Lévy processes in credit risk:
Gespeichert in:
| 1. Verfasser: | |
|---|---|
| Format: | Buch |
| Sprache: | English |
| Veröffentlicht: |
Chichester
Wiley
2009
|
| Schriftenreihe: | Wiley finance series
|
| Schlagworte: | |
| Online-Zugang: | Cover Inhaltsverzeichnis |
| Beschreibung: | IX, 185 S. graph. Darst. |
| ISBN: | 9780470743065 |
Internformat
MARC
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Datensatz im Suchindex
| _version_ | 1804140670748721152 |
|---|---|
| adam_text | Titel: Levy processes in credit risk
Autor: Schoutens, Wim
Jahr: 2009
Contents
Preface xi
Acknowledgements xiii
PART I: INTRODUCTION
1 An Introduction to Credit Risk 3
1.1 Credit Risk 3
1.1.1 Historical and Risk-Neutral Probabilities 4
1.1.2 Bond Prices and Default Probability 6
1.2 Credit Risk Modelling 8
1.3 Credit Derivatives 11
1.4 Modelling Assumptions 13
1.4.1 Probability Space and Filtrations 13
1.4.2 The Risk-Free Asset 15
2 An Introduction to Levy Processes 17
2.1 Brownian Motion 17
2.2 Levy Processes 20
2.3 Examples of Levy Processes 23
2.3.1 Poisson Process 23
2.3.2 Compound Poisson Process 25
2.3.3 The Gamma Process 27
2.3.4 Inverse Gaussian Process 29
2.3.5 The CMY Process 31
2.3.6 The Variance Gamma Process 32
2.4 Ornstein-Uhlenbeck Processes 37
2.4.1 The Gamma-OU Process 39
2.4.2 The Inverse Gaussian-OU Process 40
viii Contents
PART II: SINGLE-NAME MODELLING
3 Single-Name Credit Derivatives 45
3.1 Credit Default Swaps 45
3.1.1 Credit Default Swaps Pricing 47
3.1.2 Calibration Assumptions 49
3.2 Credit Default Swap Forwards 50
3.2.1 Credit Default Swap Forward Pricing 50
3.3 Constant Maturity Credit Default Swaps 51
3.3.1 Constant Maturity Credit Default Swaps Pricing 52
3.4 Options on CDS 54
4 Firm-Value Levy Models 57
4.1 The Merton Model 57
4.2 The Black-Cox Model with Constant Barrier 60
4.3 The Levy First-Passage Model 62
4.4 The Variance Gamma Model 63
4.4.1 Sensitivity to the Parameters 66
4.4.2 Calibration on CDS Term Structure Curve 69
4.5 One-Sided Levy Default Model 71
4.5.1 Wiener-Hopf Factorization and Default Probabilities 71
4.5.2 Illustration of the Pricing of Credit Default Swaps 75
4.6 Dynamic Spread Generator 77
4.6.1 Generating Spread Paths 77
4.6.2 Pricing of Options on CDSs 79
4.6.3 Black s Formulas and Implied Volatility 80
Appendix: Solution of the PDIE 82
5 Intensity Levy Models 87
5.1 Intensity Models for Credit Risk 87
5.1.1 Jarrow-Turnbull Model 87
5.1.2 Cox Models 91
5.2 The Intensity-OU Model 92
5.3 Calibration of the Model on CDS Term Structures 95
PART III: MULTIVARIATE MODELLING
6 Multivariate Credit Products 101
6.1 CDOs 101
6.2 Credit Indices 105
7 Collateralized Debt Obligations 109
7.1 Introduction 109
7.2 The Gaussian One-Factor Model 110
Contents ix
7.3 Generic One-Factor Levy Model 111
7.4 Examples of Levy Models 115
7.5 Levy Base Correlation 117
7.5.1 The Concept of Base Correlation 117
7.5.2 Pricing Non-Standard Tranches 119
7.5.3 Correlation Mapping for Bespoke CDOs 121
7.6 Delta-Hedging CDO tranches 122
7.6.1 Hedging with the CDS Index 122
7.6.2 Delta-Hedging with a Single-Name CDS 122
7.6.3 Mezz-Equity hedging 124
8 Multivariate Index Modelling 125
8.1 Black s Model 126
8.2 VG Credit Spread Model 127
8.3 Pricing Swaptions using FFT 128
8.4 Multivariate VG Model 130
PART IV: EXOTIC STRUCTURED CREDIT RISK PRODUCTS
9 Credit CPPIs and CPDOs 137
9.1 Introduction 137
9.2 CPPIs 137
9.3 Gap Risk 143
9.4 CPDOs 145
10 Asset-Backed Securities 149
10.1 Introduction 149
10.2 Default Models 150
10.2.1 Generalized Logistic Default Model 150
10.2.2 Levy Portfolio Default Model 152
10.2.3 Normal One-Factor Default Model 153
10.2.4 Generic One-Factor Levy Default Model 155
10.3 Prepayment Models 156
10.3.1 Constant Prepayment Model 157
10.3.2 Levy Portfolio Prepayment Model 158
10.3.3 Normal One-Factor Prepayment Model 158
10.4 Numerical Results 160
Bibliography !67
Index 173
|
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| isbn | 9780470743065 |
| language | English |
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| spelling | Schoutens, Wim Verfasser aut Lévy processes in credit risk Wim Schoutens and Jessica Cariboni Chichester Wiley 2009 IX, 185 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley finance series Mathematisches Modell Credit / Management / Mathematical models Risk management / Mathematical models Lévy processes Risikomanagement (DE-588)4121590-4 gnd rswk-swf Kreditrisiko (DE-588)4114309-7 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 gnd rswk-swf Lévy-Prozess (DE-588)4463623-4 s Kreditrisiko (DE-588)4114309-7 s Risikomanagement (DE-588)4121590-4 s DE-604 Cariboni, Jessica Sonstige oth DE-576;wiley image/jpeg http://swbplus.bsz-bw.de/bsz310815266cov.htm 20090917210536 Cover HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=018611879&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Schoutens, Wim Lévy processes in credit risk Mathematisches Modell Credit / Management / Mathematical models Risk management / Mathematical models Lévy processes Risikomanagement (DE-588)4121590-4 gnd Kreditrisiko (DE-588)4114309-7 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| subject_GND | (DE-588)4121590-4 (DE-588)4114309-7 (DE-588)4463623-4 |
| title | Lévy processes in credit risk |
| title_auth | Lévy processes in credit risk |
| title_exact_search | Lévy processes in credit risk |
| title_full | Lévy processes in credit risk Wim Schoutens and Jessica Cariboni |
| title_fullStr | Lévy processes in credit risk Wim Schoutens and Jessica Cariboni |
| title_full_unstemmed | Lévy processes in credit risk Wim Schoutens and Jessica Cariboni |
| title_short | Lévy processes in credit risk |
| title_sort | levy processes in credit risk |
| topic | Mathematisches Modell Credit / Management / Mathematical models Risk management / Mathematical models Lévy processes Risikomanagement (DE-588)4121590-4 gnd Kreditrisiko (DE-588)4114309-7 gnd Lévy-Prozess (DE-588)4463623-4 gnd |
| topic_facet | Mathematisches Modell Credit / Management / Mathematical models Risk management / Mathematical models Lévy processes Risikomanagement Kreditrisiko Lévy-Prozess |
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