Credit risk: modeling, valuation and hedging
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2004
|
| Edition: | 1. ed., corr. 2. print. |
| Series: | Springer finance
|
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XVIII, 501 S. |
| ISBN: | 3540675930 9783540675938 |
Staff View
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Record in the Search Index
| _version_ | 1804130504474099712 |
|---|---|
| adam_text | Titel: Credit risk
Autor: Bielecki, Tomasz R
Jahr: 2004
Table of Contents
Preface....................................................... V
Part I. Structural Approach
1. Introduction to Credit Risk............................... 3
1.1 Corporate Bonds....................................... 4
1.1.1 Recovery Rules .................................. 5
1.1.2 Safety Covenants................................. 6
1.1.3 Credit Spreads................................... 7
1.1.4 Credit Ratings................................... 7
1.1.5 Corporate Coupon Bonds ......................... 8
1.1.6 Fixed and Floating Rate Notes..................... 9
1.1.7 Bank Loans and Sovereign Debt.................... 11
1.1.8 Cross Default.................................... 11
1.1.9 Default Correlations.............................. 11
1.2 Vulnerable Claims...................................... 12
1.2.1 Vulnerable Claims with Unilateral Default Risk...... 12
1.2.2 Vulnerable Claims with Bilateral Default Risk....... 13
1.2.3 Defaultable Interest Rate Contracts................. 14
1.3 Credit Derivatives...................................... 16
1.3.1 Default Swaps and Options........................ 18
1.3.2 Total Rate of Return Swaps....................... 21
1.3.3 Credit Linked Notes.............................. 22
1.3.4 Asset Swaps..................................... 24
1.3.5 First-to-Default Contracts......................... 24
1.3.6 Credit Spread Swaps and Options.................. 25
1.4 Quantitative Models of Credit Risk....................... 26
1.4.1 Structural Models................................ 26
1.4.2 Reduced-Form Models............................ 27
1.4.3 Credit Risk Management.......................... 29
1.4.4 Liquidity Risk ................................... 30
1.4.5 Econometric Studies.............................. 30
XIV Table of Contents
2. Corporate Debt .......................................... 31
2.1 Defaultable Claims..................................... 33
2.1.1 Risk-Neutral Valuation Formula.................... 34
2.1.2 Self-Financing Trading Strategies................... 37
2.1.3 Martingale Measures.............................. 38
2.2 PDE Approach......................................... 40
2.2.1 PDE for the Value Function....................... 44
2.2.2 Corporate Zero-Coupon Bonds..................... 47
2.2.3 Corporate Coupon Bond.......................... 50
2.3 Merton s Approach to Corporate Debt.................... 51
2.3.1 Merton s Model with Deterministic Interest Rates .... 51
2.3.2 Distance-to-Default............................... 57
2.4 Extensions of Merton s Approach......................... 58
2.4.1 Models with Stochastic Interest Rates............... 59
2.4.2 Discontinuous Value Process....................... 60
2.4.3 Buffet s Approach................................ 64
3. First-Passage-Time Models............................... 65
3.1 Properties of First Passage Times ........................ 66
3.1.1 Probability Law of the First Passage Time........... 67
3.1.2 Joint Probability Law of Y and r .................. 69
3.2 Black and Cox Model................................... 71
3.2.1 Corporate Zero-Coupon Bond...................... 71
3.2.2 Corporate Coupon Bond.......................... 79
3.2.3 Corporate Consol Bond........................... 81
3.3 Optimal Capital Structure............................... 82
3.3.1 Black and Cox Approach.......................... 82
3.3.2 Leland s Approach................................ 84
3.3.3 Leland and Toft Approach......................... 86
3.3.4 Further Developments ............................ 88
3.4 Models with Stochastic Interest Rates..................... 90
3.4.1 Kim, Ramaswamy and Sundaresan Approach........ 96
3.4.2 Longstaff and Schwartz Approach.................. 98
3.4.3 Cathcart and El-Jahel Approach...................103
3.4.4 Briys and de Varenne Approach....................104
3.4.5 Saa-Requejo and Santa-Clara Approach.............107
3.5 Further Developments...................................113
3.5.1 Convertible Bonds................................113
3.5.2 Jump-Diffusion Models............................113
3.5.3 Incomplete Accounting Data.......................113
3.6 Dependent Defaults: Structural Approach .................114
