Model Risk

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od el Ris k Ed ite d B y D an iel Rö sch a nd H ara ld S ch eu le EditEd By daniEl Rösch and haRald schEulE

Model

PEFC Certified This book has been produced entirely from sustainable papers that are accredited as PEFC 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.

Risk

Identification,

Measurement

and Management

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Model Risk

Identification, Measurement and Management

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Haymarket House 28–29 Haymarket London SW1Y 4RX Tel: + 44 (0)20 7484 9700 Fax: + 44 (0)20 7484 9797 E-mail: [email protected] Sites: www.riskbooks.com www.incisivemedia.com © 2010 Incisive Media ISBN 978-1-906348-25-0

British Library Cataloguing in Publication Data

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Publisher: Nick Carver

Commissioning Editor: Lucie Carter Managing Editor: Jennifer Gibb Designer: Lisa Ling

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Warning: the doing of any unauthorised act in relation to this work may result in both civil and criminal liability.

Every effort has been made to ensure the accuracy of the text at the time of publication, this includes efforts to contact each author to ensure the accuracy of their details at publication is correct. However, no responsibility for loss occasioned to any person acting or refraining from acting as a result of the material contained in this publication will be accepted by the copyright owner, the editor, the authors or Incisive Media.

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List of Figures ix

List of Tables xv

About the Editors xxi

About the Authors xxiii

Introduction xxxv

PART I CONCEPTS AND STOCHASTIC FRAMEWORKS FOR

MODEL RISK 1

1 Downturn Model Risk: Another View on the Global Financial

Crisis 3

Daniel Rösch; Harald Scheule

Leibniz Universität Hannover; The University of Melbourne

2 Follow the Money from Boom to Bust 19

Jorge R. Sobehart Citi Risk Architecture

3 Model Risk and Non-Gaussian Latent Risk Factors 45

Steffi Höse and Stefan Huschens Technische Universität Dresden

4 Model Risk in Garch-Type Financial Time Series 75

Corinna Luedtke, Philipp Sibbertsen Leibniz Universität Hannover

PART II MACROECONOMIC AND CAPITAL MODELS 91

5 Monetary Policy, Asset Return Dynamics and the General

Equilibrium Effect 93

Kuang-Liang Chang; Nan-Kuang Chen; Charles Ka Yui Leung National Chiayi University; National Taiwan University; City University of Hong Kong

6 Capital Divergence: Sensitivity of Economic and Regulatory

Capital under Stress 137

Oleg Burd

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PART III CREDIT PORTFOLIO RISK MODELS 153

7 Diversified Asset Portfolio Modelling: Sources and

Mitigants of Model Risk 155

Sean Keenan, Stefano Santilli, Sukyul Suh; Andrew Barnes, Huaiyu Ma, Colin McCulloch GE Capital; GE Global Research Center

8 Transmission of Macro Shocks to Loan Losses in a Deep Crisis:

The Case of Finland 183

Esa Jokivuolle; Matti Virén; Oskari Vähämaa

Bank of Finland; University of Turku and Bank of Finland; University of Turku

9 Comparison of Credit-Risk Models for Portfolios of Retail

Loans Based on Behavioural Scores 209

Lyn C. Thomas; Madhur Malik

University of Southampton; Lloyds Banking Group

10 Validating Structural Credit Portfolio Models 233

Michael Kalkbrener, Akwum Onwunta Deutsche Bank AG

11 Asymmetric Asset Correlation: Some Implications for the

Estimation of Probability of Default 263

Peter Miu; Bogie Ozdemir

McMaster University; BMO Financial Group

12 A Latent Variable Approach to Validate Credit Rating Systems 277

Kurt Hornik, Rainer Jankowitsch, Christoph Leitner, Stefan Pichler; Manuel Lingo, Gerhard Winkler

Wirtschaftsuniversität Wien; Oesterreichische Nationalbank

PART IV LIQUIDITY, MARKET AND OPERATIONAL RISK

MODELS 297

13 Modelling Derivatives Cashflows in Liquidity Risk Models 299

Stefan Reitz

Hochschule für Technik Stuttgart

14 Potential Future Market Risk 315

Manuela Spangler, Ralf Werner Deutsche Pfandbriefbank

15 Market Risk Modelling: Approaches to Assessing

Model Adequacy 339

Carsten S. Wehn DekaBank

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16 Estimation of Operational Value-at-Risk in the Presence of

Minimum Collection Threshold: An Empirical Study 359

Anna Chernobai; Christian Menn; Svetlozar T. Rachev; Stefan Trück Syracuse University; DZ Bank AG; Universität Karlsruhe, Finanalytica Inc, University of California at Santa Barbara; Macquarie University

17 Operational Risk and Hedge Fund Performance: Evidence from

Australia 421

Robin Luo, Xiangkang Yin La Trobe University

PART V RISK TRANSFER AND SECURITISATION MODELS 435

18 Identification and Classification of Model Risks in

Counterparty Credit Risk Measurement Systems 437

Marcus R. W. Martin

University of Applied Sciences, Darmstadt

19 Quantifying Systematic Risks in a Portfolio of Collateralised

Debt Obligations 457

Martin Donhauser, Alfred Hamerle, Kilian Plank University of Regensburg

Epilogue 489

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1.1 Seasonally adjusted delinquency rates for all commercial US

banks 4

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

credit risk model 5

1.3 Credit-portfolio loss distributions 8

1.4 Volume of credit derivative transactions 9

1.5 Buyer of credit risk protection 10

1.6 Seller of credit risk protection 10

1.7 Average maturity of new credit derivatives 11 1.8 Interest and principal impairments of securitisations 12

1.9 Credit-portfolio loss distributions 12

1.10 Spread sensitivity of a senior tranche 13 1.11 Impairment rates by rating category 14 2.1 Distribution of normalised returns for the S&P 500 Index 32 2.2 Distribution of normalised returns for the DJI Index 32 2.3 Evolution of the marginal distribution of excess returns

p(ξ, t)forβ=1 andη/θ=0. 3 34 2.4 Evolution of the marginal distribution of log prices q(χ, t)for

