Introduction to credit risk modeling:
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| Main Authors: | , , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Boca Raton, [u.a.]
CRC Press
2010
|
| Edition: | 2. ed. |
| Series: | Chapman & Hall/CRC financial mathematics series
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis Klappentext |
| Physical Description: | XIX, 364 S. graph. Darst. |
| ISBN: | 9781584889922 1584889926 |
Staff View
MARC
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| 100 | 1 | |a Bluhm, Christian |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Introduction to credit risk modeling |c Christian Bluhm ; Ludger Overbeck ; Christoph Wagner |
| 250 | |a 2. ed. | ||
| 264 | 1 | |a Boca Raton, [u.a.] |b CRC Press |c 2010 | |
| 300 | |a XIX, 364 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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| 700 | 1 | |a Overbeck, Ludger |e Verfasser |4 aut | |
| 700 | 1 | |a Wagner, Christoph |e Verfasser |4 aut | |
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| _version_ | 1824553569113604097 |
| adam_text | Contents
Preface
to Second Edition
ix
Preface
xiii
About the Authors
xv
List of Figures
xvii
1
The Basics of Credit Risk Management
1
1.1
Expected Loss
.......................... 2
1.1.1
Probability of Default (PD)
.............. 4
1.1.2
The Exposure at Default
................ 15
1.1.3
The Loss Given Default
................ 20
1.1.4
A Remark on the Relation between PD. EAD. LGD
21
1.2
Unexpected Loss
........................ 22
1.2.1
Economic Capital
.................... 27
1.2.2
The Loss Distribution
................. 29
1.2.3
Modeling Correlations by Means of Factor Models
. 36
1.3
Regulatory Capital and the Basel Initiative
......... 45
2
Modeling Correlated Defaults
51
2.1
The Bernoulli Model
....................... 53
2.1.1
A General Bernoulli Mixture Model
......... 55
2.1.2
Uniform Default Probability and Uniform Correlation
56
2.2
The
Poisson
Model
....................... 58
2.2.1
A General
Poisson
Mixture Model
.......... 59
2.2.2
Uniform Default Intensity and Uniform Correlation
. 60
2.3
Bernoulli versus
Poisson
Mixture
............... 62
2.4
An Overview of Common Model Concepts
.......... 63
2.4.1
Moody s KMV s and RiskMetrics Model Approach
. 65
2.4.2
Model Approach of CreditRisk4-
........... 68
2.4.3
CreditPortfolioView
.................. 71
2.4.4
Basic Remarks on Dynamic Intensity Models
.... 78
2.5
One-Factor/Sector Models
................... 80
2.5.1
One-Factor Models in the Asset Value Model Setup
. 80
2.5.2
The
d^URisk4
One-Sector Model
.......... 97
2.5.3
Comparison of One-Factor and One-Sector Models
. 98
2.6
Loss Dependence by Means of Copula Functions
...... 99
2.6.1
Copulas: Variations of a Scheme
........... 103
2.7
Working Example on Asset Correlations
...........
Ill
2.8
Generating the Portfolio Loss Distribution
.......... 118
2.8.1
Some Prerequisites from Probability Theory
..... 120
2.8.2
Conditional Independence
............... 134
2.8.3
Technique I: Recursive Generation
.......... 136
2.8.4
Technique II: Fourier Transformation
......... 140
2.8.5
Technique III: Saddle-Point Approximation
..... 142
2.8.6
Technique IV: Importance Sampling
......... 145
Asset Value Models
151
3.1
Introduction and a Brief Guide to the Literature
...... 151
3.2
A Few Words about Calls and Puts
.............. 152
3.2.1
Geometric Brownian Motion
.............. 154
3.2.2
Put and Call Options
................. 155
3.3
Merton s Asset Value Model
.................. 162
3.3.1
Capital Structure: Option-Theoretic Approach
. . . 162
3.3.2
Asset from Equity Values
............... 167
3.4
Transforming Equity into Asset Values: A Working Approach
169
3.4.1
Itô s
Formula Light
................. 170
3.4.2
Black-Scholes Partial Differential Equation
...... 171
The
CreditRisk+
Model
179
4.1
The Modeling Framework of CreditRisk4
.......... 180
4.2
Construction Step
1:
Independent Obligors
......... 183
4.3
Construction Step
2:
Sector Model
.............. 184
4.3.1
Sector Default Distribution
.............. 186
4.3.2
Sector Compound Distribution
............ 190
4.3.3
Sector Convolution
................... 193
4.3.4
Calculating the Loss Distribution
........... 193
Risk Measures and Capital Allocation
197
5.1
Coherent Risk Measures and Expected Shortfall
....... 198
5.1.1
Expected Shortfall
................... 202
5.1.2
Spectral Risk Measures
................ 204
5.1.3
Density of a Risk Measure
............... 206
5.2
Contributory Capital
...................... 208
5.2.1
Axiomatic Approach to Capital Allocation
...... 209
5.2.2
Capital Allocation in Practice
............. 213
5.2.3
Variance/Covariance Approach
............ 215
5.2.4