3.6.1 Default Correlations: J.P. Morgan s Approach........116
3.6.2 Default Correlations: Zhou s Approach..............117
Table of Contents XV
Part II. Hazard Processes
4. Hazard Function of a Random Time......................123
4.1 Conditional Expectations w.r.t. Natural Filtrations.........123
4.2 Martingales Associated with a Continuous Hazard Function. . 127
4.3 Martingale Representation Theorem......................131
4.4 Change of a Probability Measure.........................133
4.5 Martingale Characterization of the Hazard Function........137
4.6 Compensator of a Random Time.........................140
5. Hazard Process of a Random Time.......................141
5.1 Hazard Process F ......................................141
5.1.1 Conditional Expectations.......................... 143
5.1.2 Semimartingale Representation of the Stopped Process 150
5.1.3 Martingales Associated with the Hazard Process r . . . 152
5.1.4 Stochastic Intensity of a Random Time ............. 155
5.2 Martingale Representation Theorems ..................... 156
5.2.1 General Case....................................156
5.2.2 Case of a Brownian Filtration......................159
5.3 Change of a Probability Measure.........................162
6. Martingale Hazard Process...............................165
6.1 Martingale Hazard Process A............................165
6.1.1 Martingale Invariance Property.................... 166
6.1.2 Evaluation of A: Special Case...................... 167
6.1.3 Evaluation of A: General Case ..................... 169
6.1.4 Uniqueness of a Martingale Hazard Process A........ 172
6.2 Relationships Between Hazard Processes F and A .......... 173
6.3 Martingale Representation Theorem...................... 177
6.4 Case of the Martingale Invariance Property................ 179
6.4.1 Valuation of Defaultable Claims.................... 180
6.4.2 Case of a Stopping Time.......................... 182
6.5 Random Time with a Given Hazard Process............... 183
6.6 Poisson Process and Conditional Poisson Process........... 186
7. Case of Several Random Times...........................197
7.1 Minimum of Several Random Times ......................197
7.1.1 Hazard Function.................................198
7.1.2 Martingale Hazard Process........................198
7.1.3 Martingale Representation Theorem................200
7.2 Change of a Probability Measure.........................203
7.3 Kusuoka s Counter-Example.............................209
7.3.1 Validity of Condition (F.2) ........................216
7.3.2 Validity of Condition (M.l)........................218
XVI Table of Contents
Part III. Reduced-Form Modeling
8. Intensity-Based Valuation of Defaultable Claims.......... 221
8.1 Defaultable Claims..................................... 222
8.1.1 Risk-Neutral Valuation Formula.................... 223
8.2 Valuation via the Hazard Process......................... 225
8.2.1 Canonical Construction of a Default Time........... 227
8.2.2 Integral Representation of the Value Process......... 230
8.2.3 Case of a Deterministic Intensity................... 232
8.2.4 Implied Probabilities of Default.................... 234
8.2.5 Exogenous Recovery Rules......................... 236
8.3 Valuation via the Martingale Approach.................... 239
8.3.1 Martingale Hypotheses............................ 242
8.3.2 Endogenous Recovery Rules ....................... 243
8.4 Hedging of Defaultable Claims........................... 246
8.5 General Reduced-Form Approach......................... 250
8.6 Reduced-Form Models with State Variables................ 253
8.6.1 Lando s Approach................................ 253
8.6.2 Duffie and Singleton Approach..................... 255
8.6.3 Hybrid Methodologies............................. 259
8.6.4 Credit Spread Models............................. 264
9. Conditionally Independent Defaults ......................265
9.1 Basket Credit Derivatives................................266
9.1.1 Mutually Independent Default Times...............267
9.1.2 Conditionally Independent Default Times...........268
9.1.3 Valuation of the 2th-to-Default Contract.............274
9.1.4 Vanilla Default Swaps of Basket Type...............281
9.2 Default Correlations and Conditional Probabilities..........284
9.2.1 Default Correlations..............................284
9.2.2 Conditional Probabilities..........................287
10. Dependent Defaults ......................................293
10.1 Dependent Intensities...................................295
10.1.1 Kusuoka s Approach..............................295
10.1.2 Jarrow and Yu Approach..........................296
10.2 Martingale Approach to Basket Credit Derivatives..........306
