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Risk Management in Credit Portfolios Concentration Risk and Basel II

:	Martin Hibbeln
:	Risk Management in Credit Portfolios Concentration Risk and Basel II
:	Physica-Verlag
:	9783790826074
:	1
:	CHF 85.30
:

:	Betriebswirtschaft
:	English

:	248
:	Wasserzeichen
:	PC/MAC/eReader/Tablet
:	PDF

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.

	Risk Management in Credit Portfolios	3
	Foreword	5
	Preface	7
	Contents	9
	List of Figures	13
	List of Tables	15
	Abbreviations	17
	Chapter 1: Introduction	21
	1.1 Problem Definition and Objectives of This Work	21
	1.2 Course of Investigation	22
	Chapter 2: Credit Risk Measurement in the Context of Basel II	25
	2.1 Banking Supervision and Basel II	25
	2.2 Measures of Risk in Credit Portfolios	28
	2.2.1 Risk Parameters and Expected Loss	28
	2.2.2 Value at Risk, Tail Conditional Expectation, and Expected Shortfall	31
	2.2.3 Coherency of Risk Measures	36
	2.2.4 Estimation and Statistical Errors of VaR and ES	42
	2.3 The Unconditional Probability of Default Within the Asset Value Model of Merton	45
	2.4 The Conditional Probability of Default Within the One-Factor Model of Vasicek	48
	2.5 Measuring Credit Risk in Homogeneous Portfolios with the Vasicek Model	51
	2.6 Measuring Credit Risk in Heterogeneous Portfolios with the ASRF Model of Gordy	55
	2.7 Measuring Credit Risk Within the IRB Approach of Basel II	59
	2.8 Appendix	63
	2.8.1 Alternative Representation of the ES as an Indicator Function	63
	2.8.2 Application of Itô´s Lemma	64
	2.8.3 Application of Bayes´ Theorem for Continuous Distributions	65
	2.8.4 Limit Distribution and Probability Density Function in the Vasicek Model	66
	2.8.5 VaR and ES of the Limit Distribution in the Vasicek Model	68
	2.8.6 Alternative Representation of the Bivariate Normal Distribution	69
	2.8.7 Application of the Strong Law of Large Numbers	70
	2.8.8 Application of Kronecker´s Lemma	72
	2.8.9 Identity of the VaR in the ASRF Model	73
	2.8.10 Identity of the ES in the ASRF Model	74
	Chapter 3: Concentration Risk in Credit Portfolios and Its Treatment Under Basel II	77
	3.1 Types of Concentration Risk	77
	3.2 Incurrence and Relevance of Concentration Risk	79
	3.3 Measurement and Management of Concentration Risk	82
	3.4 Heuristic Approaches for the Measurement of Concentration Risk	87
	3.5 Review of the Literature on Model-Based Approaches of Concentration Risk Measurement	90
	Chapter 4: Model-Based Measurement of Name Concentration Risk in Credit Portfolios	93
	4.1 Fundamentals and Research Questions on Name Concentration Risk	93
	4.2 Measurement of Name Concentration Using the Risk Measure Value at Risk	95
	4.2.1 Considering Name Concentration with the Granularity Adjustment	95
	4.2.1.1 First-Order Granularity Adjustment for One-Factor Models	95
	4.2.1.2 First-Order Granularity Adjustment for the Vasicek Model	100
	4.2.1.3 Second-Order Granularity Adjustment for One-Factor Models	102
	4.2.1.4 Second-Order Granularity Adjustment for the Vasicek Model	105
	4.2.2 Numerical Analysis of the VaR-Based Granularity Adjustment	107
	4.2.2.1 Impact on the Portfolio-Quantile	107
	4.2.2.2 Size of Fine Grained Risk Buckets	110
	4.2.2.3 Probing First-Order Granularity Adjustment	114
	4.2.2.4 Probing Second-Order Granularity Adjustment	118
	4.2.2.5 Probing Granularity for Inhomogeneous Portfolios	121
	4.3 Measurement of Name Concentration Using the Risk Measure Expected Shortfall	123
	4.3.1 Adjusting for Coherency by Parameterization of the Confidence Level	123
	4.3.2 Considering Name Concentration with the Granularity Adjustment	128
	4.3.2.1 First-Order Granularity Adjustment for One-Factor Models	128
	4.3.2.2 First-Order Granularity Adjustment for the Vasicek Model	131
	4.3.2.3 Second-Order Granularity Adjustment for One-Factor Models	132
	4.3.2.4 Second-Order Granularity Adjustment for the Vasicek Model	133
	4.3.3 Moment Matching Procedure for Stochastic LGDs	134
	4.3.4 Numerical Analysis of the ES-Based Granularity Adjustment	141
	4.3.4.1 Impact on the Portfolio-Quantile	141
	4.3.4.2 Size of Fine Grained Risk Buckets	143
	4.3.4.3 Probing First-Order Granularity Adjustment	146
	4.3.4.4 Probing Second-Order Granularity Adjustment	150
	4.3.4.5 Probing Granularity for Inhomogeneous Portfolios	153
	4.4 Interim Result	154
	4.5 Appendix	156
	4.5.1 Alternative Derivation of the First-Order Granularity Adjustment	156
	4.5.2 First and Second Derivative of VaR	163
	4.5.2.1 First Derivative	164
	4.5.2.2 Second Derivative	165
	4.5.3 Probability Density Function of Transformed Random Variables	167
	4.5.4 VaR-Based First-Order Granularity Adjustment for a Normally Distributed Systematic Factor	168
	4.5.5 VaR-Based First-Order Granularity Adjustment for Homogeneous Portfolios	169
	4.5.6 Arbitrary Derivatives of VaR	170
	4.5.6.1 Mathematical Basics	170
	4.5.6.1.1 Laplace Transform and Dirac´s Delta Function	170
	4.5.6.1.2 Laurent Series, Singularities, and Complex Residues	171
	4.5.6.1.3 Partitions	173
	4.5.6.2 Determination of the Derivatives	173
	4.