Capital Allocation w.r.t. Value-at-Risk
........ 217
5.2.5
Capital Allocations w.r.t. Expected Shortfall
.... 218
5.2.6
A Simulation Study
.................. 220
6
Term Structure
of Default Probability
225
6.1
Survival Function and Hazard Rate
.............. 225
6.2
Risk-Neutral vs. Actual Default Probabilities
........ 228
6.3
Term Structure Based on Historical Default Information
. . 230
6.3.1
Exponential Term Structure
.............. 230
6.3.2
Direct Calibration of
Multi-
Year Default Probabilities
231
6.3.3
Migration Technique and Q-Matrices
......... 235
6.3.4
A Non-Homogeneous Markov Chain Approach
. . . 246
6.4
Term Structure Based on Market Spreads
.......... 248
7
Credit Derivatives
255
7.1
Total Return Swaps
...................... 256
7.2
Credit Default Products
.................... 258
7.3
Basket Credit Derivatives
................... 262
7.4
Credit Spread Products
.................... 273
7.5
Credit-Linked Notes
...................... 276
8
Collateralized Debt Obligations
281
8.1
Introduction to Collateralized Debt Obligations
....... 284
8.1.1
Typical Cash Flow CDO Structure
.......... 286
8.1.2
Typical Synthetic
CLO
Structure
........... 296
8.2
Different Roles of Banks in the CDO Market
........ 298
8.2.1
The Originator s Point of View
............ 298
8.2.2
The Investor s Point of View
............. 306
8.3
CDOs from the Modeling Point of View
........... 309
8.4
Multi-Period Credit Models
.................. 314
8.4.1
Migration Model
.................... 314
8.4.2
Correlated Default Time Models
........... 319
8.4.3
First-Passage-Time Models
.............. 320
8.4.4
Stochastic Default Intensity Models
.......... 325
8.4.5
Intertemporal
Dependence and Autocorrelation
. . . 326
8.5
Former Rating Agency Model: Moody s BET
........ 330
8.6
Developments, Model Issues and Further Reading
...... 338
References
345
Index
359
Introduction
to Credit Risk Modeling
Second Edition
The recent financial crisis has shown that credit risk in particular
and finance in general remain important fields for the application
of mathematical concepts to real-life situations. While continuing
to focus on common mathematical approaches to model credit
portfolios, Introduction to Credit Risk Modeling, Second Edition
presents updates on model developments that have occurred
since the publication of the best-selling first edition.
New to the Second Edition
•
An expanded section on techniques for the generation of loss
distributions
•
Introductory sections on new topics, such as spectral risk
measures, an axiomatic approach to capital allocation, and
nonhomogeneous Markov chains
•
Updated sections on the probability of default, exposure-at-
default, loss-given-default, and regulatory capital
•
A new section on multi-period models
•
Recent developments in structured credit
The financial crisis illustrated the importance of effectively
communicating model outcomes and ensuring that the variation
in results is clearly understood by decision makers. The crisis also
showed that more modeling and more analysis are superior to only
one model. This accessible, self-contained book recommends
using a variety of models to shed light on different aspects of the
true nature of a credit risk problem, thereby allowing the problem
to be viewed from different angles.
|
| adam_txt |
Contents
Preface
to Second Edition
ix
Preface
xiii
About the Authors
xv
List of Figures
xvii
1
The Basics of Credit Risk Management
1
1.1
Expected Loss
. 2
1.1.1
Probability of Default (PD)
. 4
1.1.2
The Exposure at Default
. 15
1.1.3
The Loss Given Default
. 20
1.1.4
A Remark on the Relation between PD. EAD. LGD
21
1.2
Unexpected Loss
. 22
1.2.1
Economic Capital
. 27
1.2.2
The Loss Distribution
. 29
1.2.3
Modeling Correlations by Means of Factor Models
. 36
1.3
Regulatory Capital and the Basel Initiative
. 45
2
Modeling Correlated Defaults
51
2.1
The Bernoulli Model
. 53
2.1.1
A General Bernoulli Mixture Model
. 55
2.1.2
Uniform Default Probability and Uniform Correlation
56
2.2
The
Poisson
Model
. 58
2.2.1
A General
Poisson
Mixture Model
. 59
2.2.2
Uniform Default Intensity and Uniform Correlation
. 60
2.3
Bernoulli versus
Poisson
Mixture
. 62
2.4
An Overview of Common Model Concepts
. 63
2.4.1
Moody's KMV's and RiskMetrics' Model Approach
. 65
2.4.2
Model Approach of CreditRisk4-
. 68
2.4.3
CreditPortfolioView
. 71
2.4.4
Basic Remarks on Dynamic Intensity Models
. 78
2.5
One-Factor/Sector Models
. 80
2.5.1
One-Factor Models in the Asset Value Model Setup
. 80
2.5.2
The
d^URisk4"
One-Sector Model
. 97
2.5.3
Comparison of One-Factor and One-Sector Models
. 98
2.6
Loss Dependence by Means of Copula Functions
. 99
2.6.1
Copulas: Variations of a Scheme
. 103
2.7
Working Example on Asset Correlations
.
