model risk

Model Risk Edited By Daniel Rsch and H

arald Scheule EditEd By daniEl Rsch and haRald schEulE

Model

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The first years of the 21st Century saw the financial industry continue to pour vast resources into building models to measure financial risks. Yet, as the financial crisis that began in 2007 has shown, these models predictions were often being used without recognition of the assumptions behind the models themselves; acknowledgement of their limitations; and understanding of the context in which they were developed. The consequences of model risk have been clear to see in the financial turmoil.

Drawing on experiences and data from the financial crisis, Model Risk: Identification, Measurement and Management provides detailed analysis of the shortcomings in the design and application of modern risk models and offers solutions for better understanding and use in the post-crisis era. The book sets out how to include model risk into existing risk measurement frameworks solutions and how to build better models as a result.

Part one of the book begins by setting out frameworks for model risk. Four subsequent sections tackle the models financial institutions use by risk type:

Macroeconomic and Capital Models Credit Portfolio Risk Models Liquidity, Market and Operational Risk

Models Risk Transfer and Securitisation Models

Chapters address: Sensitivity of regulatory and

economic capital to market stress Systematic risk in a CDO

portfolio Transmission of macro shocks Improving estimations of

probably of default Cashflows from derivative

portfolios Adequacy of market risk models A new concept of potential

market risk

To date, model risk has lacked a clear definition. This book explains the different types of model risk; and illustrates these with experiences from the current financial crisis. Model Risk stands out as the guide to better risk management in uncertain times.

RiskIdentification, Measurement and Management

Model Risk

Model RiskIdentification, Measurement and Management

Edited by Harald Scheule and Daniel Rsch

Published by Risk Books, a Division of Incisive Financial Publishing Ltd

Haymarket House2829 HaymarketLondon SW1Y 4RXTel: + 44 (0)20 7484 9700Fax: + 44 (0)20 7484 9797E-mail: [email protected]: www.riskbooks.com

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2010 Incisive Media

ISBN 978-1-906348-25-0

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ContentsList of Figures ix

List of Tables xv

About the Editors xxi

About the Authors xxiii

Introduction xxxv

PART I CONCEPTS AND STOCHASTIC FRAMEWORKS FORMODEL RISK 1

1 Downturn Model Risk: Another View on the Global FinancialCrisis 3Daniel Rsch; Harald ScheuleLeibniz Universitt Hannover; The University of Melbourne

2 Follow the Money from Boom to Bust 19Jorge R. SobehartCiti Risk Architecture

3 Model Risk and Non-Gaussian Latent Risk Factors 45Steffi Hse and Stefan HuschensTechnische Universitt Dresden

4 Model Risk in Garch-Type Financial Time Series 75Corinna Luedtke, Philipp SibbertsenLeibniz Universitt Hannover

PART II MACROECONOMIC AND CAPITAL MODELS 91

5 Monetary Policy, Asset Return Dynamics and the GeneralEquilibrium Effect 93Kuang-Liang Chang; Nan-Kuang Chen; Charles Ka Yui LeungNational Chiayi University; National Taiwan University;City University of Hong Kong

6 Capital Divergence: Sensitivity of Economic and RegulatoryCapital under Stress 137Oleg BurdKfW IPEX-Bank GmbH

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MODEL RISK

PART III CREDIT PORTFOLIO RISK MODELS 153

7 Diversified Asset Portfolio Modelling: Sources andMitigants of Model Risk 155Sean Keenan, Stefano Santilli, Sukyul Suh;Andrew Barnes, Huaiyu Ma, Colin McCullochGE Capital; GE Global Research Center

8 Transmission of Macro Shocks to Loan Losses in a Deep Crisis:The Case of Finland 183Esa Jokivuolle; Matti Virn; Oskari VhmaaBank of Finland; University of Turku and Bank of Finland;University of Turku

9 Comparison of Credit-Risk Models for Portfolios of RetailLoans Based on Behavioural Scores 209Lyn C. Thomas; Madhur MalikUniversity of Southampton; Lloyds Banking Group

10 Validating Structural Credit Portfolio Models 233Michael Kalkbrener, Akwum OnwuntaDeutsche Bank AG

11 Asymmetric Asset Correlation: Some Implications for theEstimation of Probability of Default 263Peter Miu; Bogie OzdemirMcMaster University; BMO Financial Group

12 A Latent Variable Approach to Validate Credit Rating Systems 277Kurt Hornik, Rainer Jankowitsch, Christoph Leitner, Stefan Pichler;Manuel Lingo, Gerhard WinklerWirtschaftsuniversitt Wien; Oesterreichische Nationalbank

PART IV LIQUIDITY, MARKET AND OPERATIONAL RISKMODELS 297

13 Modelling Derivatives Cashflows in Liquidity Risk Models 299Stefan ReitzHochschule fr Technik Stuttgart

14 Potential Future Market Risk 315Manuela Spangler, Ralf WernerDeutsche Pfandbriefbank

15 Market Risk Modelling: Approaches to AssessingModel Adequacy 339Carsten S. WehnDekaBank

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CONTENTS

16 Estimation of Operational Value-at-Risk in the Presence ofMinimum Collection Threshold: An Empirical Study 359Anna Chernobai; Christian Menn; Svetlozar T. Rachev; Stefan TrckSyracuse University; DZ Bank AG; Universitt Karlsruhe,Finanalytica Inc, University of California at Santa Barbara;Macquarie University

17 Operational Risk and Hedge Fund Performance: Evidence fromAustralia 421Robin Luo, Xiangkang YinLa Trobe University

PART V RISK TRANSFER AND SECURITISATION MODELS 435

18 Identification and Classification of Model Risks inCounterparty Credit Risk Measurement Systems 437Marcus R. W. MartinUniversity of Applied Sciences, Darmstadt

19 Quantifying Systematic Risks in a Portfolio of CollateralisedDebt Obligations 457Martin Donhauser, Alfred Hamerle, Kilian PlankUniversity of Regensburg

Epilogue 489

Index 493

vii

List of Figures

1.1 Seasonally adjusted delinquency rates for all commercial USbanks 4

1.2 Through-the-cycle (TTC) model and a point-in-time (PIT)credit risk model 5

1.3 Credit-portfolio loss distributions 81.4 Volume of credit derivative transactions 91.5 Buyer of credit risk protection 101.6 Seller of credit risk protection 101.7 Average maturity of new credit derivatives 111.8 Interest and principal impairments of securitisations 121.9 Credit-portfolio loss distributions 121.10 Spread sensitivity of a senior tranche 131.11 Impairment rates by rating category 14

2.1 Distribution of normalised returns for the S&P 500 Index 322.2 Distribution of normalised returns for the DJI Index 322.3 Evolution of the marginal distribution of excess returns

p(, t) for = 1 and / = 0. 3 342.4 Evolution of the marginal distribution of log prices q(, t) for

= 1 and / = 0. 3 342.5 Comparison between the frequency of normalised returns

for the S&P 500 Index and Equation 2.20 for different timehorizons for the period 19502009 35

2.6 Comparison between the frequency of normalised returns forthe S&P 500 Index and Equation 2.20 as a function of thereduced variable w for different time horizons using thesame data as in Figure 2.5 36

2.7 Comparison between the frequency of normalised returns forthe DJI Index and Equation 2.20 for different time horizons inthe period 19282009 37

2.8 Comparison between the frequency of normalised returns forthe DJI Index and Equation 2.20 as a function of the reducedvariable w for different time horizons using the same data asin Figure 2.7 38

2.9 Comparison between the frequency of normalised returnsfor the FTSE Index and Equation 2.20 as a function of thereduced variable w for different time horizons in the period19842009 38

2.10 Comparison between the frequency of normalised returns forthe Nikkei Index and Equation 2.20 as a function of the

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MODEL RISK

reduced variable w for different time horizons in the period19842009 39

4.1 Quantilequantile plot of S&P 500 774.2 Returns of S&P 500 784.3 Autocorrelation function for squared returns of S&P 500 78

5.1 (a) Federal funds rate (FFR), (b) interest rate spread (SPR),(c) housing market returns (HRET) and (d) equity REITreturns (REIT) 101

5.2 Smoothed probabilities for the SVAR(1) model of (FFR, SPR,GDP, REIT) 106

5.3 Smoothed probabilities for the SVAR(1) model of (FFR, SPR,GDP, HRET) 106

5.4 Smoothed probabilities for the SVAR(1) model of (FFR, SPR,GDP, SRET) 107

5.5 Impulse responses of REIT to innovations in FFR when theeffect of SPR or GDP is shut off (FFR, SPR, GDP, REIT) 108

5.6 Impulse responses of HRET to innovations in FFR when theeffect of SPR or GDP is shut off (FFR, SPR, GDP, HRET) 109

5.7 Impulse responses of SRET to innovations in FFR when theeffect of SPR or GDP is shut off (FFR, SPR, GDP, SRET) 110

5.8 Simulation-based out-of-sample forecasts of stock returnswith 80% CI from 2006 Q1 to 2006 Q4 based on informationavailable at 2005 Q4 120



5.11 Simulation-based out-of-sample forecasts of housing returnswith 80% CI from 2006 Q1 to 2006 Q4 based on informationavailable at 2005 Q4 123