β=1 andη/θ=0. 3 34

2.5 Comparison between the frequency of normalised returns for the S&P 500 Index and Equation 2.20 for different time

horizons for the period 1950–2009 35

2.6 Comparison between the frequency of normalised returns for the S&P 500 Index and Equation 2.20 as a function of the reduced variable w for different time horizons using the

same data as in Figure 2.5 36

2.7 Comparison between the frequency of normalised returns for the DJI Index and Equation 2.20 for different time horizons in

the period 1928–2009 37

2.8 Comparison between the frequency of normalised returns for the DJI Index and Equation 2.20 as a function of the reduced variable w for different time horizons using the same data as

in Figure 2.7 38

2.9 Comparison between the frequency of normalised returns for the FTSE Index and Equation 2.20 as a function of the reduced variable w for different time horizons in the period

1984–2009 38

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

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reduced variable w for different time horizons in the period

1984–2009 39

4.1 Quantile–quantile plot of S&P 500 77

4.2 Returns of S&P 500 78

4.3 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 REIT

returns (REIT) 101

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

GDP, REIT) 106

GDP, HRET) 106

GDP, SRET) 107

5.5 Impulse responses of REIT to innovations in FFR when the effect of SPR or GDP is shut off (FFR, SPR, GDP, REIT) 108 5.6 Impulse responses of HRET to innovations in FFR when the

effect of SPR or GDP is shut off (FFR, SPR, GDP, HRET) 109 5.7 Impulse responses of SRET to innovations in FFR when the

effect of SPR or GDP is shut off (FFR, SPR, GDP, SRET) 110 5.8 Simulation-based out-of-sample forecasts of stock returns

with 80% CI from 2006 Q1 to 2006 Q4 based on information

available at 2005 Q4 120

5.9 Simulation-based out-of-sample forecasts of stock returns with 80% CI from 2007 Q1 to 2007 Q4 based on information

5.10 Simulation-based out-of-sample forecasts of stock returns with 80% CI from 2008 Q1 to 2008 Q3 based on information

5.11 Simulation-based out-of-sample forecasts of housing returns with 80% CI from 2006 Q1 to 2006 Q4 based on information

6.1 IRBA maturity adjustment as function of pd and maturity 141

6.2 Maturity distribution of portfolio 145

6.3 Regional distribution of portfolio 146

7.1 Risk streams requiring aggregation 157

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7.3 Comparison of the CCM and IPM loss distributions 169 7.4 Conditional versus unconditional loss distribution 172 7.5 Capital rates: portfolio model versus meta model 175 7.6 Model implied capital rates versus PD by maturity band 175

7.7 US public company default rates 177

7.8 US public company default rates by sector 178

8.1 Industry-specific default rates 184

8.2 Relationship between loan losses and the aggregate default

rate 184

8.3 Comparison of OLS and SUR estimates of output gap for

different sectors 193

8.4 The estimated average output gap annual LGD against the

“actual” LGD 196

8.5 Distribution of loan losses (fixed LGD) 199 8.6 Expected losses and the length of depression: feedback from

defaults to output 200

8.7 Comparison of effects of macro shocks 201 8.8 Fit of the constant LGD and the endogenous LGD loan-loss

models 203

9.1 Monte Carlo simulation run to calculate appropriate K value 217 9.2 ROC curve for model A and model B of proportional hazards

example 222

12.1 Rating bias for bank/industry combinationsµg,jof the

13 Austrian banks 289

12.2 Standard deviationsσg,jof the rating errors for

bank/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) across

the relative exposure 292

13.1 Exercise probabilities for a one-year call option 306

13.2 Simulated paths of L(t, 5, 6) 307

13.3 Probabilities for a positive cashflow at expiry 310 13.4 Simulated paths of ln(Sτ/K)and x(τ) 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 320 14.3 Joint influence of interest rate and credit-spread level on

bond value at issuance 322

14.4 Bond and portfolio values over time 322 14.5 Portfolio sensitivity over time for Niequal to€1 million 324

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14.6 Decomposition of total risk in interest rate risk and

credit-spread risk (at fixing dates) 324 14.7 Impact of ageing, interest rate and credit-spread levels on

portfolio credit-spread sensitivity 325 14.8 Impact of sensitivity and covariance parameters on portfolio

VaR 326

14.9 Interest rate and credit-spread paths obtained by historical

bootstrapping 332

14.10 Quantiles of simulated sensitivities over one year 332 14.11 Quantiles of simulated volatilities over one year 333 14.12 Potential future credit-spread VaR and actual credit-spread

VaR evolution under the bootstrapping model 333 14.13 Potential future credit-spread VaR and actual credit-spread

VaR evolution under the bootstrapping model with stressed

scenarios 335

15.1 Embedding the results of backtesting in a regular validation

and 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 to

the true (complete-data) values, for the lognormal example,

u=50,λ=100 370

16.4 Annual accumulated number of “external” operational

losses, with fitted cubic and Poisson models 372 16.5 Upper quantiles of fitted truncated loss distributions to the