Ill
2.8
Generating the Portfolio Loss Distribution
. 118
2.8.1
Some Prerequisites from Probability Theory
. 120
2.8.2
Conditional Independence
. 134
2.8.3
Technique I: Recursive Generation
. 136
2.8.4
Technique II: Fourier Transformation
. 140
2.8.5
Technique III: Saddle-Point Approximation
. 142
2.8.6
Technique IV: Importance Sampling
. 145
Asset Value Models
151
3.1
Introduction and a Brief Guide to the Literature
. 151
3.2
A Few Words about Calls and Puts
. 152
3.2.1
Geometric Brownian Motion
. 154
3.2.2
Put and Call Options
. 155
3.3
Merton's Asset Value Model
. 162
3.3.1
Capital Structure: Option-Theoretic Approach
. . . 162
3.3.2
Asset from Equity Values
. 167
3.4
Transforming Equity into Asset Values: A Working Approach
169
3.4.1
Itô's
Formula "Light"
. 170
3.4.2
Black-Scholes Partial Differential Equation
. 171
The
CreditRisk+
Model
179
4.1
The Modeling Framework of CreditRisk4"
. 180
4.2
Construction Step
1:
Independent Obligors
. 183
4.3
Construction Step
2:
Sector Model
. 184
4.3.1
Sector Default Distribution
. 186
4.3.2
Sector Compound Distribution
. 190
4.3.3
Sector Convolution
. 193
4.3.4
Calculating the Loss Distribution
. 193
Risk Measures and Capital Allocation
197
5.1
Coherent Risk Measures and Expected Shortfall
. 198
5.1.1
Expected Shortfall
. 202
5.1.2
Spectral Risk Measures
. 204
5.1.3
Density of a Risk Measure
. 206
5.2
Contributory Capital
. 208
5.2.1
Axiomatic Approach to Capital Allocation
. 209
5.2.2
Capital Allocation in Practice
. 213
5.2.3
Variance/Covariance Approach
. 215
5.2.4
Capital Allocation w.r.t. Value-at-Risk
. 217
5.2.5
Capital Allocations w.r.t. Expected Shortfall
. 218
5.2.6
A Simulation Study
. 220
6
Term Structure
of Default Probability
225
6.1
Survival Function and Hazard Rate
. 225
6.2
Risk-Neutral vs. Actual Default Probabilities
. 228
6.3
Term Structure Based on Historical Default Information
. . 230
6.3.1
Exponential Term Structure
. 230
6.3.2
Direct Calibration of
Multi-
Year Default Probabilities
231
6.3.3
Migration Technique and Q-Matrices
. 235
6.3.4
A Non-Homogeneous Markov Chain Approach
. . . 246
6.4
Term Structure Based on Market Spreads
. 248
7
Credit Derivatives
255
7.1
Total Return Swaps
. 256
7.2
Credit Default Products
. 258
7.3
Basket Credit Derivatives
. 262
7.4
Credit Spread Products
. 273
7.5
Credit-Linked Notes
. 276
8
Collateralized Debt Obligations
281
8.1
Introduction to Collateralized Debt Obligations
. 284
8.1.1
Typical Cash Flow CDO Structure
. 286
8.1.2
Typical Synthetic
CLO
Structure
. 296
8.2
Different Roles of Banks in the CDO Market
. 298
8.2.1
The Originator\s Point of View
. 298
8.2.2
The Investor's Point of View
. 306
8.3
CDOs from the Modeling Point of View
. 309
8.4
Multi-Period Credit Models
. 314
8.4.1
Migration Model
. 314
8.4.2
Correlated Default Time Models
. 319
8.4.3
First-Passage-Time Models
. 320
8.4.4
Stochastic Default Intensity Models
. 325
8.4.5
Intertemporal
Dependence and Autocorrelation
. . . 326
8.5
Former Rating Agency Model: Moody's BET
. 330
8.6
Developments, Model Issues and Further Reading
. 338
References
345
Index
359
Introduction
to Credit Risk Modeling
Second Edition
The recent financial crisis has shown that credit risk in particular
and finance in general remain important fields for the application
of mathematical concepts to real-life situations. While continuing
to focus on common mathematical approaches to model credit
portfolios, Introduction to Credit Risk Modeling, Second Edition
presents updates on model developments that have occurred
since the publication of the best-selling first edition.