6.1 IRBA maturity adjustment as function of pd and maturity 1416.2 Maturity distribution of portfolio 1456.3 Regional distribution of portfolio 146

7.1 Risk streams requiring aggregation 1577.2 Accuracy of the mark-to-par algorithm 166

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LIST OF FIGURES

7.3 Comparison of the CCM and IPM loss distributions 1697.4 Conditional versus unconditional loss distribution 1727.5 Capital rates: portfolio model versus meta model 1757.6 Model implied capital rates versus PD by maturity band 1757.7 US public company default rates 1777.8 US public company default rates by sector 178

8.1 Industry-specific default rates 1848.2 Relationship between loan losses and the aggregate default

rate 1848.3 Comparison of OLS and SUR estimates of output gap for

different sectors 1938.4 The estimated average output gap annual LGD against the

actual LGD 1968.5 Distribution of loan losses (fixed LGD) 1998.6 Expected losses and the length of depression: feedback from

defaults to output 2008.7 Comparison of effects of macro shocks 2018.8 Fit of the constant LGD and the endogenous LGD loan-loss

models 203

9.1 Monte Carlo simulation run to calculate appropriate K value 2179.2 ROC curve for model A and model B of proportional hazards

example 222

12.1 Rating bias for bank/industry combinations g,j of the13 Austrian banks 289

12.2 Standard deviations g,j of the rating errors forbank/industry combinations of the 13 Austrian banks 289

12.3 Residual analysis for all 13 banks across the legal forms:limited and unlimited companies 292

12.4 Residual analysis for two banks (bank 13 and bank 8) acrossthe relative exposure 292

13.1 Exercise probabilities for a one-year call option 30613.2 Simulated paths of L(t, 5, 6) 30713.3 Probabilities for a positive cashflow at expiry 31013.4 Simulated paths of ln(S/K) and x() 312

14.1 Time series of risk factors from February 11, 2004, to July 17,2009 319

14.2 Historical values of (a) volatilities and (b) correlations 32014.3 Joint influence of interest rate and credit-spread level on

bond value at issuance 32214.4 Bond and portfolio values over time 32214.5 Portfolio sensitivity over time for Ni equal to 1 million 324

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MODEL RISK

14.6 Decomposition of total risk in interest rate risk andcredit-spread risk (at fixing dates) 324

14.7 Impact of ageing, interest rate and credit-spread levels onportfolio credit-spread sensitivity 325

14.8 Impact of sensitivity and covariance parameters on portfolioVaR 326

14.9 Interest rate and credit-spread paths obtained by historicalbootstrapping 332

14.10 Quantiles of simulated sensitivities over one year 33214.11 Quantiles of simulated volatilities over one year 33314.12 Potential future credit-spread VaR and actual credit-spread

VaR evolution under the bootstrapping model 33314.13 Potential future credit-spread VaR and actual credit-spread

VaR evolution under the bootstrapping model with stressedscenarios 335

15.1 Embedding the results of backtesting in a regular validationand backtesting process 353

16.1 Ratios of estimated parameters to the true (complete-data)parameter values, for the lognormal example, u = 50 368

16.2 Ratios of estimated fraction of missing data (Q) to the true(complete-data) fraction, for the lognormal example, u = 50 369

16.3 Ratios of estimated one-year EL, 95% VaR and 95% CVaR tothe true (complete-data) values, for the lognormal example,u = 50, = 100 370

16.4 Annual accumulated number of external operationallosses, with fitted cubic and Poisson models 372

16.5 Upper quantiles of fitted truncated loss distributions to theexternal-type losses, together with the empirical distribution 375

16.6 Fitted frequency functions to the operational losses 39216.7 Upper quantiles of fitted truncated loss distributions to

operational losses, together with the empirical distribution 397

17.1 Distribution of operational issues contributing to operationalrisk in hedge funds 422

18.1 Sample paths for EuroStoxx50 generated by a GBM ESG 43818.2 Sample paths for a call option on EuroStoxx50 43918.3 Counterparty exposure profile for a single uncollateralised

call option on EuroStoxx50 44018.4 Portfolio of a European put and call on the EuroStoxx50 44018.5 Three steps for generating exposure profiles and

counterparty measures 44218.6 Stressing the flat implied volatility assumption by a

deterministic time-dependence for illustrative purposes 447

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LIST OF FIGURES

19.1 Hitting-probability profiles of the BBB mezzanine trancheand a BBB bond 467

19.2 EL profiles of the BBB mezzanine tranche and a BBB bond 46819.3 Goodness of fit of approximated conditional expected loss 474

xiii

List of Tables

4.1 S&P 500: descriptive statistics 764.2 Declaration of models used 834.3 Parameters of the data-generating processes 834.4 DGP Garch(1,1)-N: mean squared error and p-values of the

DieboldMariano test 844.5 DGP EGarch(1,1)-N: mean squared error and p-values of the

DieboldMariano test 844.6 DGP GJR-Garch(1,1)-N: mean squared error and p-values of

the DieboldMariano test 854.7 DGP APArch(1,1)-N: mean squared error and p-values of the

DieboldMariano test 854.8 DGP FIGarch(1,1)-N: mean squared error and p-values of the

DieboldMariano test 864.9 DGP HYGarch(1,1)-N: mean squared error and p-values of

the DieboldMariano test 86

5.1 Statistical summary of federal funds rate, interest ratespread, housing market returns, and equity REIT returns(1975 Q22008 Q1) 100

5.2 Correlation coefficients (1975 Q22008 Q1) 1025.3 AIC values for various three-variable VAR(p) models of the

REIT system 1075.4 AIC values for various three-variable VAR(p) models of the

HRET system 1075.5 Statistical summary of federal funds rate, term spread, gross

domestic production growth rate, external finance premium,market liquidity, stock index return and housing marketreturn (1975 Q22008 Q3) 113

5.6 Correlation coefficients (1975 Q22008 Q3) 1145.7 List of models 1145.8 A summary of goodness of fit for all eight models 1175.9 A summary of in-sample forecasting performance

(four-quarter-ahead forecasts) 1185.10 A summary of out-of-sample forecasting performance

(four-quarter-ahead forecasts) 1195.11 Is the forecasted stock return within the 80% confidence

interval? 1265.12 Is the forecasted housing return within the 80% confidence

interval? 127

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MODEL RISK

5.13 Do models forecast stock return better in the presence ofhousing return? 127

5.14 Do models forecast housing return better in the presence ofstock return? 128

5.15 A summary of in-sample forecasting performances(four-quarter ahead forecasts) 129

5.16 A summary of out-of-sample forecasting performances(four-quarter ahead forecasts) 130

6.1 Asset correlation in IRBA and multi-factor models 1426.2 Rating distribution of portfolio 1436.3 Single name concentration in portfolio 1446.4 Regulatory and economic capital requirements as percentage

of total exposure 1446.5 Regulatory and economic capital requirements in various

stress scenarios 1476.6 Increase in regulatory capital requirements with constant

maturity and constant correlation 1476.7 Sensitivity (%) of regulatory capital requirements with fixed

maturity and stressed correlation of 28.4% 148

8.1 Estimation results of the basic default-rate model for thevarious industries 188

8.2 Diagnostic tests 1918.3 Summary of simulations 198

9.1 KolmogorovSmirnov (KS) results for alternative models 2179.2 Coefficients in the case study of the proportional hazard model 2209.3 Numbers of predicted and actual defaults in out of time

sample using proportional hazard models 2239.4 First-order stationary transition matrix 2269.5 Parameters for second-order Markov chain with age and

economic variables 2279.6 Results of default predictions for the two transition matrix

models 230

10.1 Asset correlations of rating cohorts 24610.2 intra-correlations (%) of industry cohorts 24710.3 Variation (%) of intra-correlations over time 25110.4 intra-correlations (%) using rating data 25510.5 Variation of intra-correlation (%) and log-likelihood function

with degrees of freedom 256

11.1 True parameters of the asymmetric correlation model 27011.2 Performance of LRPDave and LRPDcc in estimating

unconditional probability of default 272

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LIST OF TABLES

11.3 Summary statistics of the asset return correlation estimator 273

12.1 Descriptive statistics of the characteristics of the ratinginformation and the 13 Austrian banks in the data set 284