“external”-type losses, together with the empirical distribution 375 16.6 Fitted frequency functions to the operational losses 392 16.7 Upper quantiles of fitted truncated loss distributions to

operational losses, together with the empirical distribution 397 17.1 Distribution of operational issues contributing to operational

risk in hedge funds 422

18.1 Sample paths for EuroStoxx50 generated by a GBM ESG 438 18.2 Sample paths for a call option on EuroStoxx50 439 18.3 Counterparty exposure profile for a single uncollateralised

call option on EuroStoxx50 440

18.4 Portfolio of a European put and call on the EuroStoxx50 440 18.5 Three steps for generating exposure profiles and

counterparty measures 442

18.6 Stressing the flat implied volatility assumption by a

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19.1 Hitting-probability profiles of the BBB mezzanine tranche

and a BBB bond 467

19.2 EL profiles of the BBB mezzanine tranche and a BBB bond 468 19.3 Goodness of fit of approximated conditional expected loss 474

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4.1 S&P 500: descriptive statistics 76

4.2 Declaration of models used 83

4.3 Parameters of the data-generating processes 83 4.4 DGP Garch(1,1)-N: mean squared error and p-values of the

Diebold–Mariano test 84

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

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

the Diebold–Mariano test 85

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

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

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

the Diebold–Mariano test 86

5.1 Statistical summary of federal funds rate, interest rate spread, housing market returns, and equity REIT returns

(1975 Q2–2008 Q1) 100

5.2 Correlation coefficients (1975 Q2–2008 Q1) 102 5.3 AIC values for various three-variable VAR(p) models of the

REIT system 107

5.4 AIC values for various three-variable VAR(p) models of the

HRET system 107

5.5 Statistical summary of federal funds rate, term spread, gross domestic production growth rate, external finance premium, market liquidity, stock index return and housing market

return (1975 Q2–2008 Q3) 113

5.6 Correlation coefficients (1975 Q2–2008 Q3) 114

5.7 List of models 114

5.8 A summary of goodness of fit for all eight models 117 5.9 A summary of in-sample forecasting performance

(four-quarter-ahead forecasts) 118

5.10 A summary of out-of-sample forecasting performance

(four-quarter-ahead forecasts) 119

5.11 Is the forecasted stock return within the 80% confidence

interval? 126

5.12 Is the forecasted housing return within the 80% confidence

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5.13 Do models forecast stock return better in the presence of

housing return? 127

5.14 Do models forecast housing return better in the presence of

stock 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 142

6.2 Rating distribution of portfolio 143

6.3 Single name concentration in portfolio 144 6.4 Regulatory and economic capital requirements as percentage

of total exposure 144

6.5 Regulatory and economic capital requirements in various

stress scenarios 147

6.6 Increase in regulatory capital requirements with constant

maturity and constant correlation 147

6.7 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 the

various industries 188

8.2 Diagnostic tests 191

8.3 Summary of simulations 198

9.1 Kolmogorov–Smirnov (KS) results for alternative models 217 9.2 Coefficients in the case study of the proportional hazard model 220 9.3 Numbers of predicted and actual defaults in out of time

sample using proportional hazard models 223 9.4 First-order stationary transition matrix 226 9.5 Parameters for second-order Markov chain with age and

economic variables 227

9.6 Results of default predictions for the two transition matrix

models 230

10.1 Asset correlations of rating cohorts 246 10.2 intra-correlations (%) of industry cohorts 247 10.3 Variation (%) of intra-correlations over time 251 10.4 intra-correlations (%) using rating data 255 10.5 Variation of intra-correlation (%) and log-likelihood function

with degrees of freedom 256

11.1 “True” parameters of the asymmetric correlation model 270 11.2 Performance of LRPDaveand LRPDccin estimating

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11.3 Summary statistics of the asset return correlation estimator 273 12.1 Descriptive statistics of the characteristics of the rating

information and the 13 Austrian banks in the data set 284 12.2 Distribution of the co-ratings of the 13 Austrian banks across

industries 285

12.3 Industry-specific meansνgand PD intervals measured in

basis points (10−4₎ ₂₈₆

12.4 Rating biasµg,jfor bank/industry combinations of the

13 Austrian banks 288

12.5 Standard deviationsσg,jof the rating errors for

bank/industry combinations of the 13 Austrian banks 290 16.1 Fraction of missing data, Fγ0(u), for the lognormal(µ0,σ0)

example with nominal threshold of u=50 369 16.2 Fitted frequency functions to the “external"-type losses 372 16.3 Estimatedγand Fγ(u)values for the “external”-type

operational loss data 374

16.4 Results of in-sample GOF tests for “external”-type

operational losses 376

16.5 Estimates of expected aggregated loss, VaR and CVaR for

“external”-type losses 377

16.6 Average estimates of forecast errors for “external”-type

aggregated losses 380

16.7 LR statistic and p-values for “external”-type aggregated

losses in the seven-year forecast period 384 16.8 Estimatedγand Fγ(u)values for the “external”-type

operational loss data, under the “robust” approach 386 16.9 Estimates of expected aggregated loss, VaR and CVaR for

“external”-type losses, under the “robust” approach 387 16.10 Average estimates of forecast errors for “external”-type

aggregated losses, under the “robust” approach 388 16.11 LR statistic and p-values for “external”-type aggregated

losses in the seven-year forecast period, under the “robust”

approach 390

16.12 Frequency functions fitted to the operational losses 392 16.13 Estimatedγand Fγ(u)values for the “relationship”,

“human”, “processes” and “technology”-type operational

loss data 393

16.14 Results of in-sample GOF tests for “relationship”-type

16.15 Results of in-sample GOF tests for “human”-type operational

losses 399

16.16 Results of in-sample GOF tests for “process”-type operational

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16.17 Results of in-sample GOF tests for “technology”-type

