Counterparty risk and funding: a tale of two puzzles
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| Main Authors: | , |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
London [u.a.]
CRC
2014
|
| Series: | Chapman & Hall/CRC financial mathematics series
|
| Subjects: | |
| Online Access: | Cover image Inhaltsverzeichnis |
| Item Description: | Includes bibliographical references and index |
| Physical Description: | XXI, 365 S. Ill., graph. Darst. |
| ISBN: | 9781466516458 |
Staff View
MARC
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| 001 | BV041981838 | ||
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| 010 | |a 014003733 | ||
| 020 | |a 9781466516458 |9 978-1-4665-1645-8 | ||
| 035 | |a (OCoLC)890137182 | ||
| 035 | |a (DE-599)BVBBV041981838 | ||
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| 100 | 1 | |a Crépey, Stéphane |d 1971- |e Verfasser |0 (DE-588)1037488725 |4 aut | |
| 245 | 1 | 0 | |a Counterparty risk and funding |b a tale of two puzzles |c Stéphane Crépey and Tomasz R. Bielecki |
| 264 | 1 | |a London [u.a.] |b CRC |c 2014 | |
| 300 | |a XXI, 365 S. |b Ill., graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 0 | |a Chapman & Hall/CRC financial mathematics series | |
| 500 | |a Includes bibliographical references and index | ||
| 650 | 7 | |a BUSINESS & ECONOMICS / Finance |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / General |2 bisacsh | |
| 650 | 7 | |a MATHEMATICS / Probability & Statistics / General |2 bisacsh | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Wirtschaft | |
| 650 | 4 | |a Finance |x Mathematical models | |
| 650 | 4 | |a Credit |x Mathematical models | |
| 650 | 4 | |a Credit derivatives |x Mathematical models | |
| 650 | 4 | |a Financial risk |x Mathematical models | |
| 650 | 4 | |a BUSINESS & ECONOMICS / Finance | |
| 650 | 4 | |a MATHEMATICS / General | |
| 650 | 4 | |a MATHEMATICS / Probability & Statistics / General | |
| 650 | 0 | 7 | |a Finanzierung |0 (DE-588)4017182-6 |2 gnd |9 rswk-swf |
| 650 | 0 | 7 | |a Kreditrisiko |0 (DE-588)4114309-7 |2 gnd |9 rswk-swf |
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| 689 | 0 | 3 | |a Finanzierung |0 (DE-588)4017182-6 |D s |
| 689 | 0 | |5 DE-604 | |
| 700 | 1 | |a Bielecki, Tomasz R. |d 1955- |e Verfasser |0 (DE-588)12323400X |4 aut | |
| 856 | 4 | |u http://images.tandf.co.uk/common/jackets/websmall/978146651/9781466516458.jpg |3 Cover image | |
| 856 | 4 | 2 | |m Digitalisierung UB Regensburg - ADAM Catalogue Enrichment |q application/pdf |u http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027424276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |3 Inhaltsverzeichnis |
| 999 | |a oai:aleph.bib-bvb.de:BVB01-027424276 | ||
Record in the Search Index
| _version_ | 1804152383126634496 |
|---|---|
| adam_text | Contents
Preface
xv
I Financial Landscape
1
1
A Galilean Dialogue on Counterparty Risk, CVA,
DVA,
Multiple Curves,
Collateral and Funding
3
1.1
To the Discerning Reader
......................... 4
1.2
The First Day
................................ 5
1.2.1
General Introduction, Size of Derivatives Markets, Exposures,
Credit
Var,
Basel
.......................... 5
1.3
The Second Day
.............................. 15
1.3.1
CVA,
DVA,
Pricing, Arbitrage Free Theory, Closeout. And the
Data? Ratings?
........................... 15
1.4
The Third Day
............................... 30
1.4.1
FVA, Hard Maths with No Data? CVA VaR, Basel III Problems,
Collateral and Gap Risk
...................... 30
1.5
The Fourth Day
............................... 38
1.5.1
Counterparty Risk Restructuring. CCDS,
Papillon,
Floating Rate
CVA and Margin Lending. Global Calibration. Global Valuation.
