Credit risk modeling using excel and VBA 2 edition

P1: TIX fm JWBK493-Lăoffler November 15, 2010 17:8 Printer: Yet to come Credit Risk Modeling Using Excel and VBA with DVD i P1: TIX fm JWBK493-Lăoffler November 15, 2010 17:8 Printer: Yet to come For other titles in the Wiley Finance series please see www.wiley.com/finance ii P1: TIX fm JWBK493-Lăoffler November 15, 2010 17:8 Printer: Yet to come Credit Risk Modeling Using Excel and VBA with DVD Gunter Lăoffler Peter N Posch A John Wiley and Sons, Ltd., Publication iii P1: TIX fm JWBK493-Lăoffler November 15, 2010 17:8 Printer: Yet to come This edition first published 2011 C 2011 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 trademarks 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 978-0-470-66092-8 A catalogue record for this book is available from the British Library Typeset in 10/12pt Times by Aptara Inc., New Delhi, India Printed in Great Britain by CPI Antony Rowe, Chippenham, Wiltshire iv P1: TIX fm JWBK493-Lăoffler November 15, 2010 17:8 Printer: Yet to come Mundus est is qui constat ex caelo, et terra et mare cunctisque sideribus Isidoro de Sevilla v P1: TIX fm JWBK493-Lăoffler November 15, 2010 17:8 Printer: Yet to come Contents Preface to the 2nd edition xi Preface to the 1st edition xiii Some Hints for Troubleshooting xv Estimating Credit Scores with Logit 1 10 12 16 20 25 25 25 25 26 Linking scores, default probabilities and observed default behavior Estimating logit coefficients in Excel Computing statistics after model estimation Interpreting regression statistics Prediction and scenario analysis Treating outliers in input variables Choosing the functional relationship between the score and explanatory variables Concluding remarks Appendix Logit and probit Marginal effects Notes and literature The Structural Approach to Default Prediction and Valuation Default and valuation in a structural model Implementing the Merton model with a one-year horizon The iterative approach A solution using equity values and equity volatilities Implementing the Merton model with a T -year horizon Credit spreads CreditGrades Appendix Notes and literature Assumptions Literature vii 27 27 30 30 35 39 43 44 50 52 52 53 P1: TIX fm JWBK493-Lăoffler viii November 15, 2010 17:8 Printer: Yet to come Contents Transition Matrices Cohort approach Multi-period transitions Hazard rate approach Obtaining a generator matrix from a given transition matrix Confidence intervals with the binomial distribution Bootstrapped confidence intervals for the hazard approach Notes and literature Appendix Matrix functions Prediction of Default and Transition Rates Candidate variables for prediction Predicting investment-grade default rates with linear regression Predicting investment-grade default rates with Poisson regression Backtesting the prediction models Predicting transition matrices Adjusting transition matrices Representing transition matrices with a single parameter Shifting the transition matrix Backtesting the transition forecasts Scope of application Notes and literature Appendix Prediction of Loss Given Default Candidate variables for prediction Instrument-related variables Firm-specific variables Macroeconomic variables Industry variables Creating a data set Regression analysis of LGD Backtesting predictions Notes and literature Appendix 55 56 61 63 69 71 74 78 78 78 83 83 85 88 94 99 100 101 103 108 108 110 110 115 115 116 117 118 118 119 120 123 126 126 Modeling and Estimating Default Correlations with the Asset Value Approach Default correlation, joint default probabilities and the asset value approach Calibrating the asset value approach to default experience: the method of moments Estimating asset correlation with maximum likelihood Exploring the reliability of