12.2 Distribution of the co-ratings of the 13 Austrian banks acrossindustries 285

12.3 Industry-specific means g and PD intervals measured inbasis points (104) 286

12.4 Rating bias g,j for bank/industry combinations of the13 Austrian banks 288

12.5 Standard deviations g,j of the rating errors forbank/industry combinations of the 13 Austrian banks 290

16.1 Fraction of missing data, F0(u), for the lognormal(0,0)example with nominal threshold of u = 50 369

16.2 Fitted frequency functions to the external"-type losses 37216.3 Estimated and F(u) values for the external-type

operational loss data 37416.4 Results of in-sample GOF tests for external-type

operational losses 37616.5 Estimates of expected aggregated loss, VaR and CVaR for

external-type losses 37716.6 Average estimates of forecast errors for external-type

aggregated losses 38016.7 LR statistic and p-values for external-type aggregated

losses in the seven-year forecast period 38416.8 Estimated and F(u) values for the external-type

operational loss data, under the robust approach 38616.9 Estimates of expected aggregated loss, VaR and CVaR for

external-type losses, under the robust approach 38716.10 Average estimates of forecast errors for external-type

aggregated losses, under the robust approach 38816.11 LR statistic and p-values for external-type aggregated

losses in the seven-year forecast period, under the robustapproach 390

16.12 Frequency functions fitted to the operational losses 39216.13 Estimated and F(u) values for the relationship,

human, processes and technology-type operationalloss data 393

16.14 Results of in-sample GOF tests for relationship-typeoperational losses 398

16.15 Results of in-sample GOF tests for human-type operationallosses 399

16.16 Results of in-sample GOF tests for process-type operationallosses 400

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MODEL RISK

16.17 Results of in-sample GOF tests for technology-typeoperational losses 401

16.18 Estimates of expected aggregated loss, VaR and CVaR forrelationship-type losses 402

16.19 Estimates of expected aggregated loss, VaR, and CVaR forhuman-type losses 403

16.20 Estimates of expected aggregated loss, VaR and CVaR forprocess-type losses 404

16.21 Estimates of expected aggregated loss, VaR and CVaR fortechnology-type losses 405

16.22 Average estimates of forecast errors for relationship-typeaggregated losses 406

16.23 Average estimates of forecast errors for human-typeaggregated losses 408

16.24 Average estimates of forecast errors for process-typeaggregated losses 410

16.25 Average estimates of forecast errors for technology-typeaggregated losses 412

16.26 LR statistic and p-values for relationship-type aggregatedlosses in the seven-year forecast period 414

16.27 LR statistic and p-values for human-type aggregated lossesin the seven-year forecast period 415

16.28 LR statistic and p-values for process-type aggregatedlosses in the seven-year forecast period 416

16.29 LR statistic and p-values for technology-type aggregatedlosses in the seven-year forecast period 417

17.1 Australian hedge funds: legal structure 42517.2 Descriptive statistics of Australian hedge funds 43017.3 Empirical results 431

19.1 Asset pool configuration 46219.2 Structure of liabilities 46219.3 Results: CDO risk measures 46519.4 Approximation results for the bond representation 47319.5 Risk measures for different portfolio sizes 47619.6 ABS CDO collateral pool composition 47919.7 Outer CDO structure based on expected tranche loss 47919.8 Risk measures for the ABS CDO 48019.9 Risk measures for thin mezzanine tranches 48219.10 Risk measures for thin senior tranche and super senior tranche 48319.11 Risk measures of investment alternatives 486

xviii

About the Editors

Harald Scheule teaches finance and banking in the Department ofFinance at the University of Melbourne. He has worked globallyas a consultant on credit risk, structured finance and securitisationprojects for banks, insurance and other financial service companies.He maintains strong research relationships with the Australian, Ger-man and Hong Kong regulators for financial institutions. He haspublished extensively and organised executive training courses inhis discipline.

Daniel Rsch is professor of finance and head of the Instituteof Banking and Finance at the Leibniz Universitt Hannover. Hereceived his PhD from the University of Regensburg. Daniels workcovers a broad range of subjects within asset pricing and empiricalfinance. He has published numerous articles on risk management,credit risk, banking and quantitative finance in leading internationaljournals. Daniel has also led numerous executive training coursesand is a consultant to financial institutions on credit risk issues.

xix

About the Authors

Andrew Barnes is a researcher at the Risk and Value Manage-ment Technologies Laboratory of the GE Global Research Centerin Niskayuna, New York. Since joining General Electric in 2004, hehas worked on quantitative finance problems with a focus on riskmeasurement and analysis for large commercial loan and asset port-folios. Before joining General Electric, Andrew spent several yearsworking on partial differential equations and electromagnetic scat-tering problems at Duke University. He holds a BS in mathemat-ics from Yale University, and a PhD in mathematics from DukeUniversity.

Joseph L. Breeden is president and chief operating officer of Strate-gic Analytics Inc. Joseph has spent the past 12 years designingand deploying risk management systems for retail loan portfolios.At Strategic Analytics, which he co-founded in 1999, he leads thedesign of advanced analytics and takes a leading role working withclient institutions. He has personally experienced and created mod-els through the 1995 Mexican peso crisis, the 1997 Asian economiccrisis, the 2001 global recession, the 2003 Hong Kong SARS recession,and the 2007 US mortgage debacle. These crises have provided himwith a unique perspective on crisis management and the analyticsneeds of executives for strategic decision-making. Joseph receivedseparate BS degrees in mathematics and physics in 1987 from Indi-ana University. He earned a PhD in physics in 1991 from the Uni-versity of Illinois. His thesis work involved real-world applicationsof chaos theory and genetic algorithms. In the mid 1990s, he was amember of the Santa Fe Institute. Since 1987, he has published morethan 40 articles in various journals on subjects including portfolioforecasting, economic capital, evolutionary computation, non-linearmodelling, astrophysics and nuclear physics.

Oleg Burd is a vice president in the risk management department ofKfW IPEX-Bank GmbH and specialises in measurement and man-agement of credit risk concentrations. His current responsibilitiesinclude credit-portfolio modelling as well as supervision and imple-mentation of active management of banks credit portfolio. Prior

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MODEL RISK

to joining KfW IPEX-Bank in 2004, Oleg worked at the Germanbranch of Maple Financial Group, Maple Bank, where he devel-oped, reviewed and implemented quantitative models for statisticalarbitrage trading. Oleg holds an MSc in economics and an MSc inmathematics, both from the University of Gttingen.

Kuang-Liang Chang received his MA and PhD at the National Tai-wan University in 1999 and 2004, respectively. He is an assistantprofessor at the Department of Applied Economics, National Chi-ayi University. Kuang-Liang has published in Applied Economics, TheManchester School and Economic Modelling, among other journals.

Nan-Kuang Chen received his BA and MA at the National TaiwanUniversity in 1987 and 1989, respectively, and his PhD at the Uni-versity of Minnesota in 1997. He is a professor in the Department ofEconomics, National Taiwan University. He was a visiting scholar atthe London School of Economics in 2003 and has published articlesin numerous journals on economics and real estate.

Anna S. Chernobai is an assistant professor of finance at the M. J.Whitman School of Management at Syracuse University, New York.The focus of her research is operational risk, default risk, stochasticprocesses, and applied statistics. She is an author of the book Opera-tional Risk: AGuide to Basel II Capital Requirements, Models, and Analysisand is an FDIC research fellow and JPMorgan Chase research fellow.Anna earned her PhD in statistics and applied probability from theUniversity of California at Santa Barbara in 2006. She also holds aMasters degree in finance from the Warwick Business School at theUniversity of Warwick, UK, and a Bachelors degree in economicsfrom Sophia University, Japan.

Martin Donhauser is a research assistant at the chair of statistics atthe University of Regensburg. He studied economics and previouslyworked as a consultant at Risk Research Prof. Hamerle GmbH, wherehe was mainly involved with the development and implementationof credit risk management techniques and solutions for medium-sized German banks and international financial institutions. Martinis finishing his doctoral dissertation. His research focuses on thevaluation and risk analysis of structured finance products and thedynamic modelling of credit risk.

Alfred Hamerle is a professor of statistics at the faculty of business,economics and information systems at the University of Regensburg.

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ABOUT THE AUTHORS

Prior to serving in his present position, he was professor of statisticsat the University of Konstanz and professor of statistics and econo-metrics at the University of Tbingen. He is the founder and CEO ofRisk Research Prof. Hamerle GmbH. His primary areas of researchinclude statistical and econometric methods in finance, credit riskmodelling and Basel II as well as multivariate statistics. Alfred haspublished eight books and more than 80 articles in scientific journals.

Kurt Hornik is the head of the Research Institute for ComputationalMethods and the chair of the Department of Statistics and Mathe-matics at the Vienna University of Economics and Business. He com-pleted his doctoral research and habilitation at the Vienna Universityof Technology. His research interests include statistical computing,statistical graphics, statistical and machine learning, data miningand a variety of application domains for quantitative data analysis,in particular quantitative risk management. Kurt has co-authoredaround 200 publications in refereed journals and conference pro-ceedings, is among the ISI 100 most highly cited researchers in theengineering category and holds the Gold Merit Decoration of theRepublic of Austria for his scientific achievements.

Steffi Hse is a postdoctoral fellow at the Technische UniversittDresden, Faculty of Business and Economics, and chair of quantita-tive methods, especially statistics, where she works in quantitativerisk analysis. Her current research focuses on credit risk manage-ment, in particular on the modelling of dependence structures bymeans of risk factor and mixture models, on the simultaneous esti-mation of dependence and default parameters and on the involvedmodel risk. Steffi has been a trainer in the SRP/IRB qualificationprogramme for supervisors of the Deutsche Bundesbank and theFederal Financial Supervisory Authority (Bundesanstalt fr Finanz-dienstleistungsaufsicht) since 2004. She holds an academic degreein business management and a doctoral degree from the TechnischeUniversitt Dresden.

Stefan Huschens holds the chair of quantitative methods, spe-cialising in statistics at the Technische Universitt Dresden. Heholds a doctoral degree in economics and a habilitation degree instatistics and economics from the Ruprecht-Karls-Universitt Hei-delberg. Stefan has been a trainer in the SRP/IRB qualificationprogramme for supervisors of the Deutsche Bundesbank and the

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MODEL RISK

Federal Financial Supervisory Authority (Bundesanstalt fr Finanz-dienstleistungsaufsicht) since 2004. His major research interestsare statistical and econometric methods of market and credit riskmanagement.

