Financial engineering with copulas explained:
Saved in:
| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Basingstoke [u.a.]
Palgrave Macmillan
2014
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| Series: | Financial engineering explained
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| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVI, 150 S. Ill., graph. Darst. |
| ISBN: | 9781137346308 |
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Record in the Search Index
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| adam_text | Titel: Financial engineering with copulas explained
Autor: Mai, Jan-Frederik
Jahr: 2014
Contents
List of Figures ix
List of Tables xiii
Preface and Acknowledgments xiv
1 What Are Copulas? 1
1.1 Two Motivating Examples 1
1.1.1 Example 1: Analyzing Dependence between Asset
Movements 1
1.1.2 Example 2: Modeling the Dependence between Default
Times 6
1.2 Copulas and Sklar s Theorem 6
1.2.1 The Generalized Inverse 9
1.2.2 Sklar s Theorem for Survival Functions 11
1.2.3 How to Apply Sklar s Theorem? 12
1.3 General Copula Properties 14
2 Which Rules for Handling Copulas Do I Need? 19
2.1 The Fréchet-Hoeffding Bounds 19
2.2 Switching from Distribution to Survival Functions 21
2.3 Invariance Under Strictly Monotone Transformations 25
2.4 Computing Probabilities from a Distribution Function 28
2.5 Copula Derivatives 30
2.6 Constructing New Copulas from Existing Ones 32
3 How to Measure Dependence? 35
3.1 Pearson s Correlation Coefficient 35
3.2 Concordance Measures 39
3.2.1 Using Kendall s x and Spearman s ps 44
3.3 Tail Dependence 45
4 What are Popular Families of Copulas? 49
4.1 Gaussian Copulas 49
4.1.1 Important Stylized Facts of the (Bivariate) Gaussian
Copula 51
4.1.2 Generalization to Elliptical Copulas 55
4.2 Archimedean Copulas 57
4.2.1 Stylized Facts of Archimedean Copulas 60
4.2.2 Hierarchical Archimedean Copulas 62
4.3 Extreme-value Copulas 64
4.3.1 Marshall-Olkin Copulas 66
4.3.2 Stylized Facts of Extreme-Value Copulas 70
4.4 Archimax Copulas 71
5 How to Simulate Multivariate Distributions? 74
5.1 How to Simulate from a Copula? 78
5.1.1 Simulation Based on Analytical Techniques 78
5.1.2 Simulation Along a Stochastic Model 79
5.1.3 Practical Guide for the Implementation 83
6 How to Estimate Parameters of a Multivariate Model? 85
6.1 The Method of Moments 86
6.1.1 Some Theoretical Background 87
6.2 Maximum-Likelihood Methods 88
6.2.1 Perfect Information about the Marginal Laws 89
6.2.2 Joint Maximization Over a and 0: Full
Maximum-Likelihood 90
6.2.3 Inference Functions for Margins (IFM) Method 90
6.3 Using A Rank Transformation to Obtain (Pseudo-)Samples 91
6.3.1 Visualization of the Methods 94
6.4 Estimation of Specific Copula Families 96
6.4.1 Taylor-made Estimation Strategies for Extreme-value
Copulas 97
6.5 A Note on Positive Semi-Definiteness 99
6.6 Some Remarks Concerning the Implementation 101
7 How to Deal with Uncertainty Concerning Dependence? 103
7.1 Bounds for the VaR of a Portfolio 105
7.2 What is the Maximal Probability for a Joint Default? 112
7.2.1 Motivation 112
7.2.2 Maximal Coupling 113
8 How to Construct a Portfolio-Default Model? 117
8.1 The Canonical Construction of Default Times 117
8.2 Classical Copula Models for Dependent Default Times 119
8.2.1 The Portfolio-loss Distribution 121
8.3 A Factor Model for CD O Pricing 126
8.3.1 An Excursion to CD O Pricing 126
8.3.2 Calibrating the Two Portfolio-default Models 134
References 138
Index
149
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| discipline | Mathematik Wirtschaftswissenschaften |
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| id | DE-604.BV042112774 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:13:01Z |
| institution | BVB |
| isbn | 9781137346308 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027553168 |
| oclc_num | 896792416 |
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| owner | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-523 |
| owner_facet | DE-91G DE-BY-TUM DE-355 DE-BY-UBR DE-523 |
| physical | XVI, 150 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | Palgrave Macmillan |
| record_format | marc |
| series2 | Financial engineering explained |
| spelling | Mai, Jan-Frederik 1982- Verfasser (DE-588)141790261 aut Financial engineering with copulas explained Jan-Frederik Mai and Matthias Scherer Basingstoke [u.a.] Palgrave Macmillan 2014 XVI, 150 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Financial engineering explained Kopula Mathematik (DE-588)4529954-7 gnd rswk-swf Financial Engineering (DE-588)4208404-0 gnd rswk-swf Kopula Mathematik (DE-588)4529954-7 s Financial Engineering (DE-588)4208404-0 s DE-604 Scherer, Matthias Sonstige (DE-588)133340937 oth HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027553168&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Mai, Jan-Frederik 1982- Financial engineering with copulas explained Kopula Mathematik (DE-588)4529954-7 gnd Financial Engineering (DE-588)4208404-0 gnd |
| subject_GND | (DE-588)4529954-7 (DE-588)4208404-0 |
| title | Financial engineering with copulas explained |
| title_auth | Financial engineering with copulas explained |
| title_exact_search | Financial engineering with copulas explained |
| title_full | Financial engineering with copulas explained Jan-Frederik Mai and Matthias Scherer |
| title_fullStr | Financial engineering with copulas explained Jan-Frederik Mai and Matthias Scherer |
| title_full_unstemmed | Financial engineering with copulas explained Jan-Frederik Mai and Matthias Scherer |
| title_short | Financial engineering with copulas explained |
| title_sort | financial engineering with copulas explained |
| topic | Kopula Mathematik (DE-588)4529954-7 gnd Financial Engineering (DE-588)4208404-0 gnd |
| topic_facet | Kopula Mathematik Financial Engineering |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027553168&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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