Risk Management in Credit Portfolios

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Risk Management in Credit PortfoliosConcentration Risk and Basel II

Series: Contributions to Economics

Hibbeln, Martin

1st Edition., 2010, XX, 247 p. 20 illus., Hardcover
ISBN: 978-3-7908-2606-7



Risk concentrations play a crucial role for the survival of individual banks and for the stability of the whole banking system. Thus, it is important from an economical and a regulatory perspective to properly measure and manage these concentrations. In this book, the impact of credit concentrations on portfolio risk is analyzed for different portfolio types and it is determined, in which cases the influence of concentration risk has to be taken into account.

Furthermore, some models for the measurement of concentration risk are modified to be consistent with Basel II and their performance is compared. Beyond that, this book integrates economical and regulatory aspects of concentration risk and seeks to provide a systematic way to get familiar with the topic of concentration risk from the basics of credit risk modeling to present research in the measurement and management of credit risk concentrations.


Content Level » Research
Keywords » Basel II - Concentration Risk - Credit Risk Modeling - Multi-Factor Models - Risk Management


Contents
1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 1
1.1 Problem Definition and Objectives of This Work . . . . . . . . . . . . . . . . . . . . . . 1
1.2 Course of Investigation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 2
2 Credit Risk Measurement in the Context of Basel II . . . . . . . . . . . . . . . . . . . 5
2.1 Banking Supervision and Basel II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 5
2.2 Measures of Risk in Credit Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.1 Risk Parameters and Expected Loss . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 8
2.2.2 Value at Risk, Tail Conditional Expectation,
and Expected Shortfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
2.2.3 Coherency of Risk Measures . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
2.2.4 Estimation and Statistical Errors of VaR and ES . . . . . . . . . . . . . . 22
2.3 The Unconditional Probability of Default Within the Asset
Value Model of Merton . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
2.4 The Conditional Probability of Default Within the One-Factor
Model of Vasicek . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
2.5 Measuring Credit Risk in Homogeneous Portfolios
with the Vasicek Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
2.6 Measuring Credit Risk in Heterogeneous Portfolios
with the ASRF Model of Gordy . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
2.7 Measuring Credit Risk Within the IRB Approach
of Basel II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
2.8 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
3 Concentration Risk in Credit Portfolios and Its Treatment
Under Basel II . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.1 Types of Concentration Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
3.2 Incurrence and Relevance of Concentration Risk . . . . . . . . . . . . . . . . . . . . . 59
3.3 Measurement and Management of Concentration Risk . . . . . . . . . . . . . . . 62
ix
3.4 Heuristic Approaches for the Measurement
of Concentration Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
3.5 Review of the Literature on Model-Based Approaches
of Concentration Risk Measurement . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
4 Model-Based Measurement of Name Concentration Risk
in Credit Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.1 Fundamentals and Research Questions on Name
Concentration Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
4.2 Measurement of Name Concentration Using the Risk
Measure Value at Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.1 Considering Name Concentration with the Granularity
Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
4.2.2 Numerical Analysis of the VaR-Based Granularity
Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 87
4.3 Measurement of Name Concentration Using the Risk Measure
Expected Shortfall . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.1 Adjusting for Coherency by Parameterization
of the Confidence Level . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 103
4.3.2 Considering Name Concentration with the Granularity
Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 108
4.3.3 Moment Matching Procedure for Stochastic LGDs . . . . . . . . . . . 114
4.3.4 Numerical Analysis of the ES-Based Granularity
Adjustment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 121
4.4 Interim Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 134
4.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 136
5 Model-Based Measurement of Sector Concentration
Risk in Credit Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.1 Fundamentals and Research Questions on Sector
Concentration Risk . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 183
5.2 Incorporation of Sector Concentrations Using Multi-Factor
Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.2.1 Structure of Multi-Factor Models and Basel II-Consistent
Parameterization Through a Correlation Matching
Procedure . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 185
5.2.2 Accounting for Sector Concentrations with the
Model of Pykhtin . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 190
5.2.3 Accounting for Sector Concentrations with the
Model of Cespedes, Herrero, Kreinin and Rosen . . . . . . . . . . . . . 197
5.2.4 Accounting for Sector Concentrations with the
Model of Du¨llmann . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 202
x Contents
5.3 Performance of Multi-Factor Models . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 212
5.3.1 Analysis for Deterministic Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . 212
5.3.2 Simulation Study for Homogeneous and Heterogeneous
Portfolios . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 215
5.4 Interim Result . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 219
5.5 Appendix . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 220
6 Conclusion . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 237
References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 241
Related subjects » Finance & Banking - Financial Economics - Quantitative Finance

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