Financial risk management with Bayesian estimation of GARCH models: theory and applications
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| Main Author: | |
|---|---|
| Format: | Book |
| Language: | English |
| Published: |
Berlin [u.a.]
Springer
2008
|
| Series: | Lecture notes in economics and mathematical systems
612 |
| Subjects: | |
| Online Access: | Inhaltsverzeichnis |
| Physical Description: | XI, 203 S. graph. Darst. |
| ISBN: | 9783540786566 9783540786573 3540786562 |
Staff View
MARC
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| 100 | 1 | |a Ardia, David |e Verfasser |4 aut | |
| 245 | 1 | 0 | |a Financial risk management with Bayesian estimation of GARCH models |b theory and applications |c David Ardia |
| 264 | 1 | |a Berlin [u.a.] |b Springer |c 2008 | |
| 300 | |a XI, 203 S. |b graph. Darst. | ||
| 336 | |b txt |2 rdacontent | ||
| 337 | |b n |2 rdamedia | ||
| 338 | |b nc |2 rdacarrier | ||
| 490 | 1 | |a Lecture notes in economics and mathematical systems |v 612 | |
| 650 | 4 | |a Gestion du risque - Modèles mathématiques | |
| 650 | 4 | |a Statistique bayésienne | |
| 650 | 4 | |a Mathematisches Modell | |
| 650 | 4 | |a Bayesian statistical decision theory | |
| 650 | 4 | |a Risk management |x Mathematical models | |
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Record in the Search Index
| _version_ | 1804137561234341888 |
|---|---|
| adam_text | Table
of
Contents
Summary
........................................................
XIII
1
Introduction
................................................. 1
2
Bayesian Statistics and MCMC Methods
.................... !)
2.1
Bayesian inference
......................................... 9
2.2
MČMC
methods
.......................................... 10
2.2.1
The Gibbs sampler
.................................. 11
2.2.2
The Metropolis-Hastings algorithm
.................... 12
2.2.3
Dealing with the MCMC output
...................... 13
3
Bayesian Estimation of the GARCH(1,
1)
Model with
Normal Innovations
.......................................... 17
3.1
The model and the priors
................................... 17
3.2
Simulating the joint posterior
............................... 18
3.2.1
Generating vector a
................................. 20
3.2.2
Generating parameter
β
.............................. 20
3.3
Empirical analysis
......................................... 22
3.3.1
Model estimation
.................................... 24
3.3.2
Sensitivity analysis
.................................. 30
3.3.3
Model diagnostics
................................... 32
3.4
Illustrative applications
.................................... 34
3.4.1
Persistence
......................................... 34
3.4.2
Stationarity
........................................
3fi
4
Bayesian Estimation of the Linear Regression Model with
Normal-GJRCl,
1)
Errors
....................................
3Í)
4.1
The model and the priors
................................... 40
4.2
Simulating the joint posterior
............................... 41
4.2.1
Generating vector
7................................. 41
4.2.2
Generating the G.IR parameters
....................... 42
Generating vector a.
................................. 43
Generating parameter
3.............................. 44
X Table of
Contents
4.3
Empirical analysis
......................................... 44
4.3.1
Model estimation
.................................... 40
4.3.2
Sensitivity analysis
.................................. 52
4.3.3
Model diagnostics
................................... 52
4.4
Illustrative applications
.................................... 53
5
Bayesian Estimation of the Linear Regression Model with
Student-t-GJRCl,
1)
Errors
.................................. 55
5.1
The model and the priors
................................... 56
5.2
Simulating the joint posterior
............................... 59
5.2.1
Generating vector
7................................. 59
5.2.2
Generating the GJR
paranieters
....................... 60
Generating vector a
................................. 61
Generating parameter
β
.............................. 62
5.2.3
Generating vector
νσ
................................ 62
5.2.4
Generating parameter
;/.............................. 63
5.3
Empirical analysis
......................................... 64
5.3.1
Model estimation
.................................... 64
5.3.2
Sensitivity analysis
.................................. 70
5.3.3
Model diagnostics
................................... 70
5.4
Illustrative1 applications
.................................... 71
6
Value at Risk and Decision Theory
.......................... 73
(i.l Introduction
.............................................. 73
0.2
The concept of Value at Risk
............................... 76
6.2.1
The one-day ahead VaR under the GARCH(1.
1)
dynamics
77
6.2.2
The s-day ahead VaR under the GARCH(1.
