Credit derivatives pricing models: models, pricing and implementation
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Chichester [u.a.]
Wiley
2005
|
| Edition: | Repr. |
| Series: | Wiley finance series
|
| Subjects: | |
| Online Access: | Contributor biographical information Table of contents Publisher description Inhaltsverzeichnis Klappentext |
| Physical Description: | XXI, 375 S. graph. Darst. |
| ISBN: | 0470842911 9780470842911 |
Staff View
MARC
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| 245 | 1 | 0 | |a Credit derivatives pricing models |b models, pricing and implementation |c Philipp J. Schönbucher |
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| 264 | 1 | |a Chichester [u.a.] |b Wiley |c 2005 | |
| 300 | |a XXI, 375 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
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Record in the Search Index
| _version_ | 1804133374253596672 |
|---|---|
| adam_text | Contents
Preface
xi
Acknowledgements
xv
Abbreviations
xvii
Notation
xix
1
Introduction
1
1.1
The world of credit risk
1
1.2
The components of credit risk
2
1.3
Market structure
4
2
Credit Derivatives: Overview and Hedge-Based Pricing
7
2.1
The emergence of a new class of derivatives
7
2.2
Terminology
7
2.3
Underlying assets
10
2.3.1
Loans
10
2.3.2
Bonds
11
2.3.3
Convertible bonds
12
2.3.4
Counterparty risk
12
2.4
Asset swaps
12
2.5
Total return swaps
13
2.6
Credit default swaps
15
2.7
Hedge-based pricing
19
2.7.1
Hedge instruments
20
2.7.2
Short positions in defaultable bonds
20
2.7.3
Asset swap packages
22
2.7.4
Total return swaps
25
2.7.5
Credit default swaps
27
2.8
Exotic credit derivatives
37
2.8.1
Default digital swaps
37
2.8.2
Exotic default payments in credit default swaps
38
Contents
2.8.3
Rating-triggered credit default swaps
39
2.8.4
Options on defaultable bonds
40
2.8.5
Credit spread options
41
2.9
Default correlation products and CDOs
43
2.9.1
Firśt-to-default
swaps and basket default swaps
43
2.9.2
First loss layers
44
2.9.3
Collateralised debt obligations
46
2.10
Credit-linked notes
49
2.11
Guide to the literature
50
3
Credit Spreads and Bond Price-Based Pricing
51
3.1
Credit spreads and implied default probabilities
52
3.1.1
Risk-neutral probabilities
52
3.1.2
Setup
52
3.1.3
The fundamental relationship
54
3.1.4
The implied survival probability
54
3.1.5
Conditional survival probabilities and implied
hazard rates
56
3.1.6
Relation to forward spreads
58
3.2
Recovery modelling
60
3.3
Building blocks for credit derivatives pricing
61
3.4
Pricing with the building blocks
64
3.4.1
Defaultable fixed-coupon bond
64
3.4.2
Defaultable floater
65
3.4.3
Variants of coupon bonds
66
3.4.4
Credit default swaps
66
3.4.5
Forward start CDSs
68
3.4.6
Default digital swaps
68
3.4.7
Asset swap packages
69
3.5
Constructing and calibrating credit spread curves
69
3.5.1
Parametric forms for the spread curves
70
3.5.2
Semi-parametric and non-parametric calibration
72
3.5.3
Approximative and aggregate fits
74
3.5.4
Calibration example
75
3.6
Spread curves: issues in implementation
77
3.6.1
Which default-free interest rates should one use?
