Pricing portfolio credit derivatives by means of evolutionary algorithms:
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| Main Author: | |
|---|---|
| Format: | Thesis Book |
| Language: | English |
| Published: |
Wiesbaden
Gabler
2008
|
| Edition: | 1. ed. |
| Series: | Gabler Edition Wissenschaft
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XXVII, 160 S. graph. Darst. 21 cm |
| ISBN: | 9783834909152 3834909157 |
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| 245 | 1 | 0 | |a Pricing portfolio credit derivatives by means of evolutionary algorithms |c Svenja Hager |
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| 264 | 1 | |a Wiesbaden |b Gabler |c 2008 | |
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| 650 | 4 | |a Dissertation / Thesis - 18 | |
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Record in the Search Index
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| adam_text | Titel: Pricing portfolio credit derivatives by means of evolutionary algorithms
Autor: Hager, Svenja
Jahr: 2008
Table of Contents
List of Tables xvii
List of Figures xix
List of Notations xxiii
1 Introduction 1
2 Collateralized Debt Obligations: Structure and Valuation 7
2.1 Introduction.................................. 7
2.2 Credit Risk Transfer Instruments...................... 9
2.2.1 Credit Default Swaps......................... 9
2.2.2 CDS Indices.............................. 9
2.2.3 Collateralized Debt Obligations................... 10
2.2.3.1 Arbitrage and Balance Sheet CDOs............ 11
2.2.3.2 Cash Flow and Market Value CDOs ........... 12
2.2.3.3 Static Structures and Managed Structures........ 13
2.2.3.4 Cash Structures and Synthetic Structures........ 13
2.2.3.5 Single-Tranche Deals.................... 15
2.2.3.6 Effect of Correlation.................... 16
2.2.4 CDS Index Tranches......................... 17
2.3 Credit Risk Modeling............................. 18
2.3.1 Single-Name Credit Risk: Intensity-Based Models......... 18
2.3.1.1 Stopping Times and the Hazard Rate Function..... 19
2.3.1.2 Homogeneous Poisson Processes.............. 22
2.3.1.3 Inhomogeneous Poisson Processes............. 23
2.3.1.4 Cox Processes........................ 24
2.3.2 Multi-Name Credit Risk: Copula Models.............. 25
2.3.3 Valuation of Synthetic CDOs .................... 29
Table of Contents
2.3.3.1 Joint Distribution of Default Times in the Gaussian Cop-
ula Approach........................ 30
2.3.3.2 Joint Distribution of Default Times in the Gaussian One-
Factor Copula Approach.................. 32
2.3.3.3 Pricing the Default Leg and the Margin Leg of a CDO . 33
2.3.3.3.1 The Default Leg ................. 33
2.3.3.3.2 The Margin Leg ................. 34
2.3.3.4 Distribution of the Portfolio Loss in the One-Factor Ap-
proach ............................ 35
2.3.3.5 Monte-Carlo Simulation of CDO Tranche Spreads .... 35
2.4 Valuation of CDOs: Literature........................ 36
3 Explaining the Implied Correlation Smile 41
3.1 Introduction.................................. 41
3.2 Sensitivity of the Tranche Price to the Level of Correlation........ 42
3.3 The Implied Tranche Correlation...................... 44
3.4 The Implied Correlation Smile........................ 45
3.5 The Implied Base Correlation........................ 47
3.6 Evolution of the Implied Correlation Smile................. 49
3.7 Modeling the Correlation Smile: Literature................. 56
3.8 Heterogeneous Dependence Structures ................... 58
3.8.1 Heterogeneous Dependence Structures Can Cause Implied Corre-
lation Smiles ............................. 60
3.8.1.1 The Existence Problem .................. 60