1)
dynamics
. 77
(i.3 Decision theory
........................................... 85
0.3.1
Bayes point
estimate
................................. 85
6.3.2
The Linex loss function
.............................. 86
6.3.3
The Monomial loss function
.......................... 90
(¡.4
Empirical application: the VaR term structure
................ 91
6.4.1
Data set and estimation design
........................ 92
6.4.2
Bayesian estimation
................................. 94
6.4.3
The term structure of the VaR density
................. 95
6.4.4
VaR point estimates
................................. 96
6.4.5
Regulatory capital
...................................100
6.4.6
Forecasting performance analysis
......................102
(І.5
The Expected Shortfall risk measure
.........................104
7
Bayesian Estimation of the Markov-Switching GJR(1,
1)
Model with Student-i Innovations
...........................109
7.1
The model and the priors
...................................
Ill
7.2
Simulating the joint posterior
...............................115
7.2.1
Generating vector
s
..................................117
7.2.2
Generating matrix
Ρ
................................118
7.2.3
Generating the G.TR parameters
.......................118
Tablo
of Contents XI
Generating vector a
.................................120
Generating vector
β
.................................121
7.2.4
Generating vector vj
................................122
7.2.5
Generating parameter
//..............................122
7.3
An application to the Swiss Market Index
....................122
7.4
In-sample performance analysis
.............................133
7.4.1
Model diagnostics
...................................133
7.4.2
Deviance information criterion
........................134
7.4.3
Model likelihood
....................................137
7.5
Forecasting performance analysis
............................144
7.() One-day ahead VaR density
................................148
7.7
Maximum Likelihood estimation
.............................152
8
Conclusion
..................................................155
A Recursive Transformations
...................................
Kil
A.I The GARCHil,
1)
model with Normal innovations
.............101
A.2 The GJR(1.
1)
model with Normal innovations
................162
A.3 The
СІЩІ.
1)
model with
Student-ŕ
innovations
..............163
В
Equivalent Specification
.....................................105
С
Conditional Moments
........................................171
Computational Details
...........................................17!)
Abbreviations and Notations
....................................181
List of Tables
....................................................187
List of Figures
...................................................189
References
.......................................................191
Index
............................................................201
|
| adam_txt |
Table
of
Contents
Summary
.
XIII
1
Introduction
. 1
2
Bayesian Statistics and MCMC Methods
. !)
2.1
Bayesian inference
. 9
2.2
MČMC
methods
. 10
2.2.1
The Gibbs sampler
. 11
2.2.2
The Metropolis-Hastings algorithm
. 12
2.2.3
Dealing with the MCMC output
. 13
3
Bayesian Estimation of the GARCH(1,
1)
Model with
Normal Innovations
. 17
3.1
The model and the priors
. 17
3.2
Simulating the joint posterior
. 18
3.2.1
Generating vector a
. 20
3.2.2
Generating parameter
β
. 20
3.3
Empirical analysis
. 22
3.3.1
Model estimation
. 24
3.3.2
Sensitivity analysis
. 30
3.3.3
Model diagnostics
. 32
3.4
Illustrative applications
. 34
3.4.1
Persistence
. 34
3.4.2
Stationarity
.
3fi
4
Bayesian Estimation of the Linear Regression Model with
Normal-GJRCl,
1)
Errors
.
3Í)
4.1
The model and the priors
. 40
4.2
Simulating the joint posterior
. 41
4.2.1
Generating vector
7. 41
4.2.2
Generating the G.IR parameters
. 42
Generating vector a.
. 43
Generating parameter
3. 44
X Table of
Contents
4.3
Empirical analysis
. 44
4.3.1
Model estimation
. 40
4.3.2
Sensitivity analysis
. 52
4.3.3
Model diagnostics
. 52
4.4
Illustrative applications
. 53
5
Bayesian Estimation of the Linear Regression Model with
Student-t-GJRCl,
1)
Errors
. 55
5.1
The model and the priors
. 56
5.2
Simulating the joint posterior
. 59
5.2.1
Generating vector
7. 59
5.2.2
Generating the GJR
paranieters
. 60
Generating vector a
. 61
Generating parameter
β
. 62
5.2.3
Generating vector
νσ
. 62
5.2.4
Generating parameter
;/. 63
5.3
Empirical analysis
. 64
5.3.1
Model estimation
. 64
5.3.2
Sensitivity analysis
. 70
5.3.3
Model diagnostics
. 70
5.4
Illustrative1 applications
. 71
6
Value at Risk and Decision Theory
. 73
(i.l Introduction
. 73
0.2
The concept of Value at Risk
. 76
6.2.1
The one-day ahead VaR under the GARCH(1.
1)
dynamics
77
6.2.2
The s-day ahead VaR under the GARCH(1.
1)
dynamics
. 77
(i.3 Decision theory
. 85
0.3.1
Bayes point
estimate
. 85
6.3.2
The Linex loss function
. 86
6.3.3
The Monomial loss function
. 90
(¡.4
Empirical application: the VaR term structure
. 91
6.4.1
Data set and estimation design
. 92
6.4.2
Bayesian estimation
. 94
6.4.3
The term structure of the VaR density
. 95
6.4.4
VaR point estimates
. 96
6.4.5
Regulatory capital
.100
6.4.6
Forecasting performance analysis
.102
(І.5
The Expected Shortfall risk measure
.104
7
Bayesian Estimation of the Markov-Switching GJR(1,
1)
Model with Student-i Innovations
.109
7.1
The model and the priors
.