10.2.1 Valuation of the ith-to-Default Claims...............311
11. Markov Chains...........................................313
11.1 Discrete-Time Markov Chains............................314
11.1.1 Change of a Probability Measure...................316
11.1.2 The Law of the Absorption Time...................320
11.1.3 Discrete-Time Conditionally Markov Chains.........322
Table of Contents XVII
11.2 Continuous-Time Markov Chains.........................324
11.2.1 Embedded Discrete-Time Markov Chain ............329
11.2.2 Conditional Expectations..........................329
11.2.3 Probability Distribution of the Absorption Time.....332
11.2.4 Martingales Associated with Transitions.............333
11.2.5 Change of a Probability Measure...................334
11.2.6 Identification of the Intensity Matrix................338
11.3 Continuous-Time Conditionally Markov Chains ............340
11.3.1 Construction of a Conditionally Markov Chain....... 342
11.3.2 Conditional Markov Property...................... 346
11.3.3 Associated Local Martingales...................... 347
11.3.4 Forward Kolmogorov Equation..................... 350
12. Markovian Models of Credit Migrations..................351
12.1 JLT Markovian Model and its Extensions..................352
12.1.1 JLT Model: Discrete-Time Case....................354
12.1.2 JLT Model: Continuous-Time Case.................362
12.1.3 Kijima and Komoribayashi Model..................367
12.1.4 Das and Tufano Model............................369
12.1.5 Thomas, Allen and Morkel-Kingsbury Model.........371
12.2 Conditionally Markov Models............................373
12.2.1 Lando s Approach................................374
12.3 Correlated Migrations...................................376
12.3.1 Huge and Lando Approach........................380
13. Heath-Jarrow-Morton Type Models ......................385
13.1 HJM Model with Default................................386
13.1.1 Model s Assumptions.............................386
13.1.2 Default-Free Term Structure.......................388
13.1.3 Pre-Default Value of a Corporate Bond .............390
13.1.4 Dynamics of Forward Credit Spreads ...............392
13.1.5 Default Time of a Corporate Bond .................394
13.1.6 Case of Zero Recovery............................397
13.1.7 Default-Free and Defaultable LIBOR Rates..........398
13.1.8 Case of a Non-Zero Recovery Rate..................400
13.1.9 Alternative Recovery Rules........................403
13.2 HJM Model with Credit Migrations.......................405
13.2.1 Model s Assumption..............................405
13.2.2 Migration Process................................407
13.2.3 Special Case.....................................408
13.2.4 General Case....................................410
13.2.5 Alternative Recovery Schemes......................413
13.2.6 Defaultable Coupon Bonds........................415
13.2.7 Default Correlations..............................416
13.2.8 Market Prices of Interest Rate and Credit Risk.......417
XVIII Table of Contents
13.3 Applications to Credit Derivatives........................421
13.3.1 Valuation of Credit Derivatives.....................421
13.3.2 Hedging of Credit Derivatives......................422
14. Defaultable Market Rates ................................423
14.1 Interest Rate Contracts with Default Risk.................424
14.1.1 Default-Free LIBOR and Swap Rates...............424
14.1.2 Defaultable Spot LIBOR Rates ....................426
14.1.3 Defaultable Spot Swap Rates......................427
14.1.4 FRAs with Unilateral Default Risk.................428
14.1.5 Forward Swaps with Unilateral Default Risk.........432
14.2 Multi-Period IRAs with Unilateral Default Risk............434
14.3 Multi-Period Defaultable Forward Nominal Rates...........438
14.4 Defaultable Swaps with Unilateral Default Risk............441
14.4.1 Settlement of the 1st Kind.........................442
14.4.2 Settlement of the 2nd Kind........................444
14.4.3 Settlement of the 3rd Kind.........................445
14.4.4 Market Conventions..............................446
14.5 Defaultable Swaps with Bilateral Default Risk .............447
14.6 Defaultable Forward Swap Rates.........................449
14.6.1 Forward Swaps with Unilateral Default Risk.........449
14.6.2 Forward Swaps with Bilateral Default Risk..........450
15. Modeling of Market Rates................................451
15.1 Models of Default-Free Market Rates .....................452
15.1.1 Modeling of Forward LIBOR Rates.................452
15.1.2 Modeling of Forward Swap Rates...................458
15.2 Modeling of Defaultable Forward LIBOR Rates............465