“relationship”-type losses 402

16.19 Estimates of expected aggregated loss, VaR, and CVaR for

“human”-type losses 403

“process”-type losses 404

“technology”-type losses 405

16.22 Average estimates of forecast errors for “relationship”-type

16.23 Average estimates of forecast errors for “human”-type

16.24 Average estimates of forecast errors for “process”-type

16.25 Average estimates of forecast errors for “technology”-type

16.26 LR statistic and p-values for “relationship”-type aggregated losses in the seven-year forecast period 414 16.27 LR statistic and p-values for “human”-type aggregated losses

in the seven-year forecast period 415

16.28 LR statistic and p-values for “process”-type aggregated

losses in the seven-year forecast period 416 16.29 LR statistic and p-values for “technology”-type aggregated

losses in the seven-year forecast period 417 17.1 Australian hedge funds: legal structure 425 17.2 Descriptive statistics of Australian hedge funds 430

17.3 Empirical results 431

19.1 Asset pool configuration 462

19.2 Structure of liabilities 462

19.3 Results: CDO risk measures 465

19.4 Approximation results for the bond representation 473 19.5 Risk measures for different portfolio sizes 476 19.6 ABS CDO collateral pool composition 479 19.7 Outer CDO structure based on expected tranche loss 479

19.8 Risk measures for the ABS CDO 480

19.9 Risk measures for thin mezzanine tranches 482 19.10 Risk measures for thin senior tranche and super senior tranche 483 19.11 Risk measures of investment alternatives 486

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Harald Scheuleteaches finance and banking in the Department of Finance at the University of Melbourne. He has worked globally as a consultant on credit risk, structured finance and securitisation projects 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 has published extensively and organised executive training courses in his discipline.

Daniel Rösch is professor of finance and head of the Institute of Banking and Finance at the Leibniz Universität Hannover. He received his PhD from the University of Regensburg. Daniel’s work covers a broad range of subjects within asset pricing and empirical finance. He has published numerous articles on risk management, credit risk, banking and quantitative finance in leading international journals. Daniel has also led numerous executive training courses and is a consultant to financial institutions on credit risk issues.

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Andrew Barnes is a researcher at the Risk and Value Manage-ment Technologies Laboratory of the GE Global Research Center in Niskayuna, New York. Since joining General Electric in 2004, he has worked on quantitative finance problems with a focus on risk measurement and analysis for large commercial loan and asset port-folios. Before joining General Electric, Andrew spent several years working 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 mathematmathemat-ics from Duke University.

Joseph L. Breedenis president and chief operating officer of Strate-gic Analytics Inc. Joseph has spent the past 12 years designing and deploying risk management systems for retail loan portfolios. At Strategic Analytics, which he co-founded in 1999, he leads the design of advanced analytics and takes a leading role working with client institutions. He has personally experienced and created mod-els through the 1995 Mexican peso crisis, the 1997 Asian economic crisis, the 2001 global recession, the 2003 Hong Kong SARS recession, and the 2007 US mortgage debacle. These crises have provided him with a unique perspective on crisis management and the analytics needs of executives for strategic decision-making. Joseph received separate 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 applications of chaos theory and genetic algorithms. In the mid 1990s, he was a member of the Santa Fe Institute. Since 1987, he has published more than 40 articles in various journals on subjects including portfolio forecasting, economic capital, evolutionary computation, non-linear modelling, astrophysics and nuclear physics.

Oleg Burdis a vice president in the risk management department of KfW IPEX-Bank GmbH and specialises in measurement and man-agement of credit risk concentrations. His current responsibilities include credit-portfolio modelling as well as supervision and imple-mentation of active management of bank’s credit portfolio. Prior

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to joining KfW IPEX-Bank in 2004, Oleg worked at the German branch of Maple Financial Group, Maple Bank, where he devel-oped, reviewed and implemented quantitative models for statistical arbitrage trading. Oleg holds an MSc in economics and an MSc in mathematics, both from the University of Göttingen.

Kuang-Liang Changreceived his MA and PhD at the National Tai-wan University in 1999 and 2004, respectively. He is an assistant professor at the Department of Applied Economics, National Chi-ayi University. Kuang-Liang has published in Applied Economics, The

Manchester School and Economic Modelling, among other journals. Nan-Kuang Chenreceived his BA and MA at the National Taiwan University in 1987 and 1989, respectively, and his PhD at the Uni-versity of Minnesota in 1997. He is a professor in the Department of Economics, National Taiwan University. He was a visiting scholar at the London School of Economics in 2003 and has published articles in numerous journals on economics and real estate.

Anna S. Chernobaiis 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, stochastic processes, and applied statistics. She is an author of the book

Opera-tional Risk: A Guide to Basel II Capital Requirements, Models, and Analysis

and is an FDIC research fellow and JPMorgan Chase research fellow. Anna earned her PhD in statistics and applied probability from the University of California at Santa Barbara in 2006. She also holds a Masters degree in finance from the Warwick Business School at the University of Warwick, UK, and a Bachelor’s degree in economics from Sophia University, Japan.

Martin Donhauseris a research assistant at the chair of statistics at the University of Regensburg. He studied economics and previously worked as a consultant at Risk Research Prof. Hamerle GmbH, where he was mainly involved with the development and implementation of credit risk management techniques and solutions for medium-sized German banks and international financial institutions. Martin is finishing his doctoral dissertation. His research focuses on the valuation and risk analysis of structured finance products and the dynamic modelling of credit risk.