New to the Second Edition
•
An expanded section on techniques for the generation of loss
distributions
•
Introductory sections on new topics, such as spectral risk
measures, an axiomatic approach to capital allocation, and
nonhomogeneous Markov chains
•
Updated sections on the probability of default, exposure-at-
default, loss-given-default, and regulatory capital
•
A new section on multi-period models
•
Recent developments in structured credit
The financial crisis illustrated the importance of effectively
communicating model outcomes and ensuring that the variation
in results is clearly understood by decision makers. The crisis also
showed that more modeling and more analysis are superior to only
one model. This accessible, self-contained book recommends
using a variety of models to shed light on different aspects of the
true nature of a credit risk problem, thereby allowing the problem
to be viewed from different angles. |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Bluhm, Christian Overbeck, Ludger Wagner, Christoph |
| author_facet | Bluhm, Christian Overbeck, Ludger Wagner, Christoph |
| author_role | aut aut aut |
| author_sort | Bluhm, Christian |
| author_variant | c b cb l o lo c w cw |
| building | Verbundindex |
| bvnumber | BV023092306 |
| classification_rvk | QK 320 SK 980 |
| classification_tum | WIR 160f MAT 902f |
| ctrlnum | (OCoLC)254451278 (DE-599)BVBBV023092306 |
| discipline | Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Mathematik Wirtschaftswissenschaften |
| edition | 2. ed. |
| format | Book |
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| id | DE-604.BV023092306 |
| illustrated | Illustrated |
| index_date | 2024-07-02T19:41:31Z |
| indexdate | 2025-02-20T06:37:57Z |
| institution | BVB |
| isbn | 9781584889922 1584889926 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016295163 |
| oclc_num | 254451278 |
| open_access_boolean | |
| owner | DE-739 DE-703 DE-945 DE-19 DE-BY-UBM DE-355 DE-BY-UBR DE-91G DE-BY-TUM DE-N2 DE-634 DE-862 DE-BY-FWS DE-384 |
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| physical | XIX, 364 S. graph. Darst. |
| publishDate | 2010 |
| publishDateSearch | 2010 |
| publishDateSort | 2010 |
| publisher | CRC Press |
| record_format | marc |
| series2 | Chapman & Hall/CRC financial mathematics series |
| spellingShingle | Bluhm, Christian Overbeck, Ludger Wagner, Christoph Introduction to credit risk modeling Risikomanagement (DE-588)4121590-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Kreditrisiko (DE-588)4114309-7 gnd |
| subject_GND | (DE-588)4121590-4 (DE-588)4114528-8 (DE-588)4114309-7 |
| title | Introduction to credit risk modeling |
| title_auth | Introduction to credit risk modeling |
| title_exact_search | Introduction to credit risk modeling |
| title_exact_search_txtP | Introduction to credit risk modeling |
| title_full | Introduction to credit risk modeling Christian Bluhm ; Ludger Overbeck ; Christoph Wagner |
| title_fullStr | Introduction to credit risk modeling Christian Bluhm ; Ludger Overbeck ; Christoph Wagner |
| title_full_unstemmed | Introduction to credit risk modeling Christian Bluhm ; Ludger Overbeck ; Christoph Wagner |
| title_short | Introduction to credit risk modeling |
| title_sort | introduction to credit risk modeling |
| topic | Risikomanagement (DE-588)4121590-4 gnd Mathematisches Modell (DE-588)4114528-8 gnd Kreditrisiko (DE-588)4114309-7 gnd |
| topic_facet | Risikomanagement Mathematisches Modell Kreditrisiko |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016295163&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016295163&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bluhmchristian introductiontocreditriskmodeling AT overbeckludger introductiontocreditriskmodeling AT wagnerchristoph introductiontocreditriskmodeling |
Indexes
THWS Schweinfurt Zentralbibliothek Lesesaal
| Call Number: |
2000 QK 320 B658(2) |
|---|---|
| Copy 1 | ausleihbar Checked out – Due: 31.12.2099 Recall This |