs 295
14.1.2 The name of the game – LTNs and NTN-Fs 295
14.1.3 Making it real – NTN-Bs 296
14.1.4 Living fossils – NTN-As 296
14.1.5 Reading the fine print 296
14.2 Local corporate bonds 297
14.3 Local funding practices 297
14.4 Offshore government and corporate bonds 297
14.5 Liquidity (or lack thereof) 297
14.6 The Brazilian repo market (Compromissadas) 298
15 Index of Choice . . . Inflation-Linked Products and Curves 301
15.1 Government inflation-linked bonds 301
15.2 Inflation-linked swaps 303
15.2.1 IGPM and IPCA publication 303
15.2.2 IGPM and IPCA swaps payoff 304
15.2.3 Dirty and clean rates . . . again 304
15.2.4 Trading conventions for IGPM and IPCA swaps. Are they liquid? 304
15.2.5 IPCA swaps pricing – the market approach 306
15.2.6 IPCA swaps pricing – the foreign currency analogy approach and why it’s complicated 306
15.2.7 IPCA swaps pricing – the IPCA forwards calibration approach 308
15.2.8 IPCA index forwards interpolation without seasonality 309
15.2.9 Adding seasonality 310
15.2.10 Joint calibration of IPCA curve with NTN-B bond quotes (reduced by asset-swap spread) and IPCA swap rate quotes 310
15.2.11 The IGPM market 312
15.3 Exchange traded inflation-linked Futures 313
16 Microstructure of the Listed Derivatives 314
16.1 Microstructure: concepts 314
16.2 Can durations be estimated? 315
16.3 What happens in practice? 316
16.4 What is the importance of the tick size? 317
16.5 The model with uncertainty zones (Robert and Rosenbaum) 319
16.5.1 Description of the model 319
16.5.2 What can we do with this model? 320
16.6 DOL 321
16.7 DI 321
17 Unlucky End: On the Obsolescence of Products and Books 322
References 323
Index 325