Rainer Jankowitsch is assistant professor of finance at the ViennaUniversity of Economics and Business. He completed his doctoralresearch at the University of Vienna and recently finished his habil-itation. His research is focused on credit and liquidity risk, banking,risk management and financial markets. In the past five years he haspublished in various finance journals such as the Journal of Bankingand Finance and The Journal of Risk. Rainer received the Best PaperAward from the German Finance Association in 2008 for his work onliquidity risk, which was produced in cooperation with New YorkUniversity. His current research is focused on the 20089 financialcrisis.

Esa Jokivuolle is a research supervisor in the Bank of FinlandsResearch Unit, specialising in financial markets research. He is alsoan adjunct professor of finance in the Helsinki School of Economics.Previously he worked in the Bank of Finlands Financial Markets andStatistics Department, and as a senior quantitative analyst in Leoniaplc in Helsinki. He has published several academic research articles.Esa earned a PhD in finance in 1996 from University of Illinois.

Michael Kalkbrener is head of the portfolio-modelling team withinthe risk analytics and instruments department of Deutsche Bankand he specialises in developing risk measurement and capital allo-cation methodologies. His responsibilities include credit-portfoliomodelling and the development of a quantitative model for oper-ational risk. Prior to joining Deutsche Bank in 1997, he worked atCornell University and the Swiss Federal Institute of Technology,where he received the Venia Legendi for mathematics. Michael holdsa PhD in mathematics from the Johannes Kepler University Linz. Hehas published numerous research articles on mathematical financeand scientific computation.

Sean Keenan is the portfolio analytics leader at GE Capital, respon-sible for credit risk systems and quantitative risk modelling. Prior tojoining GE he held quantitative research positions at Citigroup andMoodys Investors Service. He holds a PhD in economics and a BA

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ABOUT THE AUTHORS

in history, both from New York University. He has written a varietyof articles on quantitative credit risk topics and is regular speaker atconferences.

Christoph Leitner is a research assistant at the Department of Statis-tics and Mathematics, Vienna University of Economics and Busi-ness. His research interests focus on the analysis of ratings, in bothfinance and sports. He has recently contributed to several confer-ences and workshops on credit risk, including the Annual Meetingof the Southern Finance Association 2009. In the matter of sportsratings, he has contributed articles to the International Journal ofForecasting and to the proceedings of the 2nd International Confer-ence on Mathematics in Sport (IMA Sport 2009 in Groningen, TheNetherlands).

ManuelLingo is an analyst at Oesterreichische Nationalbank, wherehe is responsible for the development of operations of the InhouseCredit Assessment System (ICAS) used for Eurosystem monetaryoperations. Before joining Oesterreichische Nationalbank he workedas research assistant at the Vienna University of Economics and Busi-ness and as a freelance consultant for PricewaterhouseCoopers. Hepublishes in journals related to credit risk (The Journal of Credit Riskand The Journal of Risk Model Validation). His current research focuseson rating system development and validation. Manuel holds a PhDin finance from the Vienna University of Economics and Business.

Charles Ka Yui Leung received his BSc at the Chinese University ofHong Kong in 1991 and his PhD at the University of Rochester in1996. He taught at the Department of Economics, Chinese Universityof Hong Kong and is an associate professor at the the Department ofEconomics and Finance, City University of Hong Kong. He receivedthe Fulbright Scholarship (Research) in 20045 and has been a vis-iting scholar at both the Fisher Center for Real Estate and UrbanEconomics at the Haas School of Business, University of California,Berkeley and the Hoover Institution, Stanford University. He haspublished in the Journal of Monetary Economics, Journal of Urban Eco-nomics, Journal of Regional Science, Journal of Real Estate Finance andEconomics, Journal of Real Estate Research and Journal of Housing Eco-nomics, among other journals. He serves on the Editorial Board ofInternational Real Estate Review, the Board of Directors of the AsianReal Estate Society (AsRES) and the Board of Directors of the Global

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MODEL RISK

Chinese Real Estate Congress (GCREC). He also served as a guesteditor of the Journal of Housing Economics in 2007.

Corinna Luedtke is a PhD student at the Institute of Statistics atthe Leibniz Universitt Hannover. Her main research interests aretime series analysis and quantitative risk management. Corinnagraduated in economics and business administration at the LeibnizUniversitt Hannover in 2008.

Robin Luo is senior lecturer of finance at La Trobe University, Aus-tralia. Prior to joining La Trobe University, he taught and researchedat Auckland University of Technology in New Zealand, NanyangTechnological University in Singapore, and a couple of other tertiaryinstitutions in Asia. Dr Luo is a Financial Risk Manager (FRM), a Fel-low member of the Global Association of Risk Professionals (GARP),co-director of GARP Regional Chapter in Melbourne and director ofGARP College Chapter at La Trobe University. His current researchinterests focus on financial risk management, asset pricing, marketefficiency, international finance and Asia-Pacific financial markets.He has published in Economic Modelling, Applied Financial Economics,the Global Economy Journal and Applied Economics Letters.

Huaiyu (Harry) Ma is a statistician in the Applied Statistics Labat the GE Global Research Center. He received his PhD in decisionsciences and engineering systems from Rensselaer Polytechnic Insti-tute. His research interests include data analysis, simulation, time-series analysis, statistical computing and their applications in riskmanagement, engineering and online social networks problems.

Madhur Malik is a senior analyst with the Lloyds Banking Group,where he specialises in developing advanced financial models forportfolio credit risk, Basel II and macroeconomic time-series data.Prior to joining Lloyds Banking Group, he was a research fellowat the University of Southampton, where he applied a number ofinnovative approaches such as survival analysis and Markov chainsto estimate portfolio level credit risk of retail loans. Madhur holds aMasters degree in applied mathematics from the Indian Institute ofTechnology in Roorkee and a PhD in mathematics from the IndianStatistical Institute.

Marcus R. W. Martin is professor of financial mathematics andstochastics at the University of Applied Sciences in Darmstadt (Ger-many). From 2002 to 2008, he was with Deutsche Bundesbank,

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ABOUT THE AUTHORS

where he headed the Quantitative Risk Model Examination Group atHauptverwaltung Frankfurt of Deutsche Bundesbank from Novem-ber 2004. In this position he was responsible for conducting regula-tory audits of IRBA, IMM, IAA, internal market risk and liquidityrisk models of German banks. His current research interests focus onmodelling counterparty risk as well as asset liability, liquidity riskand commodity risk modelling.

Colin C. McCulloch is a statistician in the Applied Statistics Lab-oratory at the GE Global Research Center. He has worked in thearea of financial risk modelling for seven years. In that time hehas developed models of capital adequacy and capital allocation forGE Capitals credit and market risk exposures. Colin holds a PhDin statistics from Duke University and has published 14 articles inpeer-reviewed journals.

Christian Menn works as senior equity derivatives trader at DZBanks structured product division. Before joining DZ Bank, he heldthe position of equity derivatives trader at Sal. Oppenheim. Aftergaining his PhD in economics at the University of Karlsruhe, Chris-tian worked as visiting assistant professor at the School of Opera-tions Research at Cornell University. He holds a degree in mathe-matics from the University of Karlsruhe and the Universit JosephFourier in Grenoble.

Peter Miu is an associate professor of finance at DeGroote School ofBusiness, McMaster University. He teaches financial institutions aswell as international financial management at both the undergrad-uate and MBA levels. His research has been conducted primarily insuch areas as credit risk modelling and forecasting, pricing and riskmanagement of credit portfolios, and Basel II implementation andvalidation. He has consulted on a number of Basel II implementationprojects and is a frequent speaker at both academic and professionalconferences on credit risk and Basel II. Peter obtained his PhD andMBA in finance from the University of Toronto.

AkwumOnwunta is the Marie Curie Early Stage Research Fellow inthe COMISEF (Computational Optimization Methods in Statistics,Econometrics and Finance) project at Deutsche Bank, Frankfurt,Germany. He holds a BSc in mathematics, an MSc in physical andmathematical analysis and a Diplme Universitaire in mathematical

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MODEL RISK

models in economics and finance. His research is focused on creditrisk modelling.

Bogie Ozdemir is a vice president of the BMO Financial Groupresponsible for economic capital, stress testing, Basel analytics andjointly responsible for ICAAP. Previously he was a vice president inStandard & Poors Credit Risk Services group. In this role, he wasresponsible for globally engineering new products and solutions,business development and management. He has co-authored papersin The Journal of Credit Risk and published in the The Journal of RiskModel Validation. His joint paper Discount Rate for Workout Recov-eries: An Empirical Study with Brooks Brady, Peter Chang, PeterMiu and David Schwartz won the Best PaperAward at the Fifth NTUInternational Conference in 2007. Bogie has also co-authored a booktitled Basel II Implementation: A Guide to Developing and Validating aCompliant, Internal Risk Rating System.