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

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Prior to serving in his present position, he was professor of statistics at the University of Konstanz and professor of statistics and econo-metrics at the University of Tübingen. He is the founder and CEO of Risk Research Prof. Hamerle GmbH. His primary areas of research include statistical and econometric methods in finance, credit risk modelling and Basel II as well as multivariate statistics. Alfred has published eight books and more than 80 articles in scientific journals.

Kurt Hornikis the head of the Research Institute for Computational Methods 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 University of Technology. His research interests include statistical computing, statistical graphics, statistical and machine learning, data mining and a variety of application domains for quantitative data analysis, in particular quantitative risk management. Kurt has co-authored around 200 publications in refereed journals and conference pro-ceedings, is among the ISI 100 most highly cited researchers in the “engineering” category and holds the Gold Merit Decoration of the Republic of Austria for his scientific achievements.

Steffi Höseis a postdoctoral fellow at the Technische Universität Dresden, Faculty of Business and Economics, and chair of quantita-tive methods, especially statistics, where she works in quantitaquantita-tive risk analysis. Her current research focuses on credit risk manage-ment, in particular on the modelling of dependence structures by means of risk factor and mixture models, on the simultaneous esti-mation of dependence and default parameters and on the involved model risk. Steffi has been a trainer in the SRP/IRB qualification programme for supervisors of the Deutsche Bundesbank and the Federal Financial Supervisory Authority (Bundesanstalt für Finanz-dienstleistungsaufsicht) since 2004. She holds an academic degree in business management and a doctoral degree from the Technische Universität Dresden.

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

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Federal Financial Supervisory Authority (Bundesanstalt für Finanz-dienstleistungsaufsicht) since 2004. His major research interests are statistical and econometric methods of market and credit risk management.

Rainer Jankowitschis assistant professor of finance at the Vienna University of Economics and Business. He completed his doctoral research 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 has published in various finance journals such as the Journal of Banking

and Finance and The Journal of Risk. Rainer received the Best Paper

Award from the German Finance Association in 2008 for his work on liquidity risk, which was produced in cooperation with New York University. His current research is focused on the 2008–9 financial crisis.

Esa Jokivuolle is a research supervisor in the Bank of Finland’s Research Unit, specialising in financial markets research. He is also an adjunct professor of finance in the Helsinki School of Economics. Previously he worked in the Bank of Finland’s Financial Markets and Statistics Department, and as a senior quantitative analyst in Leonia plc in Helsinki. He has published several academic research articles. Esa earned a PhD in finance in 1996 from University of Illinois.

Michael Kalkbreneris head of the portfolio-modelling team within the risk analytics and instruments department of Deutsche Bank and he specialises in developing risk measurement and capital allo-cation methodologies. His responsibilities include credit-portfolio modelling and the development of a quantitative model for oper-ational risk. Prior to joining Deutsche Bank in 1997, he worked at Cornell University and the Swiss Federal Institute of Technology, where he received the Venia Legendi for mathematics. Michael holds a PhD in mathematics from the Johannes Kepler University Linz. He has published numerous research articles on mathematical finance and scientific computation.

Sean Keenanis the portfolio analytics leader at GE Capital, respon-sible for credit risk systems and quantitative risk modelling. Prior to joining GE he held quantitative research positions at Citigroup and Moody’s Investor’s Service. He holds a PhD in economics and a BA

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in history, both from New York University. He has written a variety of articles on quantitative credit risk topics and is regular speaker at conferences.

Christoph Leitneris a research assistant at the Department of Statis-tics and MathemaStatis-tics, Vienna University of Economics and Busi-ness. His research interests focus on the analysis of ratings, in both finance and sports. He has recently contributed to several confer-ences and workshops on credit risk, including the Annual Meeting of the Southern Finance Association 2009. In the matter of sports ratings, he has contributed articles to the International Journal of

Forecasting and to the proceedings of the 2nd International

Confer-ence on Mathematics in Sport (“IMA Sport 2009” in Groningen, The Netherlands).

Manuel Lingois an analyst at Oesterreichische Nationalbank, where he is responsible for the development of operations of the Inhouse Credit Assessment System (ICAS) used for Eurosystem monetary operations. Before joining Oesterreichische Nationalbank he worked as research assistant at the Vienna University of Economics and Busi-ness and as a freelance consultant for PricewaterhouseCoopers. He publishes in journals related to credit risk (The Journal of Credit Risk and The Journal of Risk Model Validation). His current research focuses on rating system development and validation. Manuel holds a PhD in finance from the Vienna University of Economics and Business.

Charles Ka Yui Leungreceived his BSc at the Chinese University of Hong Kong in 1991 and his PhD at the University of Rochester in 1996. He taught at the Department of Economics, Chinese University of Hong Kong and is an associate professor at the the Department of Economics and Finance, City University of Hong Kong. He received the Fulbright Scholarship (Research) in 2004–5 and has been a vis-iting scholar at both the Fisher Center for Real Estate and Urban Economics at the Haas School of Business, University of California, Berkeley and the Hoover Institution, Stanford University. He has published in the Journal of Monetary Economics, Journal of Urban

Eco-nomics, Journal of Regional Science, Journal of Real Estate Finance and Economics, Journal of Real Estate Research and Journal of Housing Eco-nomics, among other journals. He serves on the Editorial Board of International Real Estate Review, the Board of Directors of the Asian

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

Corinna Luedtkeis a PhD student at the Institute of Statistics at the Leibniz Universität Hannover. Her main research interests are time series analysis and quantitative risk management. Corinna graduated in economics and business administration at the Leibniz Universität Hannover in 2008.