3.8.1.2 The Uniqueness Problem.................. 61
3.8.1.3 Exemplary Heterogeneous Matrices............ 62
3.8.2 Different Dependence Structures Can Lead to Identical Implied
Tranche Correlations......................... 63
3.8.3 Heterogeneous Dependence Structures Do Not Necessarily Lead to
Implied Correlation Smiles...................... 64
3.8.4 Heterogeneous Dependence Structures Allow for Flexible Portfolio
Loss Distributions........................... 65
3.9 Conclusion................................... 65
4 Optimization by Means of Evolutionary Algorithms 73
4.1 Introduction.................................. 73
4.2 Evolutionary Algorithms........................... 74
Table of Contents
4.3 Notation.................................... 77
4.4 Evolutionary Operators............................ 80
4.4.1 Selection................................ 80
4.4.1.1 Elite Selection ....................... 80
4.4.1.2 Tournament Selection................... 80
4.4.1.3 Proportional Selection................... 80
4.4.2 Recombination............................
4.4.2.1 Flat Crossover .......................
4.4.2.2 Discrete iV-Point Crossover................
4.4.2.3 Discrete Uniform Crossover................
4.4.2.4 Intermediate Crossover...................
4.4.2.5 Arithmetical Crossover...................
4.4.3 Mutation ...............................
4.4.3.1 Standard Mutation..................... 82
4.4.3.2 Global Mutation Without Strategy Parameter...... 82
4.4.3.3 Global Mutation With Strategy Parameter........ 82
4.4.3.4 Local Mutation....................... 82
4.4.3.5 1/5-Rule........................... 82
4.5 Basic Algorithms............................... 83
4.5.1 Evolution Strategies ......................... 83
4.5.1.1 Hill-Climber......................... 83
4.5.1.2 The (ì, A)-Strategy and the {ì + A)-Strategy ...... 84
4.5.2 Genetic Algorithms.......................... 85
4.5.3 Monte-Carlo Search.......................... 86
4.6 Parallel Algorithms.............................. 86
4.6.1 Global Population Models...................... 87
4.6.2 Local Population Model....................... 87
4.6.3 Regional Population Models..................... 87
4.7 Evolutionary Algorithms in Finance: Literature.............. 88
5 Evolutionary Algorithms in Finance: Deriving the Dependence Struc-
ture 91
5.1 Introduction.................................. 91
5.2 The Implied Correlation Structure...................... 92
5.3 The Optimization Problem.......................... 93
5.4 Description of the Genotypes ........................ 94
Table of Contents
5.4.1 The Cholesky Approach....................... 95
5.4.1.1 Initialization........................ 96
5.4.1.2 Repair Mechanism..................... 96
5.4.1.3 Evaluation and Program Termination........... 97
5.4.1.4 Recombination....................... 98
5.4.1.5 Mutation.......................... 99
5.4.2 The One-Factor Approach...................... 100
5.4.2.1 Initialization........................ 100
5.4.2.2 Repair Mechanism..................... 100
5.4.3 The Cluster Approach........................ 100
5.4.3.1 Initialization........................ 100
5.4.3.2 Repair Mechanism..................... 101
5.5 A Systematic Approach to Describe the Dependence Structure...... 101
5.5.1 The Nearest Neighbor Algorithm.................. 103
5.5.1.1 General Scheme of the Nearest Neighbor Algorithm . . . 104
5.6 Conclusion................................... 107
6 Experimental Results 109
6.1 Introduction.................................. 109
6.2 Solution Evaluation.............................. HO
6.2.1 Using the Expected Tranche Loss as Proxy for the Tranche Spread HO