StefanPichler is a professor and the chair of the Institute for Bankingand Finance at the Vienna University of Economics and Business.He completed his doctoral studies at the University of Graz andpreviously worked as an associate professor of finance at the ViennaUniversity of Technology. He has published numerous articles in theJournal of Banking and Finance, Review of Finance, Quantitative Financeand The Journal of Risk. His research focus is on risk management infinancial and public institutions.

Kilian Plank is a research assistant and lecturer at the Universityof Regensburg. In his doctoral dissertation he was concerned withstatistical modelling of growth processes in marketing. His researchfocuses on statistical modelling and analysis of structured creditproducts. Kilian has several years of work experience in the bankingindustry and is engaged in consulting projects at Risk Research Prof.Hamerle GmbH.

Svetlozar (Zari) Rachev holds the chair-professorship in statistics,econometrics and mathematical finance at the University of Karl-sruhe, and is the author of 12 books and over 300 published arti-cles on finance, econometrics, statistics and actuarial science. At theUniversity of California at Santa Barbara, Zari founded the PhD pro-gramme in mathematical and empirical finance. He holds PhD (1979)and Doctor of Science (1986) degrees from Moscow University and

xxviii

ABOUT THE AUTHORS

Russian Academy of Sciences. Zari was a co-founder and presidentof BRAVO Risk Management Group, which has been acquired byFinAnalytica, where he serves as chief scientist.

StefanReitzholds a PhD in mathematics and is professor of financialmathematics at the University of Applied Sciences in Stuttgart, Ger-many. He also works as a consultant in the financial industry in var-ious projects (risk controlling, risk management, pricing of deriva-tives). Prior to his current position he was an auditor and audit super-visor within the banking examination department of the DeutscheBundesbanks regional office in Frankfurt. He conducted interna-tional audits at major and regional banks in portfolio risk models,pricing of derivatives, risk management, minimum requirements fortrading activities and Basel II implementation.

Stefano Santilli is vice president of portfolio analytics at GE Capi-tal in Norwalk, CT, where he is responsible for portfolio modellingin the Risk Management department. Prior to joining GE in 2003,he worked as a credit risk controller with Dresdner Bank in Frank-furt, Germany, and as an account manager with Ersel Sim in Milan,Italy. Stefano holds an undergraduate degree in Business Adminis-tration from Bocconi University, a Masters degree in finance fromthe University of Alabama and is a CFA charterholder.

PhilippSibbertsen is professor for statistics and director of the Insti-tute of Statistics at the Leibniz Universitt Hannover. His researchinterests are in financial statistics and especially in statistical modelsfor measuring financial risk and time series econometrics. Philipphas numerous publications in these areas in highly ranked inter-national journals and is a regular speaker at conferences on thesetopics. He has also experience in applying statistical models to prac-tical problems. Philipp holds a Diploma in mathematics from theUniversity of Hamburg and a PhD in statistics from the Universityof Dortmund.

Jorge R. Sobehart is a managing director at Citigroup Risk Archi-tecture. He is involved in credit risk capital measures and allocation,stress testing, advanced portfolio loss models for wholesale expo-sures, credit migration and default risk models. Previously, he was amember of Moodys Standing Committee on Quantitative Tools andVP senior analyst in Moodys Risk Management Services, where

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MODEL RISK

he developed advanced default risk models, early warning toolsand model validation metrics and procedures. During his career, hehas worked and acted as a scientific consultant for several presti-gious companies and institutions making contributions in differ-ent fields. He has also acted as a referee for many professionaljournals in finance, physics and mathematical modelling. Jorge hasadvanced degrees in physics and has postdoctoral experience at theLos Alamos National Laboratory.

Manuela Spangler works as a financial engineer in the Risk Mod-elling team at Deutsche Pfandbriefbank. She studied financial math-ematics at the Technical University of Munich and at the NationalUniversity of Singapore. Her research interests include market riskmodelling and pricing of credit derivatives.

Sukyul Suh is vice president of portfolio modelling at GE Capital,responsible for performing economic capital analyses and develop-ing a risk modelling system for capital adequacy and capital allo-cation. Prior to joining GE Capital in 2000, Sukyul was a processengineer at SK energy, where he was responsible for improvingproduct quality and yield by applying statistical process control.He holds an MBA degree from the University of Minnesota and aBE degree in chemical engineering from Korea University. He is aCFA charterholder and a Certified Financial Risk Manager.

Lyn Thomas is professor of management science at the Universityof Southampton. His interests are in applying operational researchand statistical ideas in the financial area, particularly in credit scoringand risk modelling in consumer lending. He is a founder memberof the Credit Research Centre at the University of Edinburgh andone of the principal investigators for the Quantitative Financial RiskManagement Centre based at Southampton. He has authored or co-authored four books in the area, including Consumer Credit Models:Pricing, Profit and Portfolios and Credit Scoring and its Applications. Heis a Fellow of the Royal Society of Edinburgh, a past president of theOperational Research Society and was awarded the Beale Medal ofthat Society in 2008.

Stefan Trck is an associate professor in the economics departmentof Macquarie University, Sydney. He has held positions at Queens-land University of Technology and at the University of Karlsruhe in

xxx

ABOUT THE AUTHORS

Germany, where he received a PhD in statistics. His research inter-ests focus on risk management and financial econometrics includ-ing the fields of credit risk, operational risk, power markets andreal estate finance. He has several years of consulting experiencefor financial institutions and has published in various internationaljournals including The Journal of Banking and Finance, the EuropeanJournal of Finance, Energy Economics and The Journal of Credit Risk andhe is an author of the book Rating Based Modeling of Credit Risk: Theoryand Application of Migration Matrices.

Oskari Vhmaa is a PhD student in economics at the Universityof Turku. He has previously worked as a research assistant at theResearch Unit of the Bank of Finland.

Matti Virn is a professor of economics at the University of Turkuand a scientific advisor to the Bank of Finland. Previously he workedat the Bank of Finland as a research supervisor and in the FinnishGovernment Institute for Economic Research as the research direc-tor and as deputy director. He has published more than 100 arti-cles in refereed journals and books. He studied at the Universityof Chicago with a Fulbright scholarship, and gained his doctoraldegree (economics) from the University of Helsinki in 1980.

Carsten S. Wehn is head of market risk control at DekaBank, Frank-furt. Market risk control is responsible for the measurement of mar-ket and liquidity risk of the bank and the development of risk meth-ods and models as well as the validation of the adequacy of therespective risk models. Before joining DekaBank, he was responsiblefor supervising and conducting regulatory examinations for inter-nal market risk models with Deutsche Bundesbank. Carsten studiedin Siegen, Germany, as well as in Nantes, France. He holds a PhDin mathematics and regularly gives lectures at universities. He haspublished more than 30 articles and other publications includingthree books.

Ralf Werner heads the global Risk Methods & Valuation Depart-ment at Deutsche Pfandbriefbank and is mainly in charge of riskmethodology, financial engineering and economic capital mod-elling. Before joining Deutsche Pfandbriefbank, Ralf was responsi-ble for market risk methodology at Allianz Group Risk Controlling.In the past he has held positions as financial engineer for credit

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MODEL RISK

risk topics and as consultant for investment strategies and assetliability management at Risklab Germany, as well as prop trader(Xetra, Eurex) for SchmidtBank Nrnberg. Ralf publishes regularlyin finance- and optimisation-related journals and speaks at inter-national conferences. Since 2002, he has continuously supportedthe HVB Institute for Mathematical Finance at TU Mnchen as lec-turer for financial optimisation and simulation. Ralf holds a diplomaand a PhD in mathematics from the Friedrich Alexander UniversittErlangen-Nrnberg.

GerhardWinkler is deputy head of Oesterreichische Nationalbankscredit division. His research interests focus on credit risk measure-ment, risk model validation and bank efficiency. Before joining thecentral bank he worked as an assistant professor at the Instituteof Banking and Finance at the Vienna University of Economicsand Business, where he recently completed his habilitation. He isauthor of several academic publications in the field of financial riskmanagement and credit risk measurement.

Xiangkang Yin is a professor of economics and finance at La TrobeUniversity, Australia. His research interests cover a wide range oftopics in economics and finance, including capital asset pricing, cor-porate finance and governance, industrial organisation and appliedmicroeconomic theory. Prior to jointing La Trobe University, he heldvarious positions at Shanghai Jiaotong University, Universite LouisPasteur and Monash University. Xiangkang has published articlesin top-tier economics and finance journals, including The Journal ofFinance, Journal of Development Economics, Journal of Economic Behaviorand Organization and the Australian Journal of Management.

xxxii

Introduction

The 1970s witnessed the start of a new era in finance. Starting withthe BlackScholesMerton option pricing formula, sophisticatedmathematical models for pricing risky securities found their wayinto capital markets. Banks, insurance companies and hedge funds,among others, soon migrated to using these models for pricing,hedging, arbitrage or speculation.

At the same time the breakdown of the Bretton Woods systemrendered the financial world riskier and the increased use of riskmeasurement and management methods led to globalised, inter-dependent markets and strongly increasing trading volumes in moreand more complex financial instruments. Consequently, the risk oflarge failures due to mis-pricing and mismanagement increased andmany of these realised failures are still important objects in learn-ing lessons about the malfunctioning of risk models. Among others,these include the cases of Metallgesellschaft in 1993, the Bank ofTokyo and Mitsubishi in 1997 and NatWest Capital Markets in 1997and most recently the global financial crisis.