Robin Luois senior lecturer of finance at La Trobe University, Aus-tralia. Prior to joining La Trobe University, he taught and researched at Auckland University of Technology in New Zealand, Nanyang Technological University in Singapore, and a couple of other tertiary institutions 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 of GARP College Chapter at La Trobe University. His current research interests focus on financial risk management, asset pricing, market efficiency, 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) Mais a statistician in the Applied Statistics Lab at the GE Global Research Center. He received his PhD in decision sciences and engineering systems from Rensselaer Polytechnic Insti-tute. His research interests include data analysis, simulation, time-series analysis, statistical computing and their applications in risk management, engineering and online social networks problems.

Madhur Malikis a senior analyst with the Lloyds Banking Group, where he specialises in developing advanced financial models for portfolio credit risk, Basel II and macroeconomic time-series data. Prior to joining Lloyds Banking Group, he was a research fellow at the University of Southampton, where he applied a number of innovative approaches such as survival analysis and Markov chains to estimate portfolio level credit risk of retail loans. Madhur holds a Master’s degree in applied mathematics from the Indian Institute of Technology in Roorkee and a PhD in mathematics from the Indian Statistical Institute.

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

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where he headed the Quantitative Risk Model Examination Group at Hauptverwaltung 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 liquidity risk models of German banks. His current research interests focus on modelling counterparty risk as well as asset liability, liquidity risk and commodity risk modelling.

Colin C. McCullochis a statistician in the Applied Statistics Lab-oratory at the GE Global Research Center. He has worked in the area of financial risk modelling for seven years. In that time he has developed models of capital adequacy and capital allocation for GE Capital’s credit and market risk exposures. Colin holds a PhD in statistics from Duke University and has published 14 articles in peer-reviewed journals.

Christian Menn works as senior equity derivatives trader at DZ Bank’s structured product division. Before joining DZ Bank, he held the position of equity derivatives trader at Sal. Oppenheim. After gaining 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 Université Joseph Fourier in Grenoble.

Peter Miuis an associate professor of finance at DeGroote School of Business, McMaster University. He teaches financial institutions as well as international financial management at both the undergrad-uate and MBA levels. His research has been conducted primarily in such areas as credit risk modelling and forecasting, pricing and risk management of credit portfolios, and Basel II implementation and validation. He has consulted on a number of Basel II implementation projects and is a frequent speaker at both academic and professional conferences on credit risk and Basel II. Peter obtained his PhD and MBA in finance from the University of Toronto.

Akwum Onwuntais the Marie Curie Early Stage Research Fellow in the 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 and mathematical analysis and a Diplôme Universitaire in mathematical

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

Bogie Ozdemir is a vice president of the BMO Financial Group responsible for economic capital, stress testing, Basel analytics and jointly responsible for ICAAP. Previously he was a vice president in Standard & Poor’s Credit Risk Services group. In this role, he was responsible for globally engineering new products and solutions, business development and management. He has co-authored papers in The Journal of Credit Risk and published in the The Journal of Risk

Model Validation. His joint paper “Discount Rate for Workout

Recov-eries: An Empirical Study” with Brooks Brady, Peter Chang, Peter Miu and David Schwartz won the Best Paper Award at the Fifth NTU International Conference in 2007. Bogie has also co-authored a book titled Basel II Implementation: A Guide to Developing and Validating a

Compliant, Internal Risk Rating System.

Stefan Pichleris a professor and the chair of the Institute for Banking and Finance at the Vienna University of Economics and Business. He completed his doctoral studies at the University of Graz and previously worked as an associate professor of finance at the Vienna University of Technology. He has published numerous articles in the

Journal of Banking and Finance, Review of Finance, Quantitative Finance

and The Journal of Risk. His research focus is on risk management in financial and public institutions.

Kilian Plank is a research assistant and lecturer at the University of Regensburg. In his doctoral dissertation he was concerned with statistical modelling of growth processes in marketing. His research focuses on statistical modelling and analysis of structured credit products. Kilian has several years of work experience in the banking industry and is engaged in consulting projects at Risk Research Prof. Hamerle GmbH.

Svetlozar (Zari) Rachevholds 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 the University 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

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

Stefan Reitzholds a PhD in mathematics and is professor of financial mathematics 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 Deutsche Bundesbank’s 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 for trading activities and Basel II implementation.

Stefano Santilliis vice president of portfolio analytics at GE Capi-tal in Norwalk, CT, where he is responsible for portfolio modelling in 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 Master’s degree in finance from the University of Alabama and is a CFA charterholder.

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

Jorge R. Sobehartis 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 a member of Moody’s Standing Committee on Quantitative Tools and VP senior analyst in Moody’s Risk Management Services, where

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he developed advanced default risk models, early warning tools and model validation metrics and procedures. During his career, he has 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 professional journals in finance, physics and mathematical modelling. Jorge has advanced degrees in physics and has postdoctoral experience at the Los Alamos National Laboratory.

Manuela Spanglerworks 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 National University of Singapore. Her research interests include market risk modelling and pricing of credit derivatives.

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

Lyn Thomasis professor of management science at the University of Southampton. His interests are in applying operational research and statistical ideas in the financial area, particularly in credit scoring and risk modelling in consumer lending. He is a founder member of the Credit Research Centre at the University of Edinburgh and one of the principal investigators for the Quantitative Financial Risk Management 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. He

is a Fellow of the Royal Society of Edinburgh, a past president of the Operational Research Society and was awarded the Beale Medal of that Society in 2008.

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

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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 and real estate finance. He has several years of consulting experience for financial institutions and has published in various international journals including The Journal of Banking and Finance, the European

Journal of Finance, Energy Economics and The Journal of Credit Risk and

he is an author of the book Rating Based Modeling of Credit Risk: Theory

and Application of Migration Matrices.