77
3.6.2
Recovery uncertainty
79
3.6.3
Bucket hedging
81
3.7
Spread curves: discussion
82
3.8
Guide to the literature
83
4
Mathematical Background
85
4.1
Stopping times
86
4.2
The hazard rate
87
4.3
Point processes
88
4.4
The intensity
88
4.5
Marked point processes and the jump measure
91
Contents
4.6
The compensator measure
93
4.6.1
Random measures in discrete time
95
4.7
Examples for compensator measures
97
4.8
Itô s
lemma for jump processes
100
4.9
Applications of
Itô s
lemma
101
4.9.1
Predictable compensators for jump processes
102
4.9.2
Ito
product rule and
Ito
quotient rule
103
4.9.3
The stochastic exponential
104
4.10
Martingale measure, fundamental pricing rule and incompleteness
105
4.11
Change of numeraire and pricing measure
107
4.11.1
The Radon-Nikodym theorem
107
4.11.2
The Girsanov theorem
108
4.12
The change of measure/change of numeraire technique
109
5
Advanced Credit Spread Models 111
5.1
Poisson
processes
111
5.1.1
A model for default arrival risk
111
5.1.2
Intuitive construction of
a Poisson
process
112
5.1.3
Properties of
Poisson
processes
113
5.1.4
Spreads with
Poisson
processes
115
5.2
Inhomogeneous
Poisson
processes
115
5.2.1
Pricing the building blocks
117
5.3
Stochastic credit spreads
118
5.3.1
Cox processes
119
5.3.2
Pricing the building blocks
125
5.3.3
General point processes
126
5.3.4
Compound
Poisson
processes
128
6
Recovery Modelling
131
6.1
Presentation of the different recovery models
132
6.1.1
Zero recovery
132
6.1.2
Recovery of treasury
133
6.1.3
Multiple defaults and recovery of market value
135
6.1.4
Recovery of par
141
6.1.5
Stochastic recovery and recovery risk
143
6.1.6
Common parametric distribution functions for recoveries
147
6.1.7
Valuation of the delivery option in a CDS
148
6.2
Comparing the recovery models
150
6.2.
í
Theoretical comparison of the recovery models
150
6.2.2
Empirical analysis of recovery rates
159
7
Implementation of Intensity-Based Models
165
7.1
Tractable models of the spot intensity
166
7.1.1
The two-factor Gaussian model
167
7.1.2
The multifactor Gaussian model
171
7.1.3
Implied survival probabilities
172
7.1.4
Payoffs at default
174
Contents
7.2 The multifactor
CIR
model
174
7.2.1
Bond prices
175
7.2.2 Affine
combinations of independent non-central
chi-squared distributed random variables
176
7.2.3
Factor distributions
178
7.3
Credit derivatives in the
CIR
model
179
7.3.1
Default digital payoffs
180
7.3.2
Calculations to the Gaussian model
180
7.3.3
Calculations to the
CIR
model
184
7.4
Tree models
187
7.4.1
The tree implementation: inputs
187
7.4.2
Default branching
188
7.4.3
The implementation steps
190
7.4.4
Building trees: the Hull-White algorithm
190
7.4.5
Fitting the tree: default-free interest rates
193
7.4.6
Combining the trees
194
7.4.7
Fitting the combined tree
197
7.4.8
Applying the tree
198
7.4.9
Extensions and conclusion
199
7.5
PDE-Based implementation
200
7.6
Modelling term structures of credit spreads
204
7.6.1
Intensity models in a Heath, Jarrow,
Morton framework
206
7.7
Monte Carlo simulation
211
7.7.1
Pathwise simulation of diffusion processes
214
7.7.2
Simulation of recovery rates
219
7.8
Guide to the literature
220
8
Credit Rating Models
223
8.1
Introduction
223
8.1.1
Empirical observations
224
8.1.2
An example
225
8.2
The rating process and transition probabilities
226
8.2.1
Discrete-time Markov chains
229
8.2.2
Continuous-time Markov chains
229
8.2.3
Connection to
Poisson
processes
231
8.3
Estimation of transition intensities
233
8.3.1
The cohort method
233
8.3.2
The embedding problem: finding a generator matrix
234
8.4
Direct estimation of transition intensities
238
8.5
Pricing with deterministic generator matrix
239
8.5.1
Pricing zero-coupon bonds
239
8.5.2
Pricing derivatives on the credit rating
240
8.5.3
General payoffs
241
8.5.4
Rating trees
242
8.5.5
Downgrade triggers
243
8.5.6
Hedging rating transitions
245
Contents
8.6
The calibration of rating transition models
246
8.6.1
Deterministic intensity approaches
246
8.6.2
Incorporating rating momentum
249
8.6.3
Stochastic rating transition intensities
250
8.7
A general HJM framework
251
8.8
Conclusion
253
9
Firm Value and Share Price-Based Models
255
9.1
The approach
255
9.1.1
Modelling philosophy
255
9.1.2
An example
256
9.1.3
State variables and modelling
259
9.1.4