6.2.2 Equivalent Information Content: Density of the Portfolio Loss and
Expected Tranche Loss........................ 112
6.2.2.1 Deriving the Expected Tranche Loss from the Density of
the Portfolio Loss...................... 113
6.2.2.2 Deriving the Density of the Portfolio Loss from the Ex-
pected Tranche Loss.................... 113
6.3 Performance Comparison: Basic Strategies................. 113
6.3.1 Setup ................................. 113
6.3.2 Results................................. 116
6.4 Performance Comparison: More Advanced Algorithms........... 120
6.4.1 Setup ................................. 120
6.4.2 Results................................. 122
6.4.2.1 Monte-Carlo Search vs. (1+1)-ES............. 125
6.4.2.2 (1+1)-ES vs. Multistart (1+1)-ES............ 125
6.4.2.3 (4,2O)-ES vs. GA(40) ................... 126
Table of Contents
6.4.2.3.1 Cholesky Approach................ 127
6.4.2.3.2 One-Factor Approach .............. 134
6.5 Implementation of a Parallel System .................... 135
6.6 Performance Comparison: Parallel Algorithms............... 136
6.6.1 Setup ................................. 136
6.6.2 Results................................. 138
6.7 Deriving the Dependence Structure From Market Data.......... 138
6.8 Conclusion................................... 141
7 Summary and Outlook 143
References 147
|
| adam_txt |
Titel: Pricing portfolio credit derivatives by means of evolutionary algorithms
Autor: Hager, Svenja
Jahr: 2008
Table of Contents
List of Tables xvii
List of Figures xix
List of Notations xxiii
1 Introduction 1
2 Collateralized Debt Obligations: Structure and Valuation 7
2.1 Introduction. 7
2.2 Credit Risk Transfer Instruments. 9
2.2.1 Credit Default Swaps. 9
2.2.2 CDS Indices. 9
2.2.3 Collateralized Debt Obligations. 10
2.2.3.1 Arbitrage and Balance Sheet CDOs. 11
2.2.3.2 Cash Flow and Market Value CDOs . 12
2.2.3.3 Static Structures and Managed Structures. 13
2.2.3.4 Cash Structures and Synthetic Structures. 13
2.2.3.5 Single-Tranche Deals. 15
2.2.3.6 Effect of Correlation. 16
2.2.4 CDS Index Tranches. 17
2.3 Credit Risk Modeling. 18
2.3.1 Single-Name Credit Risk: Intensity-Based Models. 18
2.3.1.1 Stopping Times and the Hazard Rate Function. 19
2.3.1.2 Homogeneous Poisson Processes. 22
2.3.1.3 Inhomogeneous Poisson Processes. 23
2.3.1.4 Cox Processes. 24
2.3.2 Multi-Name Credit Risk: Copula Models. 25
2.3.3 Valuation of Synthetic CDOs . 29
Table of Contents
2.3.3.1 Joint Distribution of Default Times in the Gaussian Cop-
ula Approach. 30
2.3.3.2 Joint Distribution of Default Times in the Gaussian One-
Factor Copula Approach. 32
2.3.3.3 Pricing the Default Leg and the Margin Leg of a CDO . 33
2.3.3.3.1 The Default Leg . 33
2.3.3.3.2 The Margin Leg . 34
2.3.3.4 Distribution of the Portfolio Loss in the One-Factor Ap-
proach . 35
2.3.3.5 Monte-Carlo Simulation of CDO Tranche Spreads . 35
2.4 Valuation of CDOs: Literature. 36
3 Explaining the Implied Correlation Smile 41
3.1 Introduction. 41
3.2 Sensitivity of the Tranche Price to the Level of Correlation. 42
3.3 The Implied Tranche Correlation. 44
3.4 The Implied Correlation Smile. 45
3.5 The Implied Base Correlation. 47
3.6 Evolution of the Implied Correlation Smile. 49
3.7 Modeling the Correlation Smile: Literature. 56
3.8 Heterogeneous Dependence Structures . 58
3.8.1 Heterogeneous Dependence Structures Can Cause Implied Corre-
lation Smiles . 60
3.8.1.1 The Existence Problem . 60
3.8.1.2 The Uniqueness Problem. 61
3.8.1.3 Exemplary Heterogeneous Matrices. 62
3.8.2 Different Dependence Structures Can Lead to Identical Implied
Tranche Correlations. 63
3.8.3 Heterogeneous Dependence Structures Do Not Necessarily Lead to