Oskari Vähämaais a PhD student in economics at the University of Turku. He has previously worked as a research assistant at the Research Unit of the Bank of Finland.

Matti Virénis a professor of economics at the University of Turku and a scientific advisor to the Bank of Finland. Previously he worked at the Bank of Finland as a research supervisor and in the Finnish Government Institute for Economic Research as the research direc-tor and as deputy direcdirec-tor. He has published more than 100 arti-cles in refereed journals and books. He studied at the University of Chicago with a Fulbright scholarship, and gained his doctoral degree (economics) from the University of Helsinki in 1980.

Carsten S. Wehnis 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 the respective risk models. Before joining DekaBank, he was responsible for supervising and conducting regulatory examinations for inter-nal market risk models with Deutsche Bundesbank. Carsten studied in Siegen, Germany, as well as in Nantes, France. He holds a PhD in mathematics and regularly gives lectures at universities. He has published more than 30 articles and other publications including three books.

Ralf Wernerheads the global Risk Methods & Valuation Depart-ment at Deutsche Pfandbriefbank and is mainly in charge of risk methodology, 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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risk topics and as consultant for investment strategies and asset liability management at Risklab Germany, as well as prop trader (Xetra, Eurex) for SchmidtBank Nürnberg. Ralf publishes regularly in finance- and optimisation-related journals and speaks at inter-national conferences. Since 2002, he has continuously supported the HVB Institute for Mathematical Finance at TU München as lec-turer for financial optimisation and simulation. Ralf holds a diploma and a PhD in mathematics from the Friedrich Alexander Universität Erlangen-Nürnberg.

Gerhard Winkleris deputy head of Oesterreichische Nationalbank’s credit division. His research interests focus on credit risk measure-ment, risk model validation and bank efficiency. Before joining the central bank he worked as an assistant professor at the Institute of Banking and Finance at the Vienna University of Economics and Business, where he recently completed his habilitation. He is author of several academic publications in the field of financial risk management and credit risk measurement.

Xiangkang Yinis a professor of economics and finance at La Trobe University, Australia. His research interests cover a wide range of topics in economics and finance, including capital asset pricing, cor-porate finance and governance, industrial organisation and applied microeconomic theory. Prior to jointing La Trobe University, he held various positions at Shanghai Jiaotong University, Universit’e Louis Pasteur and Monash University. Xiangkang has published articles in top-tier economics and finance journals, including The Journal of

Finance, Journal of Development Economics, Journal of Economic Behavior and Organization and the Australian Journal of Management.

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The 1970s witnessed the start of a new era in finance. Starting with the Black–Scholes–Merton option pricing formula, sophisticated mathematical models for pricing risky securities found their way into 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 system rendered the financial world riskier and the increased use of risk measurement and management methods led to globalised, inter-dependent markets and strongly increasing trading volumes in more and more complex financial instruments. Consequently, the risk of large failures due to mis-pricing and mismanagement increased and many of these realised failures are still important objects in learn-ing lessons about the malfunctionlearn-ing of risk models. Among others, these include the cases of Metallgesellschaft in 1993, the Bank of Tokyo and Mitsubishi in 1997 and NatWest Capital Markets in 1997 and most recently the global financial crisis.

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

Financial risk models have become increasingly important for financial institutions, markets and instruments. These models are individually crafted and then generally assembled to generate port-folio measures. The occurrence of the 2008–9 global financial crisis suggests that many existing financial risk models were unable to predict the increase in loss rates prior to the crisis. This was partic-ularly true for new markets such as asset securitisations and credit derivatives. The consequence was a general loss in credibility, which has resulted in changes of economic and regulatory requirements.

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

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(Basel Committee on Banking Supervision 2009) issued, in July, new risk weights for rated resecuritisations and is stresses the importance of “bank internal” due diligence processes:

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

In addition to this, “The Turner Review: A Regulatory Response to the Global Banking Crisis” (Financial Services Authority 2009) has also stressed the importance of increased capital ratios for market risk exposures to reflect the interaction between market and liquidity risk.

One lesson learned is that risk models are substantial parts of a sound risk management process and important ingredients for financial decision making. As important as risk models themselves is knowledge about the limitations and shortcomings of the models, ie, the acknowledgement that risk models and their outcomes may be wrong.

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

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

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investors’ behaviour. In Chapter 3 Steffi Höse and Stefan Huschens measure model risk in relation to non-Gaussian latent risk factors. After defining model risk in general, they show the impact of a potential misspecification of the factor distributions on credit risk measures 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 models with respect to their in-sample robustness and their out-of-sample performance when the value-at-risk is forecasted using alternative model specifications. They show that various stylised facts may have a 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 Ka Yui Leung analyse asset return dynamics and monetary policy. Oleg Burd (Chapter 6) shows ways to manage economic and regulatory capital through the business cycle. He finds that economic capital is 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 capital management process.

Part III focuses on credit risk models. Chapter 7 Andrew Barnes, Sean Keenan, Harry Ma, Colin McColloch, Stefano Santilli and Sukyul Suh present their experiences on credit risk models dur-ing the financial crisis. Esa Jokivuolle, Oskari Vähämaa and Matti Virén (Chapter 8) show the transmission of macro shocks to loan losses. Lyn Thomas and Madhur Malik (Chapter 9) compare credit risk models for portfolios of retail loans based on behavioural scores. Michael Kalkbrener and Akwum Onwunta (Chapter 10) val-idate structural credit-portfolio models. They review moment and maximum-likelihood estimators for intra- and inter-sector asset cor-relations under different distributional assumptions and analyse their ability to capture the dependence structures. Peter Miu and Bogie Ozdemir (Chapter 11) show the implications on estimating and validating the probability of default if asset correlations are stochastic. 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 approach to validate credit rating systems. Using a large sample of Austrian

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banks and obligors, the authors conduct an extensive benchmarking exercise.