After introducing a global regulation framework for strength-ening the equity positions of financial institutions (the so-calledBasel Accord or Basel I), banks were allowed to calculate capitalcharges by using internal models for market risk, thereby honour-ing the industrys advances in risk measurement approaches. Sim-ilarly, Basel II acknowledges efforts made in recent years by basingregulatory capital on bank-internal credit-rating models.

Financial risk models have become increasingly important forfinancial institutions, markets and instruments. These models areindividually crafted and then generally assembled to generate port-folio measures. The occurrence of the 20089 global financial crisissuggests that many existing financial risk models were unable topredict the increase in loss rates prior to the crisis. This was partic-ularly true for new markets such as asset securitisations and creditderivatives. The consequence was a general loss in credibility, whichhas resulted in changes of economic and regulatory requirements.

The global financial crisis has resulted in changes for regulatoryrequirements. The Basel Enhancement to the Basel II framework

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(Basel Committee on Banking Supervision 2009) issued, in July, newrisk weights for rated resecuritisations and is stresses the importanceof bank internal due diligence processes:

A bank should conduct analyses of the underlying risks wheninvesting in the structured products and must not solely rely on theexternal credit ratings assigned to securitization exposures by thecredit rating agencies. Abank should be aware that external ratingsare a useful starting point for credit analysis, but are no substitutefor full and proper understanding of the underlying risk, espe-cially where ratings for certain asset classes have a short history orhave been shown to be volatile. Moreover, a bank also should con-duct credit analyses of the securitization exposure at acquisitionand on an ongoing basis. It should also have in place the necessaryquantitative tools, valuation models and stress tests of sufficientsophistication to reliably assess all relevant risks.

In addition to this, The Turner Review: ARegulatory Response tothe Global Banking Crisis (Financial Services Authority 2009) hasalso stressed the importance of increased capital ratios for marketrisk exposures to reflect the interaction between market and liquidityrisk.

One lesson learned is that risk models are substantial parts ofa sound risk management process and important ingredients forfinancial decision making. As important as risk models themselvesis knowledge about the limitations and shortcomings of the models,ie, the acknowledgement that risk models and their outcomes maybe wrong.

In the spirit of Socrates (we should be aware of our own igno-rance), this book is designed to illuminate shortcomings and toshow ways overcoming the limitations within sound risk manage-ment processes. The book examines the failings of existing financialrisk models, and shows ways to address this model risk in existingrisk measurement and management frameworks. A portfolio of casestudies, lessons learned and implications of the financial crisis arepresented. Twenty groups of authors from around the world havewritten contributions about their work experiences and results; theseare arranged into five parts, organised by various risk categories.

Part I shows concepts and stochastic frameworks for model risk.In Chapter 1 Daniel Rsch and Harald Scheule address the interac-tion of the economy and credit-portfolio model risk. In Chapter 2Jorge Sobehart investigates the role of imperfect information and

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INTRODUCTION

investors behaviour. In Chapter 3 Steffi Hse and Stefan Huschensmeasure model risk in relation to non-Gaussian latent risk factors.After defining model risk in general, they show the impact of apotential misspecification of the factor distributions on credit riskmeasures and derive upper and lower bounds for the value-at-risk.In Chapter 4 Corinna Luedtke and Philipp Sibbertsen analyse time-series properties of value-at-risk. They compare Garch-type modelswith respect to their in-sample robustness and their out-of-sampleperformance when the value-at-risk is forecasted using alternativemodel specifications. They show that various stylised facts may havea serious impact on forecasting errors.

Part II looks at model risk in general economic and capital models.In Chapter 5 Kuang-Liang Chang, Nan-Kuang Chen and Charles KaYui Leung analyse asset return dynamics and monetary policy. OlegBurd (Chapter 6) shows ways to manage economic and regulatorycapital through the business cycle. He finds that economic capitalis much more sensitive to stress scenarios than regulatory capital,mainly due to maturity adjustment and asset correlation specifica-tion, and that this fact must be taken into account in the capitalmanagement process.

Part III focuses on credit risk models. Chapter 7 Andrew Barnes,Sean Keenan, Harry Ma, Colin McColloch, Stefano Santilli andSukyul Suh present their experiences on credit risk models dur-ing the financial crisis. Esa Jokivuolle, Oskari Vhmaa and MattiVirn (Chapter 8) show the transmission of macro shocks to loanlosses. Lyn Thomas and Madhur Malik (Chapter 9) compare creditrisk models for portfolios of retail loans based on behaviouralscores. Michael Kalkbrener and Akwum Onwunta (Chapter 10) val-idate structural credit-portfolio models. They review moment andmaximum-likelihood estimators for intra- and inter-sector asset cor-relations under different distributional assumptions and analysetheir ability to capture the dependence structures. Peter Miu andBogie Ozdemir (Chapter 11) show the implications on estimatingand validating the probability of default if asset correlations arestochastic. Finally, Kurt Hornik, Rainer Jankowitsch, Christoph Leit-ner, Manuel Lingo, Stefan Pichler and Gerhard Winkler (Chapter 12)focus on rating validation in terms of tests of the accuracy of prob-ability of default estimates and present a latent variable approachto validate credit rating systems. Using a large sample of Austrian

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banks and obligors, the authors conduct an extensive benchmarkingexercise.

Part IV combines liquidity, market and operational risk models. InChapter 13 Stefan Reitz addresses liquidity in derivatives contracts.He shows how pricing models can be used to derive the expectedcashflow for non-path-dependent and path-dependent derivatives.Manuela Spangler and Ralf Werner (Chapter 14) are concerned withthe quantification of market risk over longer horizons. They derivethe concept of potential future market risk, a promising approachsimilar to the concept of potential future exposure in counterpartycredit risk. In Chapter 15 Carsten Wehn focuses on market risk mod-els. He systematically addresses the most common model errors inmarket risk and provides an overview of the most recent back-testingapproaches.Anna Chernobai, Christian Menn, Svetlozar Rachev andStefan Trck (Chapter 16) develop operational risk models for value-at-risk in the presence of data biases. Robin Luo and Xiangkang Yin(Chapter 17) analyse the operational risk for hedge funds.

Part V looks at risk transfer and securitisation models. In Chap-ter 18 Marcus Martin models counterparty risk for over-the-counterderivatives and develops a framework for addressing model riskissues therein. Martin Donhauser, Alfred Hamerle and Kilian Plank(Chapter 19) quantify the systematic risk of securitisations by con-sidering various risk measures. The authors introduce the concept ofa bond representation and examine typical pooling and structuringapproaches with respect to their systematic risk exposure.

ACKNOWLEDGEMENTSWe thank Joe Breeden for writing the epilogue to this book. We arevery grateful for the support from Lucie Carter and Jennifer Gibbfrom Risk Books and Journals for their tremendous help in man-aging the editing process. We hope that the book will provide newinsights for practitioners and regulators, as well as researchers onapplications, regulations and techniques presented in this book andwe encourage the reader to share any thoughts and experiences withour community.

Daniel Rsch and Harald ScheuleMelbourne and Hannover, November 2009

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Part I

Concepts and StochasticFrameworks for ModelRisk

1Downturn Model Risk: AnotherView on the Global Financial Crisis

Daniel Rsch; Harald ScheuleLeibniz Universitt Hannover; The University of Melbourne

Researchers and practitioners have spent ample resources mod-elling credit, explaining correlations between risk models as wellas inputs and outputs. One popular example is asset correlation,which describes the co-movement between the asset value returnsof corporate borrowers or issuers. Other examples are default cor-relations, correlations between default and recovery processes andcorrelations between risk categories such as credit, interest, liquidityor market risk.

In statistical terms, correlations are often placeholders for relation-ships which cannot be explained and are also known as seemingcorrelations. The 20089 global financial crisis caught us by sur-prise and showed that, starting with US subprime mortgage mar-kets, other markets such as equity, credit and commodity marketshave declined globally. These links have not been included into exist-ing risk models, and this chapter identifies these links and showshow to address these relationships in risk models.

We show that the insufficient incorporation of economic infor-mation into valuation models for financial instruments may partlyexplain why the financial industry was unable to predict, mitigateand cover the recent losses. Economic downturns are generally well-known. Unfortunately, to date the financial industry has struggled toincorporate econometric properties into forecasting models. Thesemodels were often propagated by the industry and supported bya number of academic studies on the information content of creditratings.

We do not claim, nor intend, to address the financial crisis compre-hensively in this chapter, and other experts have put complementary

3

MODEL RISK

Figure 1.1 Seasonally adjusted delinquency rates for all commercialUS banks

0

2

4

6

8

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Del

inqu

ency

rate

(%)

Business loansLoans secured by real estate

Source: Board of Governors of the US Federal Reserve System and authors cal-culations. Delinquency rates are the ratios of the US dollar amount of a banksdelinquent loans to the US dollar amount of total loans outstanding in that category.

proposals forward (Hull 2009; Crouhy et al 2008; Franke and Krah-nen 2008). Their explanations mainly focus on misaligned incentivestructures and a lack of transparency as a consequence thereof. Thischapter provides another perspective on the lack of transparency:the ignorance of risk models with regard to econometric proper-ties of risk, as well as the assessment of model risk. Credit and creditderivative markets may not be able to recover unless these importantissues have been resolved.