The time of default
261
9.2
Pricing equations
263
9.2.1
The firm s value model
263
9.2.2
The pricing equation
264
9.2.3
Some other securities
265
9.2.4
Hedging
268
9.3
Solutions to the pricing equation
269
9.3.1
The
Г
-forward
measure
269
9.3.2
Time change
270
9.3.3
The hitting probability
270
9.3.4
Putting it together
271
9.3.5
The Longstaff-Schwartz results
271
9.3.6
Strategic default
273
9.4
A practical implementation: KMV
275
9.4.1
The default point
275
9.4.2
The time horizon
275
9.4.3
The initial value of the firm s assets and its volatility
275
9.4.4
The distance to default
276
9.5
Unobservable firm s values and CreditGrades
277
9.5.1
A simple special case: delayed observation
280
9.5.2
The idea of Lardy and Finkelstein: CreditGrades and E2C
281
9.6
Advantages and disadvantages
284
9.6.1
Empirical evidence
284
9.6.2
Discussion
286
9.7
Guide to the literature
286
10
Models for Default Correlation
289
10.1
Default correlation basics
290
10.1.1
Empirical evidence
290
10.1.2
Terminology
291
10.1.3
Linear default correlation, conditional default probabilities, joint
default probabilities
292
10.1.4
The size of the impact of default correlation
293
10.1.5
Price bounds for FtD swaps
293
10.1.6
The need for theoretical models of default correlations
297
Contents
10.2
Independent
defaults
298
10.2.1
The binomial distribution function
298
10.2.2
Properties of the binomial distribution function
299
10.2.3
The other extreme: perfectly dependent defaults
300
10.3
The binomial expansion method
301
10.4
Factor models
305
10.4.1
One-factor dependence of defaults
305
10.4.2
A simplified firm s value model
305
10.4.3
The distribution of the defaults
307
10.4.4
The iarge portfolio approximation
309
10.4.5
Generalisations
312
10.4.6
Portfolios of two asset classes
313
10.4.7
Some remarks on implementation
314
10.5
Correlated defaults in intensity models
315
10.5.1
The intensity of the default counting process
315
10.5.2
Correlated intensities
316
10.5.3
Stress events in intensity models
318
10.5.4
Default contagion/infectious defaults
321
10.6
Correlated defaults in firm s value models
321
10.7
Copula functions and dependency concepts
326
10.7.1
Copula functions
327
10.7.2
Examples of copulae
330
10.7.3
Archimedean copulae
333
10.8
Default modelling with copula functions
337
10.8.1
Static copula models for default correlation
337
10.8.2
Large portfolio loss distributions for Archimedean copulae
340
10.8.3
A semi-dynamic copula model
343
10.8.4
Dynamic copula-dependent defaults
349
Bibliography
361
Index
369
Credit
derivatives
pricing models
Philipp
Schönbucher
covers all the important model¬
ling approaches from hedge-based pricing to
stochastic-intensity models, credit rating models and
firms value based models, concluding with a large
chapter on portfolio credit risk models. The author
builds the models starting from simple basics, intro¬
ducing complexity only where it is needed, and
explaining implementation, data collection and
calibration on the way. The advantages and disadvan¬
tages of the different pricing approaches are clearly
confronted, and the effects of hidden assumptions
on the output of the models are identified.
The book is an indispensable tool for credit
derivatives traders, quantitative analysts, software
developers, risk managers, regulators, auditors, and
anybody interested in how credit derivatives are
priced.
|
| any_adam_object | 1 |
| author | Schönbucher, Philipp J. 1969- |
| author_GND | (DE-588)121905977 |
| author_facet | Schönbucher, Philipp J. 1969- |
| author_role | aut |
| author_sort | Schönbucher, Philipp J. 1969- |
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| ctrlnum | (OCoLC)248932534 (DE-599)BVBBV019856170 |
| dewey-full | 332.64521 332.645 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.645 21 332.645 |
| dewey-search | 332.645 21 332.645 |
| dewey-sort | 3332.645 221 |
| dewey-tens | 330 - Economics |
| discipline | Wirtschaftswissenschaften |
| edition | Repr. |
| format | Book |
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| id | DE-604.BV019856170 |
| illustrated | Illustrated |
| indexdate | 2024-07-09T20:07:41Z |
| institution | BVB |
| isbn | 0470842911 9780470842911 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-013180757 |
| oclc_num | 248932534 |
| open_access_boolean | |