Available CVA Books and Forthcoming CVA Books
........ 38
2
The Whys of the LOIS
47
2.1
Financial Setup
............................... 48
2.2
Indifference Valuation
Modei
....................... 49
2.2.1
Credit and Funding Costs Specification
.............. 51
2.3
LOIS Formula
............................... 52
2.4
Numerical Study
.............................. 55
II Model-Free Developments
61
3
Pure Counterparty Risk
65
3.1
Cash Flows
................................. 65
3.1.1
Promised Dividend
......................... 67
3.1.2
Collateral
.............................. 67
3.1.3
Closeout Cash Flow
........................ 68
vu
viii Contents
3.2
Valuation and Hedging
........................... 69
3.2.1
Valuation of the Contract
...................... 70
3.2.2
Valuation of Counterparty Risk
.................. 72
3.2.3
Exposure at Default
........................ 73
3.2.4
TVA
and CVA/DVA/RC
...................... 74
3.2.4.1
Expected Positive/Negative Exposures
......... 75
3.2.4.2
Unilateral Counterparty Risk
.............. 75
3.2.5
Dynamic Hedging of Counterparty Risk
.............. 76
3.2.5.1
Min-
Variance Hedging
................. 77
3.3
CSA Specifications
............................ 77
3.3.1
Close Out Valuation Schemes
................... 77
3.3.2
CollateraHzation Schemes
..................... 78
3.3.3
Cure Period
............................. 81
3.3.4
Rehypothecation Risk and Segregation
.............. 82
33.5
Haircuts
............................... 82
3.3.6
Centrally Cleared Trading
..................... 83
4
Bilateral Counterparty Risk under Funding Constraints
85
4.1
Introduction
................................ 85
4.1.1
Outline
............................... 85
4.2
Market Model
............................... 86
4.2.1
Hedging Assets
........................... 87
4.2.2
Funding Assets
........................... 89
4.3
Trading Strategies
............................. 91
4.3.1
Self-Financing Condition
...................... 91
4.3.2
General Price-and-Hedge
...................... 94
4.4
Martingale Pricing Approach
....................... 95
4.4.1
Primary Market
........................... 96
4.4.2
Q-Price-and-Hedge BSDE
..................... 98
4.4.3
Arbitrage, Replication and Computational Issues
......... 100
4.5
TVA
..................................... 103
4.5.1
Clean Price
............................. 103
4.5.2
CSA Close-Out Cash-Flow
..................... 103
4.5.3
TVA
Representation
........................ 103
4.5.3.1
CCDS Static Hedging Interpretation
.......... 105
4.6
Example
.................................. 106
4.6.1
Setup
................................ 106
4.6.2
Analysis of a Solution
....................... 107
4.6.2.1
TVA
........................... 110
4.6.2.2
CSA Close-Out Pricing Schemes
............
Ill
Contenta
ix
4.6.3
Comparison with the Results of
Burgård
and Kjaer
........
Ill
III Reduced-Form BSDE Modeling
113
5
A Reduced-Form
TVA BSDE
Approach to Counterparty Risk under
Funding Constraints
115
5.1
Introduction
................................ 115
5.1.1
Outline
............................... 115
5.2
Pre-Default BSDE Modeling
........................ 116
5.2.1
Bilateral Reduced Form Setup
...................
П6
5.2.2
Reduction of Filtration
....................... 117
5.23
Modeling Assumption
....................... 120
5.2.4
Cost Processes Analysis
...................... 123
5.3
Markov Case
................................ 124
5.3.1
Factor Process
........................... 125
5.3.2
Min-
Variance Hedging of Market Risk
.............. 126
5.3.3
Min-
Variance Hedging Constrained to Perfect Hedging of Jump-
to-Default Risk
........................... 128
5.3.4
Unilateral or Bilateral in the End ?
................. 133
6
The Four Wings of the
TVA
135
6.1
Introduction
................................ 135
6.2
TVA
Representations
............................ 135
6.2.1
Setup
................................
Í35
6.2.2
BSDEs
............................... 137
6.2.2.1
Pre-default Markov Setup
................ 139
6.2.3
CVA,
DVA, LVA
and RC
......................