Implied Correlation Smiles. 64
3.8.4 Heterogeneous Dependence Structures Allow for Flexible Portfolio
Loss Distributions. 65
3.9 Conclusion. 65
4 Optimization by Means of Evolutionary Algorithms 73
4.1 Introduction. 73
4.2 Evolutionary Algorithms. 74
Table of Contents
4.3 Notation. 77
4.4 Evolutionary Operators. 80
4.4.1 Selection. 80
4.4.1.1 Elite Selection . 80
4.4.1.2 Tournament Selection. 80
4.4.1.3 Proportional Selection. 80
4.4.2 Recombination.
4.4.2.1 Flat Crossover .
4.4.2.2 Discrete iV-Point Crossover.
4.4.2.3 Discrete Uniform Crossover.
4.4.2.4 Intermediate Crossover.
4.4.2.5 Arithmetical Crossover.
4.4.3 Mutation .
4.4.3.1 Standard Mutation. 82
4.4.3.2 Global Mutation Without Strategy Parameter. 82
4.4.3.3 Global Mutation With Strategy Parameter. 82
4.4.3.4 Local Mutation. 82
4.4.3.5 1/5-Rule. 82
4.5 Basic Algorithms. 83
4.5.1 Evolution Strategies . 83
4.5.1.1 Hill-Climber. 83
4.5.1.2 The (ì, A)-Strategy and the {ì + A)-Strategy . 84
4.5.2 Genetic Algorithms. 85
4.5.3 Monte-Carlo Search. 86
4.6 Parallel Algorithms. 86
4.6.1 Global Population Models. 87
4.6.2 Local Population Model. 87
4.6.3 Regional Population Models. 87
4.7 Evolutionary Algorithms in Finance: Literature. 88
5 Evolutionary Algorithms in Finance: Deriving the Dependence Struc-
ture 91
5.1 Introduction. 91
5.2 The Implied Correlation Structure. 92
5.3 The Optimization Problem. 93
5.4 Description of the Genotypes . 94
Table of Contents
5.4.1 The Cholesky Approach. 95
5.4.1.1 Initialization. 96
5.4.1.2 Repair Mechanism. 96
5.4.1.3 Evaluation and Program Termination. 97
5.4.1.4 Recombination. 98
5.4.1.5 Mutation. 99
5.4.2 The One-Factor Approach. 100
5.4.2.1 Initialization. 100
5.4.2.2 Repair Mechanism. 100
5.4.3 The Cluster Approach. 100
5.4.3.1 Initialization. 100
5.4.3.2 Repair Mechanism. 101
5.5 A Systematic Approach to Describe the Dependence Structure. 101
5.5.1 The Nearest Neighbor Algorithm. 103
5.5.1.1 General Scheme of the Nearest Neighbor Algorithm . . . 104
5.6 Conclusion. 107
6 Experimental Results 109
6.1 Introduction. 109
6.2 Solution Evaluation. HO
6.2.1 Using the Expected Tranche Loss as Proxy for the Tranche Spread HO
6.2.2 Equivalent Information Content: Density of the Portfolio Loss and
Expected Tranche Loss. 112
6.2.2.1 Deriving the Expected Tranche Loss from the Density of
the Portfolio Loss. 113
6.2.2.2 Deriving the Density of the Portfolio Loss from the Ex-
pected Tranche Loss. 113
6.3 Performance Comparison: Basic Strategies. 113
6.3.1 Setup . 113
6.3.2 Results. 116
6.4 Performance Comparison: More Advanced Algorithms. 120
6.4.1 Setup . 120
6.4.2 Results. 122
6.4.2.1 Monte-Carlo Search vs. (1+1)-ES. 125
6.4.2.2 (1+1)-ES vs. Multistart (1+1)-ES. 125
6.4.2.3 (4,2O)-ES vs. GA(40) . 126
Table of Contents
6.4.2.3.1 Cholesky Approach. 127
6.4.2.3.2 One-Factor Approach . 134
6.5 Implementation of a Parallel System . 135
6.6 Performance Comparison: Parallel Algorithms. 136
6.6.1 Setup . 136
6.6.2 Results. 138
6.7 Deriving the Dependence Structure From Market Data. 138
6.8 Conclusion. 141
7 Summary and Outlook 143
References 147 |
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| bvnumber | BV023392388 |
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| ctrlnum | (OCoLC)254632944 (DE-599)DNB98714362X |
| dewey-full | 332.6320151962 |
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| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.6320151962 |
| dewey-search | 332.6320151962 |
| dewey-sort | 3332.6320151962 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| discipline_str_mv | Wirtschaftswissenschaften |
| edition | 1. ed. |
| format | Thesis Book |
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| index_date | 2024-07-02T21:20:29Z |