15.2.1 Lotz and Schlogl Approach........................465
15.2.2 Schonbucher s Approach ..........................469
References....................................................479
Basic Notation ...............................................495
Subject Index ................................................497
|
| any_adam_object | 1 |
| author | Bielecki, Tomasz R. 1955- Rutkowski, Marek |
| author_GND | (DE-588)12323400X (DE-588)171429893 |
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| dewey-full | 332.7/01/5118 |
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| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.7/01/5118 |
| dewey-search | 332.7/01/5118 |
| dewey-sort | 3332.7 11 45118 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| edition | 1. ed., corr. 2. print. |
| format | Book |
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| id | DE-604.BV017806169 |
| illustrated | Not Illustrated |
| indexdate | 2024-07-09T19:22:05Z |
| institution | BVB |
| isbn | 3540675930 9783540675938 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-010692768 |
| oclc_num | 223248313 |
| open_access_boolean | |
| owner | DE-91G DE-BY-TUM DE-384 DE-19 DE-BY-UBM DE-20 DE-11 DE-634 DE-706 |
| owner_facet | DE-91G DE-BY-TUM DE-384 DE-19 DE-BY-UBM DE-20 DE-11 DE-634 DE-706 |
| physical | XVIII, 501 S. |
| publishDate | 2004 |
| publishDateSearch | 2004 |
| publishDateSort | 2004 |
| publisher | Springer |
| record_format | marc |
| series2 | Springer finance |
| spelling | Bielecki, Tomasz R. 1955- Verfasser (DE-588)12323400X aut Credit risk modeling, valuation and hedging Tomasz R. Bielecki ; Marek Rutkowski 1. ed., corr. 2. print. Berlin [u.a.] Springer 2004 XVIII, 501 S. txt rdacontent n rdamedia nc rdacarrier Springer finance Administração de risco (modelos matemáticos) larpcal Crédito (modelos matemáticos) larpcal Hedging (finanças) larpcal Matemática financeira larpcal Mathematisches Modell Credit Mathematical models Risk management Mathematical models Kreditrisiko (DE-588)4114309-7 gnd rswk-swf Kreditgeschäft (DE-588)4134687-7 gnd rswk-swf Modell (DE-588)4039798-1 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf Kreditgeschäft (DE-588)4134687-7 s Kreditrisiko (DE-588)4114309-7 s Risikomanagement (DE-588)4121590-4 s Modell (DE-588)4039798-1 s DE-604 Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Rutkowski, Marek Verfasser (DE-588)171429893 aut HBZ Datenaustausch application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010692768&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Bielecki, Tomasz R. 1955- Rutkowski, Marek Credit risk modeling, valuation and hedging Administração de risco (modelos matemáticos) larpcal Crédito (modelos matemáticos) larpcal Hedging (finanças) larpcal Matemática financeira larpcal Mathematisches Modell Credit Mathematical models Risk management Mathematical models Kreditrisiko (DE-588)4114309-7 gnd Kreditgeschäft (DE-588)4134687-7 gnd Modell (DE-588)4039798-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Risikomanagement (DE-588)4121590-4 gnd |
| subject_GND | (DE-588)4114309-7 (DE-588)4134687-7 (DE-588)4039798-1 (DE-588)4114528-8 (DE-588)4121590-4 |
| title | Credit risk modeling, valuation and hedging |
| title_auth | Credit risk modeling, valuation and hedging |
| title_exact_search | Credit risk modeling, valuation and hedging |
| title_full | Credit risk modeling, valuation and hedging Tomasz R. Bielecki ; Marek Rutkowski |
| title_fullStr | Credit risk modeling, valuation and hedging Tomasz R. Bielecki ; Marek Rutkowski |
| title_full_unstemmed | Credit risk modeling, valuation and hedging Tomasz R. Bielecki ; Marek Rutkowski |
| title_short | Credit risk |
| title_sort | credit risk modeling valuation and hedging |
| title_sub | modeling, valuation and hedging |
| topic | Administração de risco (modelos matemáticos) larpcal Crédito (modelos matemáticos) larpcal Hedging (finanças) larpcal Matemática financeira larpcal Mathematisches Modell Credit Mathematical models Risk management Mathematical models Kreditrisiko (DE-588)4114309-7 gnd Kreditgeschäft (DE-588)4134687-7 gnd Modell (DE-588)4039798-1 gnd Mathematisches Modell (DE-588)4114528-8 gnd Risikomanagement (DE-588)4121590-4 gnd |
| topic_facet | Administração de risco (modelos matemáticos) Crédito (modelos matemáticos) Hedging (finanças) Matemática financeira Mathematisches Modell Credit Mathematical models Risk management Mathematical models Kreditrisiko Kreditgeschäft Modell Risikomanagement |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=010692768&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT bieleckitomaszr creditriskmodelingvaluationandhedging AT rutkowskimarek creditriskmodelingvaluationandhedging |