Part IV combines liquidity, market and operational risk models. In Chapter 13 Stefan Reitz addresses liquidity in derivatives contracts. He shows how pricing models can be used to derive the expected cashflow for non-path-dependent and path-dependent derivatives. Manuela Spangler and Ralf Werner (Chapter 14) are concerned with the quantification of market risk over longer horizons. They derive the concept of potential future market risk, a promising approach similar to the concept of potential future exposure in counterparty credit risk. In Chapter 15 Carsten Wehn focuses on market risk mod-els. He systematically addresses the most common model errors in market risk and provides an overview of the most recent back-testing approaches. Anna Chernobai, Christian Menn, Svetlozar Rachev and Stefan Trück (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 counChap-terparty risk for over-the-counChap-ter derivatives and develops a framework for addressing model risk issues 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 of a ‘bond representation’ and examine typical pooling and structuring approaches with respect to their systematic risk exposure.

ACKNOWLEDGEMENTS

We thank Joe Breeden for writing the epilogue to this book. We are very grateful for the support from Lucie Carter and Jennifer Gibb from Risk Books and Journals for their tremendous help in man-aging the editing process. We hope that the book will provide new insights for practitioners and regulators, as well as researchers on applications, regulations and techniques presented in this book and we encourage the reader to share any thoughts and experiences with our community.

Daniel Rösch and Harald Scheule Melbourne and Hannover, November 2009

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Part I

Concepts and Stochastic

Frameworks for Model

Risk

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Downturn Model Risk: Another

View on the Global Financial Crisis

Daniel Rösch; Harald Scheule

Leibniz Universität Hannover; The University of Melbourne

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

In statistical terms, correlations are often placeholders for relation-ships which cannot be explained and are also known as “seeming correlations”. The 2008–9 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 markets have declined globally. These links have not been included into exist-ing risk models, and this chapter identifies these links and shows how to address these relationships in risk models.

We show that the insufficient incorporation of economic infor-mation into valuation models for financial instruments may partly explain why the financial industry was unable to predict, mitigate and cover the recent losses. Economic downturns are generally well-known. Unfortunately, to date the financial industry has struggled to incorporate econometric properties into forecasting models. These models were often propagated by the industry and supported by a number of academic studies on the information content of credit ratings.

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

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Figure 1.1 Seasonally adjusted delinquency rates for all commercial US banks 0 2 4 6 8 1987 1989 1991 1993 1995 1997 1999 2001 2003 2005 2007 Delinquency rate (%) Business loans

Loans 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 bank’s delinquent 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 incentive structures and a lack of transparency as a consequence thereof. This chapter 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 credit derivative markets may not be able to recover unless these important issues have been resolved.

CREDIT RISK AND BUSINESS CYCLES

Figure 1.1 shows a proxy for credit-portfolio risk, the delinquency rate. It is apparent that the delinquency rate, and thus credit risk, changes over time and follows cyclical patterns. For instance, the years 1991 (first Gulf War) and 2001–2 (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 (2008–9) financial crisis, while loans secured by real estate have dramatically increased.

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

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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 Delinquency rate (%) GAP GAP GAP Delinquency rate TTC PIT

Source: Board of Governors of the US Federal Reserve System. Delinquency rates

are the ratios of the US dollar amount of a bank’s delinquent loans to the US dollar amount of total loans outstanding in that category. A TTC model assumes the average default rate for every period. A PIT model forecasts the default rate based on 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 forecast models, which explain the credit risk for a future point in time, by information which is available at the time when the forecast is made. Figure 1.2 shows the real delinquency rate for loans secured by real estate, as well as the estimated delinquency rate by a TTC model and a PIT model.

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

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

• Simplicity. TTC approaches have gained acceptance because

they offer simplicity. PIT models have been propagated but estimated based on modest recent loss experiences due to lim-ited data availability. In other words, building a risk model based on the experience of multiple boom years may be inadequate to provision for credit losses during downturns.

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• Regulatory requirements. Regulators have accepted both TTC

and 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 capital of financial institutions may fluctuate with the credit risk assessment during the business cycle. This pro-cyclicality may require the issue of new capital during an economic downturn when capital is expensive or restricted in availability. In other words, regulators tried to avoid pro-cyclicality by accepting risk models which do not take the current state of the economy into account. The current crisis demonstrated that accounting practice implies a pro-cyclical capital requirement for market risk exposures, as the accounting values of marketable assets based on current market values, delinquent credit exposures are provisioned for and defaulted credit exposures are written off.

• 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) and C (C) for Standard & Poor’s rating agency and Fitch rating agency (Moody’s rating agency). These agencies have histor-ically propagated TTC models and have explicitly excluded the economy and focused on idiosyncratic risk drivers which were considered to be fundamental. For these efforts, credit ratings reflect an opaque mix of a TTC and PIT model out-put, as some idiosyncratic information naturally reflects the business cycle. As a result, the degree of cyclicality which is embedded in public credit ratings is difficult to assess and investors are uncertain as to whether they should associate time-constant, time-varying (or a mix of both) default rates to these ratings categories. Rating agencies may have no incen-tive to change this opaque practice, as the crucial calibration step (ie, the conversion from categorical ratings to numeric default rates needed by modern risk models) lies within the responsibility of investors.

The result of using a through-the-cycle approach is obvious: the model 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 2008–9 financial crisis) as the loss outcome