| indexdate | 2024-07-09T21:17:34Z |
| institution | BVB |
| isbn | 9783834909152 3834909157 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016575308 |
| oclc_num | 254632944 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-703 |
| owner_facet | DE-355 DE-BY-UBR DE-703 |
| physical | XXVII, 160 S. graph. Darst. 21 cm |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Gabler |
| record_format | marc |
| series2 | Gabler Edition Wissenschaft |
| spelling | Hager, Svenja Verfasser aut Pricing portfolio credit derivatives by means of evolutionary algorithms Svenja Hager 1. ed. Wiesbaden Gabler 2008 XXVII, 160 S. graph. Darst. 21 cm txt rdacontent n rdamedia nc rdacarrier Gabler Edition Wissenschaft Zugl.: Tübingen, Univ., Diss., 2007 Collateralized debt obligation - Kreditrisiko - Evolutionärer Algorithmus Dissertation / Thesis - 18 Finanzderivat / Kreditrisiko / Kapitalmarkttheorie / Evolutionsökonomik / Monte-Carlo-Methode Evolutionärer Algorithmus (DE-588)4366912-8 gnd rswk-swf Kreditrisiko (DE-588)4114309-7 gnd rswk-swf Collateralized debt obligation (DE-588)7548936-3 gnd rswk-swf (DE-588)4113937-9 Hochschulschrift gnd-content Collateralized debt obligation (DE-588)7548936-3 s Kreditrisiko (DE-588)4114309-7 s Evolutionärer Algorithmus (DE-588)4366912-8 s DE-604 HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016575308&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Hager, Svenja Pricing portfolio credit derivatives by means of evolutionary algorithms Collateralized debt obligation - Kreditrisiko - Evolutionärer Algorithmus Dissertation / Thesis - 18 Finanzderivat / Kreditrisiko / Kapitalmarkttheorie / Evolutionsökonomik / Monte-Carlo-Methode Evolutionärer Algorithmus (DE-588)4366912-8 gnd Kreditrisiko (DE-588)4114309-7 gnd Collateralized debt obligation (DE-588)7548936-3 gnd |
| subject_GND | (DE-588)4366912-8 (DE-588)4114309-7 (DE-588)7548936-3 (DE-588)4113937-9 |
| title | Pricing portfolio credit derivatives by means of evolutionary algorithms |
| title_auth | Pricing portfolio credit derivatives by means of evolutionary algorithms |
| title_exact_search | Pricing portfolio credit derivatives by means of evolutionary algorithms |
| title_exact_search_txtP | Pricing portfolio credit derivatives by means of evolutionary algorithms |
| title_full | Pricing portfolio credit derivatives by means of evolutionary algorithms Svenja Hager |
| title_fullStr | Pricing portfolio credit derivatives by means of evolutionary algorithms Svenja Hager |
| title_full_unstemmed | Pricing portfolio credit derivatives by means of evolutionary algorithms Svenja Hager |
| title_short | Pricing portfolio credit derivatives by means of evolutionary algorithms |
| title_sort | pricing portfolio credit derivatives by means of evolutionary algorithms |
| topic | Collateralized debt obligation - Kreditrisiko - Evolutionärer Algorithmus Dissertation / Thesis - 18 Finanzderivat / Kreditrisiko / Kapitalmarkttheorie / Evolutionsökonomik / Monte-Carlo-Methode Evolutionärer Algorithmus (DE-588)4366912-8 gnd Kreditrisiko (DE-588)4114309-7 gnd Collateralized debt obligation (DE-588)7548936-3 gnd |
| topic_facet | Collateralized debt obligation - Kreditrisiko - Evolutionärer Algorithmus Dissertation / Thesis - 18 Finanzderivat / Kreditrisiko / Kapitalmarkttheorie / Evolutionsökonomik / Monte-Carlo-Methode Evolutionärer Algorithmus Kreditrisiko Collateralized debt obligation Hochschulschrift |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016575308&sequence=000004&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT hagersvenja pricingportfoliocreditderivativesbymeansofevolutionaryalgorithms |