CREDIT RISK AND BUSINESS CYCLESFigure 1.1 shows a proxy for credit-portfolio risk, the delinquencyrate. It is apparent that the delinquency rate, and thus credit risk,changes over time and follows cyclical patterns. For instance, theyears 1991 (first Gulf War) and 20012 (terrorist attacks on the US)were periods of high delinquency rates for business loans. Delin-quency rates for business loans have changed surprisingly little dur-ing the current (20089) financial crisis, while loans secured by realestate have dramatically increased.

Generally speaking, the risk may be measured by two funda-mentally different approaches (Rsch and Scheule 2005). Firstly, wecan take the average over the business cycle; this is known as thethrough-the-cycle (TTC) approach. Secondly, we can try to measure

4

DOWNTURN MODEL RISK: ANOTHER VIEW ON THE GLOBAL FINANCIAL CRISIS

Figure 1.2 Through-the-cycle (TTC) model and a point-in-time (PIT)credit risk model

0

2

4

6

8

1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007

Del

inqu

ency

rate

(%) GAP

GAP

GAP

Delinquency rateTTCPIT

Source:Board of Governors of the US Federal Reserve System.Delinquency ratesare the ratios of the US dollar amount of a banks delinquent loans to the US dollaramount of total loans outstanding in that category. A TTC model assumes theaverage default rate for every period. A PIT model forecasts the default rate basedon an empirical model.

the credit risk for a given point in time; this is known as the point-in-time (PIT) approach. PIT models are generally based on forecastmodels, which explain the credit risk for a future point in time, byinformation which is available at the time when the forecast is made.

Figure 1.2 shows the real delinquency rate for loans secured byreal estate, as well as the estimated delinquency rate by a TTC modeland a PIT model.

It can be seen that neither model estimates the default rate accu-rately. However, PIT models generally approximate the default ratebetter for most points in time. Thus, a PIT model reflects the realitymuch better and should be the aim of every sound risk measurementframework.

Unfortunately, the majority of the financial industry focuses onTTC approaches. Various reasons for this deserve to be mentioned.

Simplicity. TTC approaches have gained acceptance becausethey offer simplicity. PIT models have been propagated butestimated based on modest recent loss experiences due to lim-ited data availability. In other words, building a risk modelbased on the experience of multiple boom years may beinadequate to provision for credit losses during downturns.

5

MODEL RISK

Regulatory requirements. Regulators have accepted both TTCand PIT methods but have often preferred TTC methods(Financial Services Authority 2009). In addition, with the intro-duction of Basel II, the concern was raised that the capitalof financial institutions may fluctuate with the credit riskassessment during the business cycle. This pro-cyclicality mayrequire the issue of new capital during an economic downturnwhen capital is expensive or restricted in availability. In otherwords, regulators tried to avoid pro-cyclicality by acceptingrisk models which do not take the current state of the economyinto account. The current crisis demonstrated that accountingpractice implies a pro-cyclical capital requirement for marketrisk exposures, as the accounting values of marketable assetsbased on current market values, delinquent credit exposuresare provisioned for and defaulted credit exposures are writtenoff.

Guidance by rating agencies. Rating agencies provide cate-gorical ratings; common rating categories are AAA (Aaa), AA(Aa), A (A), BBB (Baa), BA (Ba), B (B), CCC (Caa), CC (Ca) andC (C) for Standard & Poors rating agency and Fitch ratingagency (Moodys rating agency). These agencies have histor-ically propagated TTC models and have explicitly excludedthe economy and focused on idiosyncratic risk drivers whichwere considered to be fundamental. For these efforts, creditratings reflect an opaque mix of a TTC and PIT model out-put, as some idiosyncratic information naturally reflects thebusiness cycle. As a result, the degree of cyclicality which isembedded in public credit ratings is difficult to assess andinvestors are uncertain as to whether they should associatetime-constant, time-varying (or a mix of both) default rates tothese ratings categories. Rating agencies may have no incen-tive to change this opaque practice, as the crucial calibrationstep (ie, the conversion from categorical ratings to numericdefault rates needed by modern risk models) lies within theresponsibility of investors.

The result of using a through-the-cycle approach is obvious: themodel positively surprises in an economic boom, as the loss out-come is less than predicted by the model and disappoints in an eco-nomic downturn (eg, the 20089 financial crisis) as the loss outcome

6


is higher than predicted by the model. As a result, parties that reliedon these models were disappointed in the 20089 crisis. This maybe confirmed by the public criticism of rating agencies during thecurrent and previous financial crises.

CORRELATIONSIn credit-portfolio risk measurement, correlations play a central role.Credit defaults happen very rarely and a corporate borrower oftenceases to exist after a default event. Thus, for any given pair ofborrowers, it may be difficult to estimate correlations, as multipledefault observations are not available. Some financial institutionsapply expert values between zero and one. For instance, the defaultcorrelation for two borrowers which are part of the same holdingcompany may be set to one.

This apparent co-movement is generally driven by systematic riskfactors and may be quantified by specifying an econometric factormodel or correlations if a credit-portfolio risk model is unable orunwilling to include parts of the systematic (economic) informa-tion. In other words, correlations may be derived which capture thegap between a portfolios actual and a models predicted credit loss.Figure 1.2 shows that the gap is dependent on the period as well asthe applied model. In other words, the chosen model methodology(TTC or PIT) has a major impact on the correlations. The correlationis high for a TTC model and low for a PIT model. This is empiri-cally confirmed by a number of studies including Rsch and Scheule(2005).1

Generally speaking, the econometric estimation of correlationsrequires the availability of long data histories, ie, multiples of wholebusiness cycles. Note that the estimation of correlations is more com-plicated for securitisations such as asset-backed securities, collater-alised debt obligations and mortgage-backed securities. Many ofthese products have been issued recently and long default historiesare unavailable. We will refer to this point below.

CREDIT PORTFOLIO RISKSCredit-portfolio risk models aggregate the risk characteristics forindividual borrowers on a portfolio level. The financial industry hasidentified a set of key risk drivers which are probabilities of default,

7

MODEL RISK

Figure 1.3 Credit-portfolio loss distributions

0 10 20 30 40 50 60 70 80 90 100

PIT (boom) PD = 0.5%PIT (recess.) PD = 10%TTC PD = 1%

Portfolio loss (%)

Den

sity

A TTC model assumes the average default rate for every period. A PIT modelforecasts the default rate based on an empirical model.

loss rates given default, exposures at default and default correla-tions. Alarge literature exists for every one of these parameters. Notethat default events are often generated based on so-called asset valuemodels, which rely on asset rather than default correlations. Proba-bilities of default, loss rates given default and exposures at defaultdescribe expectations for random variables. For example, a proba-bility of default generally describes the expectation of occurrence, ie,the likelihood of a default event during an observation period. Con-trarily, the default or non-default observation describes the outcomeof this random variable.

In an uncertain world, the credit loss of a portfolio is random,and modern credit-portfolio risk measurement focuses on the quan-tification of the loss distribution. A loss distribution describes thefrequency for various levels of future losses. Figure 1.3 shows thatthe loss distribution depends on the risk of the individual borrow-ers (eg, the probability of default, PD) as well as the correlations (eg,the asset correlation). Figure 1.3 shows three loss distributions: oneis based on a PIT model during an economic boom, one is basedon a TTC model and the other is based on a PIT model during aneconomic downturn.

In this example, the 99.9th percentile which is often used as aproxy for credit-portfolio risk is 7%, 15% and 46%. This may lead tothe interpretation that during an economic downturn the PIT modelmay provide the highest risk assessment and thus the highest levelof capital, and thus the highest required level of protection for credit

8


Figure 1.4 Volume of credit derivative transactions

0

5,000

10,000

15,000

20,000

25,000

30,000

35,000

200220012000 2003 20062004 2008

Glo

bal c

redi

t der

ivtive

s vo

lum

e(U

S$ bi

llion)

1996 1998 1999

Source: British Bankers Association.

losses. Conversely, financial institutions which rely on TTC modelsdramatically underestimate credit-portfolio risks during economicdownturns (15% versus the reasonable number of 46%)! Similar con-clusions may be drawn for other risk parameters such as loss ratesgiven default and the correlation between the default and recoveryprocesses (Rsch and Scheule 2009a, 2010).

SECURITISATIONSSecuritisations involve a real or synthetic sale of an asset portfolio toinvestors. Common assets are of a financial nature such as insurancepolicies, leases or loans. Many securitisations involve large mone-tary values and investors are pooled. Important investors are gen-erally large financial institutions and hedge funds. Some countrieslike Australia and New Zealand enable retail investors (also knownas mums and dads) to trade a small selection of such securities atpublic exchanges. The following figures describe the credit deriva-tive market prior to the financial crisis. Figure 1.4 shows that theglobal monetary volume of credit derivatives has increased expo-nentially during the past decade. Credit derivative and securitisa-tion markets shared similar trends in the past. The numbers for 2008are projections made before the financial crisis. Figure 1.5 identifiesbanks and hedge funds as the main buyers of credit protection, whileFigure 1.6 identifies banks, insurance companies and hedge fundsas the main sellers of credit protection. Figure 1.7 shows that the

9

MODEL RISK

Figure 1.5 Buyer of credit risk protection

8070

90

5040

60

20100

30Fr

actio

n of

glo

bal m

arke

t (%)

Banks Hedgefunds

Corporate Insurance Others

2000 2002 2004 2006 2008


Figure 1.6 Seller of credit risk protection

70

50

40

60

20

10

0

30

Frac

tion

of g

loba

l mar

ket (%

)

Banks Hedgefunds

Corporate Insurance Others

2000 2002 2004 2006 2008


maturities of new securitisations are generally between one and fiveyears.