| owner | DE-473 DE-BY-UBG DE-1102 DE-355 DE-BY-UBR DE-739 DE-521 |
| owner_facet | DE-473 DE-BY-UBG DE-1102 DE-355 DE-BY-UBR DE-739 DE-521 |
| physical | XXI, 375 S. graph. Darst. |
| publishDate | 2005 |
| publishDateSearch | 2005 |
| publishDateSort | 2005 |
| publisher | Wiley |
| record_format | marc |
| series2 | Wiley finance series |
| spelling | Schönbucher, Philipp J. 1969- Verfasser (DE-588)121905977 aut Credit derivatives pricing models models, pricing and implementation Philipp J. Schönbucher Repr. Chichester [u.a.] Wiley 2005 XXI, 375 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Wiley finance series Kredietbank (DE-588)4440948-5 gnd rswk-swf Kreditrisiko - Derivat <Wertpapier> Credit derivatives Credit derivatives Prices Kreditrisiko (DE-588)4114309-7 gnd rswk-swf Mathematisches Modell (DE-588)4114528-8 gnd rswk-swf Derivat Wertpapier (DE-588)4381572-8 gnd rswk-swf Kreditderivat (DE-588)7660453-6 gnd rswk-swf Preisbildung (DE-588)4047103-2 gnd rswk-swf Preismodell (DE-588)4175626-5 gnd rswk-swf Kreditderivat (DE-588)7660453-6 s Preismodell (DE-588)4175626-5 s DE-604 Kreditrisiko (DE-588)4114309-7 s Derivat Wertpapier (DE-588)4381572-8 s Preisbildung (DE-588)4047103-2 s Mathematisches Modell (DE-588)4114528-8 s 1\p DE-604 Kredietbank (DE-588)4440948-5 b 2\p DE-604 http://www.loc.gov/catdir/bios/wiley043/2004298895.html Contributor biographical information http://www.loc.gov/catdir/toc/wiley041/2004298895.html Table of contents http://www.loc.gov/catdir/description/wiley041/2004298895.html Publisher description Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180757&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180757&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA Klappentext 1\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk 2\p cgwrk 20201028 DE-101 https://d-nb.info/provenance/plan#cgwrk |
| spellingShingle | Schönbucher, Philipp J. 1969- Credit derivatives pricing models models, pricing and implementation Kredietbank (DE-588)4440948-5 gnd Kreditrisiko - Derivat <Wertpapier> Credit derivatives Credit derivatives Prices Kreditrisiko (DE-588)4114309-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Kreditderivat (DE-588)7660453-6 gnd Preisbildung (DE-588)4047103-2 gnd Preismodell (DE-588)4175626-5 gnd |
| subject_GND | (DE-588)4440948-5 (DE-588)4114309-7 (DE-588)4114528-8 (DE-588)4381572-8 (DE-588)7660453-6 (DE-588)4047103-2 (DE-588)4175626-5 |
| title | Credit derivatives pricing models models, pricing and implementation |
| title_auth | Credit derivatives pricing models models, pricing and implementation |
| title_exact_search | Credit derivatives pricing models models, pricing and implementation |
| title_full | Credit derivatives pricing models models, pricing and implementation Philipp J. Schönbucher |
| title_fullStr | Credit derivatives pricing models models, pricing and implementation Philipp J. Schönbucher |
| title_full_unstemmed | Credit derivatives pricing models models, pricing and implementation Philipp J. Schönbucher |
| title_short | Credit derivatives pricing models |
| title_sort | credit derivatives pricing models models pricing and implementation |
| title_sub | models, pricing and implementation |
| topic | Kredietbank (DE-588)4440948-5 gnd Kreditrisiko - Derivat <Wertpapier> Credit derivatives Credit derivatives Prices Kreditrisiko (DE-588)4114309-7 gnd Mathematisches Modell (DE-588)4114528-8 gnd Derivat Wertpapier (DE-588)4381572-8 gnd Kreditderivat (DE-588)7660453-6 gnd Preisbildung (DE-588)4047103-2 gnd Preismodell (DE-588)4175626-5 gnd |
| topic_facet | Kredietbank Kreditrisiko - Derivat <Wertpapier> Credit derivatives Credit derivatives Prices Kreditrisiko Mathematisches Modell Derivat Wertpapier Kreditderivat Preisbildung Preismodell |
| url | http://www.loc.gov/catdir/bios/wiley043/2004298895.html http://www.loc.gov/catdir/toc/wiley041/2004298895.html http://www.loc.gov/catdir/description/wiley041/2004298895.html http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180757&sequence=000003&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=013180757&sequence=000004&line_number=0002&func_code=DB_RECORDS&service_type=MEDIA |
| work_keys_str_mv | AT schonbucherphilippj creditderivativespricingmodelsmodelspricingandimplementation |