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Counterparty Credit Risk for Other Titles in the Wiley Finance Series Please See Counterparty Credit Risk Thispageintentionallyleftblank Counterparty Credit Risk For other titles in the Wiley Finance series please see www.wiley.com/finance Counterparty Credit Risk The New Challenge for Global Financial Markets Jon Gregory A John Wiley and Sons, Ltd, Publication This edition first published in 2010 Copyright# 2010 John Wiley & Sons Ltd Registered office John Wiley & Sons Ltd, The Atrium, Southern Gate, Chichester, West Sussex, PO19 8SQ, United Kingdom For details of our global editorial offices, for customer services and for information about how to apply for permission to reuse the copyright material in this book please see our website at www.wiley.com The right of the author to be identified as the author of this work has been asserted in accordance with the Copyright, Designs and Patents Act 1988. All rights reserved. No part of this publication may be reproduced, stored in a retrieval system, or transmitted, in any form or by any means, electronic, mechanical, photocopying, recording or otherwise, except as permitted by the UK Copyright, Designs and Patents Act 1988, without the prior permission of the publisher. Wiley also publishes its books in a variety of electronic formats. Some content that appears in print may not be available in electronic books. Designations used by companies to distinguish their products are often claimed as trademarks. All brand names and product names used in this book are trade names, service marks, trademarks or registered trade- marks of their respective owners. The publisher is not associated with any product or vendor mentioned in this book. This publication is designed to provide accurate and authoritative information in regard to the subject matter covered. It is sold on the understanding that the publisher is not engaged in rendering professional services. If professional advice or other expert assistance is required, the services of a competent professional should be sought. ISBN 978-0-470-68576-1 A catalogue record for this book is available from the British Library. Project Management by OPS Ltd, Gt Yarmouth, Norfolk Typeset in 10/12pt Times Printed in Great Britain by CPI Antony Rowe Ltd, Chippenham, Wiltshire Contents Acknowledgements xvii List of Spreadsheets xviii List of Abbreviations xix Introduction xxi 1 Setting the Scene 1 1.1 Financial risk management 1 1.1.1 Market risk 1 1.1.2 Liquidity risk 2 1.1.3 Operational risk 2 1.1.4 Credit risk 2 1.1.5 Value-at-risk 3 1.1.6 Disadvantages of value-at-risk 3 1.2 The failure of models 4 1.2.1 Why models? 4 1.2.2 Good model, bad model 5 1.3 The derivatives market 6 1.3.1 What is a derivative? 6 1.3.2 Market structure 6 1.4 Risks of derivatives 7 1.4.1 Too big to fail 7 1.4.2 Systemic risk 8 1.4.3 Compensation culture 8 1.4.4 Credit derivatives 9 1.5 Counterparty risk in context 9 1.5.1 What is counterparty risk? 9 1.5.2 Mitigation of counterparty risk 10 1.5.3 Counterparty risk and integration of risk types 10 1.5.4 Counterparty risk and today’s derivatives market 11 vi Contents 2 Defining Counterparty Credit Risk 13 2.1 Introducing counterparty risk 13 2.1.1 Origins of counterparty risk 13 2.1.2 Repos 14 2.1.3 Exchange-traded derivatives 14 2.1.4 OTC derivatives 14 2.1.5 Counterparty risk 16 2.1.6 Counterparty risk versus lending risk 17 2.1.7 Mitigating counterparty risk 18 2.1.8 Counterparty risk players 19 2.2 Components and terminology 20 2.2.1 Credit exposure 20 2.2.2 Default probability and credit migration 21 2.2.3 Recovery 22 2.2.4 Mark-to-market 22 2.2.5 Replacement cost 23 2.2.6 Exposure 23 2.2.7 Exposure as a short option position 24 2.2.8 Potential future exposure (PFE) 24 2.3 Controlling counterparty credit risk 25 2.3.1 Trading with high-quality counterparties 25 2.3.2 Cross-product netting 26 2.3.3 Close-out 27 2.3.4 Collateralisation 27 2.3.5 Walkaway features 28 2.3.6 Monolines 29 2.3.7 Diversification of counterparty risk 29 2.3.8 Exchanges and centralised clearing houses 29 2.4 Quantifying counterparty risk 30 2.4.1 Credit lines 30 2.4.2 Pricing counterparty risk 32 2.4.3 Hedging counterparty risk 33 2.4.4 Capital requirements and counterparty risk 34 2.5 Metrics for credit exposure 35 2.5.1 Expected MtM 35 2.5.2 Expected exposure 35 2.5.3 Potential future exposure 36 2.5.4 EE and PFE for a normal distribution 36 2.5.5 Overview of exposure metrics 36 2.5.6 Expected positive exposure 37 2.5.7 Effective EPE 38 2.5.8 Maximum PFE 38 2.6 Summary 38 Appendix 2.A Characterising exposure for a normal distribution 39 Contents vii 3 Mitigating Counterparty Credit Risk 41 3.1 Introduction 41 3.1.1 Two-way or one-way agreements 41 3.1.2 Standardisation 42 3.2 Default-remote entities 42 3.2.1 High-quality counterparties 42 3.2.2 Special purpose vehicles 42 3.2.3 Central