Different investors have different requirements in relation to theriskreturn profile of their investments. Thus, large asset securi-tisations generally involve the separation (tranching) of investorsinto distinct riskreturn categories where the proceeds from theasset portfolio are forwarded according to an agreed set of rules.Most securitisations have a unique structure which may or may notbe different from the examples presented here. The International

10


Figure 1.7 Average maturity of new credit derivatives

50

40

60

20

10

0

30

Frac

tion

of g

loba

l mar

ket (%

)

10 years

2000 2002 2004 2006 2008


Swaps and Derivatives Association (ISDA)2 has published guide-lines to improve the standardisation of securitisations and creditderivatives.

In the example presented, investors invest in a junior tranche,a mezzanine tranche and a senior tranche. The yield to maturitydecreases from the junior to the senior tranche. Typical yields mayinclude a credit spread (above a reference rate) of 30% for juniorinvestors, 3% for mezzanine investors and 50 basis points for seniorinvestors. Generally, 10% of the total investment amount may beraised with junior investors, 20% with mezzanine investors and 70%with senior investors.

The proceeds are forwarded to the senior, then to the mezzanineand lastly to the junior investors according to predetermined rules ifthe asset portfolio cashflows are sufficient. The junior tranche is alsoknown as the equity tranche due to this conditional and thus residualpayout policy. If a tranche does not receive an agreed payment, it isimpaired. The concept of impairment is comparable to the conceptof default for loans. Impairment is most likely to happen upon thepayment of the largest contractual amount: the principal. Figure 1.8shows that principal impairments are far more common than interestimpairments.

In addition, Figure 1.8 shows that the number of impairmentsincreased dramatically during the GFC. There may be severalreasons for this. Firstly, the economy is currently3 experiencing a

11

MODEL RISK

Figure 1.8 Interest and principal impairments of securitisations

Interest payment yearPrincipal payment year

Impa

irmen

t rat

e

0.2

0

0.4

0.6

0.8

1.0

1997 1999 2001 2003 2005 2007

Source: Rsch and Scheule (2009b), Moodys credit rating agency. Impairmentscomprise principal and interest impairments. Principal impairments include secu-rities that have suffered principal write-downs or principal losses at maturity andsecurities that have been downgraded to Ca/C, even if they have not yet experi-enced an interest shortfall or principal write-down. Interest impairments, or interest-impaired securities, include securities that are not principal impaired and haveexperienced only interest shortfalls.

Figure 1.9 Credit-portfolio loss distributions

Junior Mezz. Senior

Den

sity

Portfolio loss (%)0 10 20 30 40 50 60 70 80 90 100

PIT (boom), PD = 0.5%TTC, PD = 1%PIT (recess.), PD = 10%

A TTC model assumes the average default rate for every period. A PIT modelforecasts the default rate based on an empirical model.

downturn. In particular the asset class US mortgage loans are expe-riencing a major stress. Secondly, a comparison of Figures 1.1 and 1.4reveals that the growth in the securitisation market occurred dur-ing an economic boom, ie, good years. This has the implicationthat no market participant has a loss experience, which comprisesa whole business cycle to calibrate econometric models. Thirdly, a

12


Figure 1.10 Spread sensitivity of a senior tranche

0

20

40

60

80

100

0

40

80

120

160

200Sp

read

(bp)

Spre

ad(m

illions

,% of

5% be

nchm

ark)

Spread (bp)Spread (% of 5% benchmark)

0 0.1 0.2 0.3 0.4 0.5Correlation

comparison of Figures 1.8, 1.4 and 1.7 provides evidence that prin-cipal impairments are the most common, that most securitisationswere originated in recent years (ie, the past 15 years) and that mostsecuritisations pay back the principal after 15 years. These factorsmay explain the low impairment rates in recent years which areno longer true. Fourthly, market participants may have relied onTTC models. Figure 1.9 shows the implications for the example fromFigure 1.3 (junior tranche equals 10%, mezzanine tranche 20% andsenior tranche 70% of total assets).

It is obvious that the attachment probability is higher for the mez-zanine and senior tranches during an economic downturn and thePIT model. As the PIT model is more accurate than the TTC model,the use of the latter results in a dramatic underestimation of creditrisk for mezzanine and senior tranches during economic downturns.The attachment probabilities for losses for the mezzanine tranche are0.4% in the TTC model and 39.8% in the PIT (recession) model. Theattachment probabilities for losses for the senior tranche are 0% inthe TTC model and 2% in the PIT (recession) model. In summary, aTTC rating model may underestimate the risk to the mezzanine andthe senior tranches dramatically.

Generally speaking, tranche credit risk as measured by a riskmodel is crucially influenced by the rating methodology and thecorrelations used in the model. Chernih et al (2006) show that thecorrelation may vary from 0.5% to 45%, depending on the estimationmethodology and the data used.

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MODEL RISK

Figure 1.11 Impairment rates by rating category

1997 1999 2001 2003 2005 2007

0.8

0.6

0.4

0.2

0

Impa

irmen

t rat

e

AaaA Baa Ba B

Source: Rsch and Scheule (2009b), Moodys credit rating agency. Impairmentrates per Moodys rating category. A TTC model results in increased default orimpairment rates during an economic downturn such as the financial crisis.

As an example for the correlation sensitivity of tranches, considera tranching which employs a simple credit risk model to calculatethe fair spread of the senior tranche. Figure 1.10 shows on the leftaxis that the implied spread of the tranche is close to zero for low cor-relations and increases monotonically with the correlation. The rightaxis exhibits the spread measured relatively to the spread which isbased on a correlation benchmark of 5%. For higher correlations thespread may be up to a multiple of many hundreds of thousand timesof the benchmark.

Rating agencies are one of the most prominent proponents of TTCmodels as well as levels of asset correlations. Figure 1.11 shows theimpairment rates of securitisations rated by Moodys rating agency.

The impairment rates per rating category fluctuate over time asthe ratings are TTC. See Rsch and Scheule (2009b) for a discussionof the performance of public credit ratings of securitisations.

CATALYST I: RESECURITISATIONSIt was shown by Hull (2008) that demand for medium-rated mezza-nine tranches was limited before the 20089 financial crisis. Hence,the originating institutions pooled unsold mezzanine tranches andresecuritised these assets, which led to a new set of junior, mezza-nine and senior investment tranches. Resecuritisations are found to

14


magnify the problem presented in the previous section. The impliedcorrelations may be higher for resecuritisations than for plain vanillaasset securitisations.

CATALYST II: CONCENTRATION OF THE MODEL PROVIDER,FINANCIAL INTERMEDIATION AND MODEL AUDITINGINDUSTRYThe model provider, financial intermediation and model auditingindustry are highly concentrated. The concentration leads to sys-temic risk. Several examples suffice: the small number of credit rat-ing agencies for bond and structured finance issues; the growingmarket share of too big to fail financial institutions; joint ven-tures in model construction designed to reduce costs. The problem iscompounded by the use of similar quantitative frameworks and/orframeworks which are calibrated based on similar loss experiences.An anecdote illustrates this point: some years ago the chief risk offi-cer of a major US bank presented the asset correlation matrix usedby that institution. Another major financial institution present atthe event confirmed its use of the same matrix. While the institu-tions were fundamentally different in nature, they shared the samereputable consulting firm. To date, the firms model has not beenformally validated. The oligopolistic structure was nurtured andpromoted by the data available to a limited few as well as by thepropensity of financial institutions to outsource risk modelling.

WHAT LESSONS CAN BE LEARNED GOING FORWARD?Franke and Krahnen (2008) show that structured finance transac-tions offer many benefits such as improved risk allocation and diver-sification. Therefore, a strict ban of securitisations may contradictmarket efficiency. However, the lack of transparency leads to illiq-uidity of the associated assets and liabilities and is thus a majordriver of the current financial crisis. Appropriate risk measurementand management may have to complement government financialstability programmes to provide equity, debt or financial guarantees.

Our main objective in this chapter was to show the impact ofthe economy on credit-portfolio risk and derivative products. Theinclusion of the impact of the economy is paramount to a sound mea-surement and management of credit-portfolio risks. Historically, the

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MODEL RISK

financial industry did not exploit all the available econometric infor-mation. Transparency may increase with the econometric forecastingof credit-portfolio risks. Credibility in internal and external modelsmay not be restored otherwise.

The following complementary suggestions may contribute addi-tional elements for a new framework of global financial markets.

Homogenisation and refinement of regulationThis chapter recommends changes in regulations for the followingareas.

Bank models should be point-in-time and be able to forecastthe credit risk for future periods with a reasonable degree ofaccuracy.

Regulation should address pro-cyclicality. Firstly, it has to bedetermined whether financial institution capital should bepro-cyclical, neutral or countercyclical. While regulators inthe past have

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