Í39
6.3
CSA Specifications
............................. 140
6.3.1
Clean CSA Recovery Scheme
................... 140
6.3.2
Pre-Default CSA Recovery Scheme
................ 141
6.3.3
Fuli
CoIIateralization CSA
..................... 142
6.3.4
Pure Funding
............................ 142
6.3.5
Asymmetrical
TVA
Approach
................... 142
6.4
Clean Valuations
.............................. 143
6.4.1
Products
.............................. 144
6.4.2
Gaussian Vasicek Short Rate Model
................ 146
6A2.1 Caplet
.......................... 147
6.4.3
Levy Hull-White Short Rate Model
................ 148
6.4.3.1
Caplet
.......................... 149
6.4.4
Numerics
.............................. 150
6.5
TVA
Computations
............................. 154
6.5.1
TVA
Equations
........................... 154
6.5.2
Numerics
.............................. 154
x
Contents
IV
Dynamic
Copula
Models 165
7 Dynamic
Gaussian
Copula
Model 169
7.1
Introduction
................................ 169
7.2 Model.................................... 170
7.2.1
Gaussian Distributions
....................... 170
7.2.2
Model of Default Times
...................... 171
7.2.2.1
Conditional Survival Distribution
............ 174
7.2.3
Fundamental Martingales
..................... 175
7.2.3.1
Univariate Case
..................... 175
7.2.3.2
Portfolio Case
...................... 177
7.3
Clean Valuation and Hedging of Credit Derivatives
............ 178
7.3.1
Pricing of a CDS
.......................... 178
7.3.2
Pricing of a CDO
.......................... 179
7.3.3
Hedging CDO with CDS
...................... 182
7.4
Counterparty Risk
............................. 187
7.4.1
Numerics
.............................. 188
7.4.1.1
Spread Volatilities
.................... 189
7.4.1.2
CVA
........................... 190
8
Common-Shock Model
193
8.1
Introduction
................................ 193
8.2
Model of Default Times
.......................... 193
8.2.1
Conditional Joint Survival Function
................ 197
8.2.1.1
Conditional Common-Shock Model
.......... 199
8.2.2
Itô-Markov
Formula
........................ 200
8.2.3
Intensity Structure
......................... 203
8.3
Clean Pricing, Calibration and Hedging
.................. 204
8.3.
і
Pricing Equations
.......................... 205
8.3.1.1
Rolling CDS
....................... 206
8.3.2
Min-
Variance Hedging
....................... 207
8.3.2.1
Hedging of a CDO Tranche Using Rolling CDS
Contracts
......................... 207
8.3.3
Convolution Recursion Pricing Schemes
.............. 210
8.3.4
Random Recoveries
........................ 212
8.4
Numerical Results
............................. 215
8.4.1
Calibration Methodology with Piecewise Constant Default
Intensities and Constant Recoveries
................ 216
8.4.2
Calibration Methodology with Piecewise Constant Default
intensities and Stochastic Recoveries
............... 217
8.4.3
Calibration Results with Piecewise Constant Default Intensities
. 219
8.4.3.
1 The Implied Loss Distribution
.............. 224
8.4.4
Calibration Methodology and Results with Stochastic Intensities
. 225
Contents xi
8.4.5 Min-
Variance Hedging
Deltas................... 228
8.5
CVA
Pricing and Hedging
......................... 234
9
CVA Computations for One CDS in the Common-Shock Model
239
9.1
Introduction
................................ 239
9.2
Generalities
................................. 239
9.2.1
Specification-Free Results in a Common-Shock Setup
...... 241
9.2.1.1
Clean Valuation
..................... 241
9.2.1.2
Min-
Variance Hedging of the CVA Jump-To-Counterparty-
Default Exposure
.................... 242
9.3
Common-Shock Model with Deterministic Intensities
.......... 242
9.3.1
Implementation
........................... 246
9.3.1.1
Linear Intensities
.................... 246
9.3.1.2
Calibration Issues
.................... 246
9.3.1.3
Constant Intensities
................... 246
9.4
Numerical Results with Deterministic Intensities
............. 247
9.5
Common-Shock Model with Stochastic Intensities
............ 252
9.5.1
CIR++Intensities
.......................... 252
9.5.1.1
Calibration Methodology
................ 253
9.5.2
Extended
CIR
Intensities
...................... 254
9.5.2.1
Implementation
..................... 254
9.6
Numerics
.................................. 255