counterparties 43 3.3 Termination and walkaway features 44 3.3.1 Termination events 44 3.3.2 Additional termination events 45 3.3.3 Walkaway features 45 3.4 Netting and close-out 46 3.4.1 Close-out 47 3.4.2 Payment and close-out netting 48 3.4.3 The need for close-out netting 48 3.4.4 The birth of netting 50 3.4.5 Netting agreements 50 3.4.6 The ISDA Master Agreement 50 3.4.7 Product coverage 51 3.4.8 Netting and exposure 51 3.4.9 Advantages and disadvantages of netting 51 3.4.10 Multilateral netting 53 3.5 Netting and exposure 54 3.5.1 Negativity of MtM 54 3.5.2 Impact of correlation 55 3.5.3 Negative MtM of a netting set 57 3.5.4 Positive MtM of a netting set 58 3.6 Collateral 59 3.6.1 The basics of collateralisation 60 3.6.2 Analogy with mortgages 61 3.6.3 Setting up a collateral agreement 61 3.6.4 Valuation agent 62 3.6.5 Types of collateral 63 3.6.6 Coverage of collateralisation 63 3.6.7 Disputes and reconciliations 64 3.7 The mechanics of collateralisation 65 3.7.1 Linkage of collateral parameters to credit quality 65 3.7.2 Margin call frequency 66 3.7.3 Threshold 66 3.7.4 Independent amount 67 3.7.5 Minimum transfer amount 68 3.7.6 Rounding 68 3.7.7 Haircuts 68 viii Contents 3.7.8 Coupons and interest payments 70 3.7.9 Substitution, reuse of collateral and rehypothecation 71 3.7.10 Call-and-return example 71 3.8 Is risk mitigation always a good thing? 73 3.9 Summary 74 Appendix 3.A EE of independent normal variables 74 4 Quantifying Counterparty Credit Exposure, I 77 4.1 Quantifying credit exposure 77 4.1.1 Mark-to-market þ add-ons 78 4.1.2 Semi-analytical methods 79 4.1.3 Monte Carlo simulation 80 4.1.4 Roll-off risk 82 4.2 Typical credit exposures 84 4.2.1 Loans, bonds and repos 84 4.2.2 Swaps 84 4.2.3 FX products 85 4.2.4 Options 85 4.2.5 Credit derivatives 86 4.2.6 Payment frequencies 89 4.2.7 Exercise dates 89 4.3 Models for credit exposure 90 4.3.1 Calibration 91 4.3.2 Risk-neutral or real? 91 4.3.3 Equities 93 4.3.4 FX 94 4.3.5 Commodities 94 4.3.6 Credit spreads 94 4.3.7 Interest rates 95 4.3.8 Advanced models 96 4.3.9 Model validation 97 4.3.10 Correlations 97 4.4 Netting 98 4.4.1 Modelling netting 98 4.4.2 Netting factor 99 4.4.3 Examples 99 4.5 Exposure contributions 101 4.5.1 Marginal EE 102 4.5.2 Simple two-trade marginal EE example 102 4.5.3 Marginal EE and correlation 103 4.5.4 General example 104 4.6 Summary 104 Appendix 4.A Semi-analytical formula for exposure of a forward contract 105 Appendix 4.B Computing marginal EE 106 Contents ix 5 Quantifying Counterparty Credit Exposure, II: The Impact of Collateral 107 5.1 Introduction 107 5.2 The impact of collateral on credit exposure 107 5.2.1 Remargin period 107 5.2.2 Potential future exposure with collateral 109 5.2.3 Volatility of exposure 110 5.2.4 Collateral volatility 110 5.2.5 Correlation between collateral and exposure 111 5.3 Modelling collateral 112 5.3.1 Parameters 113 5.3.2 Collateral logic 114 5.4 Full collateralisation 114 5.4.1 Parameters 114 5.4.2 Scenarios 115 5.4.3 Exposure distributions 116 5.4.4 Simple approximation – idealised case 117 5.4.5 Simple approximation – impact of minimum transfer amount 119 5.4.6 Impact of threshold 120 5.4.7 Simple approximation – impact of threshold 121 5.4.8 Operational cost versus reduction of exposure 122 5.5 The risks of collateralisation 123 5.5.1 Operational risk 123 5.5.2 Default risk 124 5.5.3 FX risk 124 5.5.4 Liquidity and liquidation risk 124 5.6 Summary 125 Appendix 5.A Calculation of collateralised PFE (cash collateral) 125 Appendix 5.B Calculation of collateralised netted exposure with collateral value uncertainty 126 Appendix 5.C Mathematical treatment of a collateralised exposure 126 6 Overview of Credit Risk and Credit Derivatives 129 6.1 Defaults, recovery rates, credit spreads and credit derivatives 129 6.1.1 Default rates 130 6.1.2 Recovery rates 130 6.1.3 Credit spreads 132 6.2 Credit derivatives 133 6.2.1 Market growth and uses 133 6.2.2 Credit default swaps (CDSs) 134 6.2.3 Credit-linked notes 135 6.2.4 Asset swaps 135 6.2.5 Linkage between bonds, asset swaps and CDS premiums 136 6.2.6 Contingent credit default swap (CCDS) 138 6.2.7 Fixed and digital CDSs and recovery swaps 138 x Contents 6.3 Credit default swaps 139 6.3.1 Reference entity and obligation 139 6.3.2 Credit events 139 6.3.3 Settlement of CDS 140 6.3.4 Cheapest-to-deliver option and restructuring 141 6.3.5 Delivery squeeze 143 6.3.6 CDS risks 144 6.3.7 ISDA 2009, Big Bang Protocol, Small Bang Protocol and new trading conventions 146 6.4 Estimating default probability 147 6.4.1 Defining default probability 148 6.4.2 Historical estimation 148 6.4.3 Equity-based approaches 151 6.4.4 Market-implied default probabilities 153 6.5 Portfolio credit derivatives 155 6.5.1 CDS index products 155 6.5.2 Index tranches 156 6.5.3 Super senior risk 159 6.5.4 Collateralised debt obligations
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