Simulation techniques for credit and operational risk management:
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| Format: | Abschlussarbeit Buch |
| Sprache: | English |
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2008
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| Online-Zugang: | Inhaltsverzeichnis |
| Beschreibung: | XVII, 127 S. graph. Darst. |
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MARC
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Datensatz im Suchindex
| _version_ | 1804138898482266112 |
|---|---|
| adam_text | Titel: Simulation techniques for credit and operational risk management
Autor: Popp, Monika
Jahr: 2008
Contents
List of Figures XI
List of Tables XIII
Abbreviations XV
List of Symbols XVII
Introduction 1
1 Quantitative Risk Management 3
1.1 Risk Measurement and Management .................. 3
1.2 Risk Types ................................ :
1.2.1 Credit Risk............................ 5
1.2.2 Operational Risk......................... 7
1.3 Regulatory Conditions.......................... 8
1.3.1 The New Regulatory Framework ................ 9
1.3.2 Eeonomie Capital......................... 10
2 Mathematical Modeling 11
2.1 Risk Measures............................... 11
2.1.1 Coherent Measures of Risk.................... 13
2.1.2 Yahie-at-Risk and Expected Shortfall.............. l. i
2.2 Modeling Credit Risk........................... 18
2.2.1 Structural Models of Default................... 19
2.2.2 Threshold Models......................... 24
2.2.3 Mixture Models in Credit Risk Modeling............ 2(i
2.3 Modeling Operational Risk........................ 31
2.3.1 The Elementary Approaches................... 31
2.3.2 The Advanced Measurement Approach............. 32
2.4 Rare Events and Simulation Based Techniques............. 36
VII
vnl CONTENTS
3 Efficient Calculation of Expected Shortfall Contributions in Large
Credit Portfolios 41
3.1 Introduction................................
3.2 Loss Distributions of Gaussian Multi-Factor Models..........44
3.2.1 The Two-State Credit Portfolio Model.............4*
3.2.2 Analytic Approximations..................... 45
3.3 Importance Sampling Applied to Systematic Factors.......... 49
3.3.1 Straightforward Monte Carlo Simulation............°0
3.3.2 Monte Carlo Simulation Based on Importance Sampling ... 50
3.3.3 Approximation by a Homogeneous Portfolio.......... 52
3.3.4 Optimal Mean for Infinite Homogeneous Portfolios ......53
3.3.5 Numerical Analysis........................ ^
3.4 Variance Reduction Based on Conditional Independence of Specific
Factors...................................58
3.4.1 Importance Sampling on Specific Factors............ 58
3.4.2 Conditional Expected Shortfall Allocation........... 59
3.4.3 Normal Approximations.....................61
3.5 Numerical Results.............................63
3.6 Generalization to Multi-state Models..................68
3.6.1 Rating Migration.........................68
3.6.2 Importance Sampling in a Multi-state Model..........68
3.6.3 Conditional Allocation in a Multi-state Model.........69
3.7 Conclusion of Chapter 3.........................70
4 Second-order Approximation for Portfolio Losses 71
4.1 Introduction................................ 71
4.2 Approximation and Error Bounds ................... 72
4.3 Numerical Case Studies......................... 76
4.3.1 The Algorithms.......................... 76
4.3.2 Numerical Results ........................ 78
4.3.3 Application to Synthetic CDO Tranches ............ 83
4.3.4 Analysis of Computational Effort and Theoretical Error . ... 88
4.4 Conclusion of Chapter 4......................... 89
5 Simulation Techniques for Operational Risk 91
5.1 Subexponential Distributions ...................... 91
5.2 Operational Risk: The One-Cell Case..................94
5.2.1 Estimation of Exceedance Probabilities............. 94
5.2.2 Estimation of Value-at-Risk and Expected Shortfall......95
5.2.3 Numerical Analysis........................96
5.3 Operational Risk: the Multi-Cell Case .................103
5.3.1 The Portfolio Model.......................103
5.3.2 Estimation of Exceedance Probabilities.............104
CONTENTS IX
5.3.3 Value-at-Risk and Expected Shortfall.............. 105
5.3.4 Expected Shortfall Contributions................ 106
5.3.5 Numerical Analysis of the Algorithm in the Multi-Cell Case . 107
5.4 Further Enhancements.......................... 113
5.5 The Analysis of Specific Parameter Settings.............. 115
5.6 Conclusion of Chapter 5......................... 119
Bibliography 121
List of Figures
3.1 Monte Carlo sampling error as a function of the importance sampling
shift....................................57
3.2 Distribution of the relative difference of expected shortfall contribu-
tions to the benchmark..........................66
3.3 Distribution of statistical fluctuation of expected shortfall contribu-
tions....................................67
4.1 Impact of varying p............................ 80
4.2 Impact of varying p............................ 81
4.3 Impact of portfolio size.......................... 82
4.4 Impact of heterogeneity. ......................... 83