9.6.1
Calibration Results
......................... 255
9.6.2
CVA Stylized Features
....................... 255
9.6.3
Case of a Low-Risk Reference Entity
............... 260
9.6.4
CDS Options-Implied Volatilities
................. 260
9.6.5
Contribution of the Joint Default
.................. 264
10
CVA Computations for Credit Portfolios in the Common-Shock Model
267
10.1
Portfolio of CDS
.............................. 267
10.1.1
Common-Shock Model Specification
............... 268
10.1.2
Numerical Results
......................... 268
10.2
CDO Tranches
............................... 273
10.2.1
Numerical Results
......................... 274
V Further Developments
277
11
Rating Triggers and Credit Migrations
279
11.1
Introduction
................................ 279
11.2
Credit Value Adjustment and Collateralization under Rating Triggers
. . 280
11.2.1
Pricing Bilateral Counterparty Risk with Rating Triggers
..... 281
11.2.2
Dynamic
Col laterali
zation
..................... 284
11.3
Markov Copula Approach for Rating-Based Pricing
........... 285
xii Contents
11.4 Applications ................................ 286
11.4.1
Interest
Rate
Swap with
Rating Triggers.............. 287
11.4.2 CDS
with
Rating Triggers..................... 291
12
A Unified Perspective
297
12.1
Introduction
................................ 297
12.2
Marked Default Time Reduced-Form Modeling
............. 298
12.2.1
Pre-default Setup
.......................... 299
12.3
Dynamic Gaussian Copula
TVA
Model
.................. 301
12.3.1
Model of Default Times
...................... 301
12.3.2
Pre-default
TVA
Model
....................... 302
12.4
Dynamic Marshall-Olkin Copula
TVA
Model
............... 304
12.4.1
Model of Default Times
...................... 304
12.4.2
TVA
Model
............................. 306
12.4.3
Reduced-Form
TVA
Approach
................... 307
VI Mathematical Appendix
309
13
Stochastic Analysis Prerequisites
311
13.1
Stochastic Integration
........................... 311
13.1.1
Semimartingales
.......................... 311
13.1.2
Random Measures Integration Theory
............... 313
13.2
Ito
Processes
................................ 316
13.2.1
Finite Variation Jumps
....................... 317
13.2.2
General Case
............................ 318
13.2.2.1
Brackets
......................... 321
13.3
Jump-Diffusions
.............................. 322
13.4
Feynman-Kac Formula
.......................... 324
13.4.1
An
Affine
Formula
......................... 325
13.5
Backward Stochastic Differential Equations
................ 327
13.6
Measure Changes and Random Intensity of Jumps
............ 328
13.7
Reduction of Filtration and Hazard Intensity Pre-Default Credit Risk
Modeling
.................................. 330
13.7.1
Portfolio Credit Risk
........................ 332
14
Markov Consistency and Markov Copulas
335
14.1
Introduction
................................ 335
14.2
Consistent Markov Processes
....................... 336
14.3
Markov Copulas
.............................. 337
14.4
Examples
.................................. 337
14.4.1
Diffusions
.............................. 337
14.4.2
Jump-Diffusions
.......................... 338
14.4.2.1
Finite Markov Chains
.................. 339
Contents xiii
14.4.3
Diffusion Modulated Markov Jump Processes
........... 340
Bibliography
343
Index
357
|
| any_adam_object | 1 |
| author | Crépey, Stéphane 1971- Bielecki, Tomasz R. 1955- |
| author_GND | (DE-588)1037488725 (DE-588)12323400X |
| author_facet | Crépey, Stéphane 1971- Bielecki, Tomasz R. 1955- |
| author_role | aut aut |
| author_sort | Crépey, Stéphane 1971- |
| author_variant | s c sc t r b tr trb |
| building | Verbundindex |
| bvnumber | BV041981838 |
| callnumber-first | H - Social Science |
| callnumber-label | HG106 |
| callnumber-raw | HG106 |
| callnumber-search | HG106 |
| callnumber-sort | HG 3106 |
| callnumber-subject | HG - Finance |
| classification_rvk | QK 320 SK 980 |
| ctrlnum | (OCoLC)890137182 (DE-599)BVBBV041981838 |
| dewey-full | 332.64/57 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.64/57 |
| dewey-search | 332.64/57 |
| dewey-sort | 3332.64 257 |
| dewey-tens | 330 - Economics |
| discipline | Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV041981838 |
| illustrated | Illustrated |