estimators with a Monte Carlo study Concluding remarks Notes and literature 131 131 133 136 144 147 147 P1: TIX fm JWBK493-Lăoffler November 15, 2010 17:8 Printer: Yet to come Contents Measuring Credit Portfolio Risk with the Asset Value Approach A default-mode model implemented in the spreadsheet VBA implementation of a default-mode model Importance sampling Quasi Monte Carlo Assessing Simulation Error Exploiting portfolio structure in the VBA program Dealing with parameter uncertainty Extensions First extension: Multi-factor model Second extension: t-distributed asset values Third extension: Random LGDs Fourth extension: Other risk measures Fifth extension: Multi-state modeling Notes and literature Validation of Rating Systems Cumulative accuracy profile and accuracy ratios Receiver operating characteristic (ROC) Bootstrapping confidence intervals for the accuracy ratio Interpreting caps and ROCs Brier score Testing the calibration of rating-specific default probabilities Validation strategies Testing for missing information Notes and literature Validation of Credit Portfolio Models Testing distributions with the Berkowitz test Example implementation of the Berkowitz test Representing the loss distribution Simulating the critical chi-square value Testing modeling details: Berkowitz on subportfolios Assessing power Scope and limits of the test Notes and literature 10 Credit Default Swaps and Risk-Neutral Default Probabilities Describing the term structure of default: PDs cumulative, marginal and seen from today From bond prices to risk-neutral default probabilities Concepts and formulae Implementation Pricing a CDS Refining the PD estimation ix 149 149 152 156 160 162 165 168 170 170 171 173 175 177 179 181 182 185 187 190 191 192 195 198 201 203 203 206 207 209 211 214 216 217 219 220 221 221 225 232 234 P1: TIX fm JWBK493-Lăoffler x November 15, 2010 17:8 Printer: Yet to come Contents Market values for a CDS Example Estimating upfront CDS and the ‘Big Bang’ protocol Pricing of a pro-rata basket Forward CDS spreads Example Pricing of swaptions Notes and literature Appendix Deriving the hazard rate for a CDS 237 239 240 241 242 243 243 247 247 247 11 Risk Analysis and Pricing of Structured Credit: CDOs and First-to-Default Swaps Estimating CDO risk with Monte Carlo simulation The large homogeneous portfolio (LHP) approximation Systemic risk of CDO tranches Default times for first-to-default swaps CDO pricing in the LHP framework Simulation-based CDO pricing Notes and literature Appendix Closed-form solution for the LHP model Cholesky decomposition Estimating PD structure from a CDS 12 Basel II and Internal Ratings Calculating capital requirements in the Internal Ratings-Based (IRB) approach Assessing a given grading structure Towards an optimal grading structure Notes and literature 249 249 253 256 259 263 272 281 282 282 283 284 285 285 288 294 297 Appendix A1 Visual Basics for Applications (VBA) 299 Appendix A2 Solver 307 Appendix A3 Maximum Likelihood Estimation and Newton’s Method 313 Appendix A4 Testing and Goodness of Fit 319 Appendix A5 User-defined Functions 325 Index 333 ... 171 173 175 177 179 181 1 82 185 187 190 191 1 92 195 198 20 1 20 3 20 3 20 6 20 7 20 9 21 1 21 4 21 6 21 7 21 9 22 0 22 1 22 1 22 5 23 2 23 4 P1: TIX fm JWBK493-Lăoffler x November 15, 20 10 17:8 Printer: Yet to... literature 24 9 24 9 25 3 25 6 25 9 26 3 27 2 28 1 28 2 28 2 28 3 28 4 28 5 28 5 28 8 29 4 29 7 Appendix A1 Visual Basics for Applications (VBA) 29 9 Appendix A2 Solver 307 Appendix A3 Maximum Likelihood Estimation and. .. 1 .29 0.11 0.15 … 108 21 … 4001 830 1999 20 00 20 01 20 02 2003 20 04 1999 20 00 0 0 0 0 0.50 0.55 0.45 0.31 0.45 0.46 0.01 -0.11 0.33 0.33 0 .25 0 .25 0 .28 0. 32 0 .25 0. 32 1996 0.36 0.06 0.03 3 .20 0 .28