5.1 Comparison of the stability of both algorithms for the estimation of
P(L c).................................. 99
5.2 Comparison of the stability of both algorithms for the estimation of
value-at-risk................................100
5.3 Comparison of the stability of both algorithms for the estimation of
expected shortfall.............................101
5.4 Plots of 500 results for ES0.99 obtained by Monte Carlo Simulation
and the order statistics algorithm.....................102
5.5 Comparison of the stability of both algorithms in the two-cell case
for the estimation of VaRo and ESQ...................Ill
5.6 Comparison of the stability of both algorithms in the two-cell case
for the estimation of ESC^ and ESC;;..................112
5.7 The effect of importance sampling....................115
5.8 Deviations of the results for expected shortfall and expected shortfall
contributions from their mean in Scenario 1...............117
5.9 Deviations of the results for expected shortfall and expected shortfall
contributions from their mean in Scenario 2...............118
5.10 Deviations of expected shortfall and expected shortfall contributions
from their mean in Scenario 3.......................120
XI
List of Tables
2.1 Rating migration matrix.......................... 23
3.1 Average relative error (% of benchmark) in 25,000 loan portfolio. . . 64
3.2 Average standard deviation {% of benchmark) in 25,000 loan portfolio. 64
3.3 Average relative error (% of benchmark) in 1,000 loan portfolio. ... 65
3.4 Average standard deviation (% of benchmark) in 1,000 loan portfolio. 65
4.1 Fair spreads for CDO tranches......................87
4.2 Comparison of computing times for the calculation of exceedance
probabilities and CDO spreads with first-order and second-order ap-
proximation................................. 88
4.3 Comparison of the theoretical error given in Corollary 4.2.4 and the
maximum difference between second-order results and the true dis-
tribution..................................89
5.1 Convergence of the order statistics algorithm, absolute results for
P(L c)..................................98
5.2 Convergence of the order statistics algorithm, absolute results for ES0 9. 98
5.3 Computational effort of the order statistics algorithm and Monte
Carlo simulation..............................102
5.4 Parameter choices for the analysis of the order statistics algorithm in
the multi-cell case.............................107
5.5 Convergence of the order statistics algorithm, absolute results for
P(L c), with c = 40,000,000......................110
5.6 Convergence of the order statistics algorithm, absolute results for ES0.9IIO
5.7 Absolute results for expected shortfall and expected shortfall contri-
butions in Scenario 1............................117
5.8 Absolute results for expected shortfall and expected shortfall contri-
butions in Scenario 2............................118
5.9 Absolute results for expected shortfall and expected shortfall contri-
butions in Scenario 3............................119
XIII
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| any_adam_object | 1 |
| author | Popp, Monika 1979- |
| author_GND | (DE-588)137927924 |
| author_facet | Popp, Monika 1979- |
| author_role | aut |
| author_sort | Popp, Monika 1979- |
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| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.1 |
| dewey-search | 332.1 |
| dewey-sort | 3332.1 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| format | Thesis Book |
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| spelling | Popp, Monika 1979- Verfasser (DE-588)137927924 aut Simulation techniques for credit and operational risk management vorgelegt von Monika Popp 2008 XVII, 127 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Leipzig, Univ., Diss., 2008 Kreditmanagement (DE-588)4138463-5 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Kreditmanagement (DE-588)4138463-5 s Risikomanagement (DE-588)4121590-4 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=017368746&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
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| subject_GND | (DE-588)4138463-5 (DE-588)4121590-4 (DE-588)4113937-9 |
| title | Simulation techniques for credit and operational risk management |
| title_auth | Simulation techniques for credit and operational risk management |
| title_exact_search | Simulation techniques for credit and operational risk management |
| title_full | Simulation techniques for credit and operational risk management vorgelegt von Monika Popp |
| title_fullStr | Simulation techniques for credit and operational risk management vorgelegt von Monika Popp |
| title_full_unstemmed | Simulation techniques for credit and operational risk management vorgelegt von Monika Popp |
| title_short | Simulation techniques for credit and operational risk management |
| title_sort | simulation techniques for credit and operational risk management |
| topic | Kreditmanagement (DE-588)4138463-5 gnd Risikomanagement (DE-588)4121590-4 gnd |
| topic_facet | Kreditmanagement Risikomanagement Hochschulschrift |
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