| indexdate | 2024-07-10T01:09:50Z |
| institution | BVB |
| isbn | 9781466516458 |
| language | English |
| lccn | 014003733 |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-027424276 |
| oclc_num | 890137182 |
| open_access_boolean | |
| owner | DE-384 DE-355 DE-BY-UBR |
| owner_facet | DE-384 DE-355 DE-BY-UBR |
| physical | XXI, 365 S. Ill., graph. Darst. |
| publishDate | 2014 |
| publishDateSearch | 2014 |
| publishDateSort | 2014 |
| publisher | CRC |
| record_format | marc |
| series2 | Chapman & Hall/CRC financial mathematics series |
| spelling | Crépey, Stéphane 1971- Verfasser (DE-588)1037488725 aut Counterparty risk and funding a tale of two puzzles Stéphane Crépey and Tomasz R. Bielecki London [u.a.] CRC 2014 XXI, 365 S. Ill., graph. Darst. txt rdacontent n rdamedia nc rdacarrier Chapman & Hall/CRC financial mathematics series Includes bibliographical references and index BUSINESS & ECONOMICS / Finance bisacsh MATHEMATICS / General bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Wirtschaft Finance Mathematical models Credit Mathematical models Credit derivatives Mathematical models Financial risk Mathematical models BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Finanzierung (DE-588)4017182-6 gnd rswk-swf Kreditrisiko (DE-588)4114309-7 gnd rswk-swf Bewertung (DE-588)4006340-9 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Kreditrisiko (DE-588)4114309-7 s Bewertung (DE-588)4006340-9 s Mathematisches Modell (DE-588)4114528-8 s Finanzierung (DE-588)4017182-6 s DE-604 Bielecki, Tomasz R. 1955- Verfasser (DE-588)12323400X aut http://images.tandf.co.uk/common/jackets/websmall/978146651/9781466516458.jpg Cover image Digitalisierung UB Regensburg - ADAM Catalogue Enrichment application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027424276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Crépey, Stéphane 1971- Bielecki, Tomasz R. 1955- Counterparty risk and funding a tale of two puzzles BUSINESS & ECONOMICS / Finance bisacsh MATHEMATICS / General bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Wirtschaft Finance Mathematical models Credit Mathematical models Credit derivatives Mathematical models Financial risk Mathematical models BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Finanzierung (DE-588)4017182-6 gnd Kreditrisiko (DE-588)4114309-7 gnd Bewertung (DE-588)4006340-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| subject_GND | (DE-588)4017182-6 (DE-588)4114309-7 (DE-588)4006340-9 (DE-588)4114528-8 |
| title | Counterparty risk and funding a tale of two puzzles |
| title_auth | Counterparty risk and funding a tale of two puzzles |
| title_exact_search | Counterparty risk and funding a tale of two puzzles |
| title_full | Counterparty risk and funding a tale of two puzzles Stéphane Crépey and Tomasz R. Bielecki |
| title_fullStr | Counterparty risk and funding a tale of two puzzles Stéphane Crépey and Tomasz R. Bielecki |
| title_full_unstemmed | Counterparty risk and funding a tale of two puzzles Stéphane Crépey and Tomasz R. Bielecki |
| title_short | Counterparty risk and funding |
| title_sort | counterparty risk and funding a tale of two puzzles |
| title_sub | a tale of two puzzles |
| topic | BUSINESS & ECONOMICS / Finance bisacsh MATHEMATICS / General bisacsh MATHEMATICS / Probability & Statistics / General bisacsh Mathematisches Modell Wirtschaft Finance Mathematical models Credit Mathematical models Credit derivatives Mathematical models Financial risk Mathematical models BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Finanzierung (DE-588)4017182-6 gnd Kreditrisiko (DE-588)4114309-7 gnd Bewertung (DE-588)4006340-9 gnd Mathematisches Modell (DE-588)4114528-8 gnd |
| topic_facet | BUSINESS & ECONOMICS / Finance MATHEMATICS / General MATHEMATICS / Probability & Statistics / General Mathematisches Modell Wirtschaft Finance Mathematical models Credit Mathematical models Credit derivatives Mathematical models Financial risk Mathematical models Finanzierung Kreditrisiko Bewertung |
| url | http://images.tandf.co.uk/common/jackets/websmall/978146651/9781466516458.jpg http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=027424276&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
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