Ill
7.2
Simulating the joint posterior
.115
7.2.1
Generating vector
s
.117
7.2.2
Generating matrix
Ρ
.118
7.2.3
Generating the G.TR parameters
.118
Tablo
of Contents XI
Generating vector a
.120
Generating vector
β
.121
7.2.4
Generating vector vj
.122
7.2.5
Generating parameter
//.122
7.3
An application to the Swiss Market Index
.122
7.4
In-sample performance analysis
.133
7.4.1
Model diagnostics
.133
7.4.2
Deviance information criterion
.134
7.4.3
Model likelihood
.137
7.5
Forecasting performance analysis
.144
7.() One-day ahead VaR density
.148
7.7
Maximum Likelihood estimation
.152
8
Conclusion
.155
A Recursive Transformations
.
Kil
A.I The GARCHil,
1)
model with Normal innovations
.101
A.2 The GJR(1.
1)
model with Normal innovations
.162
A.3 The
СІЩІ.
1)
model with
Student-ŕ
innovations
.163
В
Equivalent Specification
.105
С
Conditional Moments
.171
Computational Details
.17!)
Abbreviations and Notations
.181
List of Tables
.187
List of Figures
.189
References
.191
Index
.201 |
| any_adam_object | 1 |
| any_adam_object_boolean | 1 |
| author | Ardia, David |
| author_facet | Ardia, David |
| author_role | aut |
| author_sort | Ardia, David |
| author_variant | d a da |
| building | Verbundindex |
| bvnumber | BV023255699 |
| callnumber-first | H - Social Science |
| callnumber-label | HD61 |
| callnumber-raw | HD61 |
| callnumber-search | HD61 |
| callnumber-sort | HD 261 |
| callnumber-subject | HD - Industries, Land Use, Labor |
| classification_rvk | QH 233 QK 600 QP 710 SI 853 |
| classification_tum | MAT 634f WIR 160f MAT 624f |
| ctrlnum | (OCoLC)221218065 (DE-599)DNB987538780 |
| dewey-full | 332.015195 |
| dewey-hundreds | 300 - Social sciences |
| dewey-ones | 332 - Financial economics |
| dewey-raw | 332.015195 |
| dewey-search | 332.015195 |
| dewey-sort | 3332.015195 |
| dewey-tens | 330 - Economics |
| discipline | Rechtswissenschaft Mathematik Wirtschaftswissenschaften |
| discipline_str_mv | Rechtswissenschaft Mathematik Wirtschaftswissenschaften |
| format | Book |
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| id | DE-604.BV023255699 |
| illustrated | Illustrated |
| index_date | 2024-07-02T20:29:42Z |
| indexdate | 2024-07-09T21:14:15Z |
| institution | BVB |
| isbn | 9783540786566 9783540786573 3540786562 |
| language | English |
| oai_aleph_id | oai:aleph.bib-bvb.de:BVB01-016440983 |
| oclc_num | 221218065 |
| open_access_boolean | |
| owner | DE-355 DE-BY-UBR DE-384 DE-703 DE-91G DE-BY-TUM DE-945 DE-83 DE-20 |
| owner_facet | DE-355 DE-BY-UBR DE-384 DE-703 DE-91G DE-BY-TUM DE-945 DE-83 DE-20 |
| physical | XI, 203 S. graph. Darst. |
| publishDate | 2008 |
| publishDateSearch | 2008 |
| publishDateSort | 2008 |
| publisher | Springer |
| record_format | marc |
| series | Lecture notes in economics and mathematical systems |
| series2 | Lecture notes in economics and mathematical systems |
| spelling | Ardia, David Verfasser aut Financial risk management with Bayesian estimation of GARCH models theory and applications David Ardia Berlin [u.a.] Springer 2008 XI, 203 S. graph. Darst. txt rdacontent n rdamedia nc rdacarrier Lecture notes in economics and mathematical systems 612 Gestion du risque - Modèles mathématiques Statistique bayésienne Mathematisches Modell Bayesian statistical decision theory Risk management Mathematical models Bayes-Inferenz (DE-588)4648118-7 gnd rswk-swf Risikomanagement (DE-588)4121590-4 gnd rswk-swf GARCH-Prozess (DE-588)4346436-1 gnd rswk-swf Volatilität (DE-588)4268390-7 gnd rswk-swf Volatilität (DE-588)4268390-7 s Risikomanagement (DE-588)4121590-4 s Bayes-Inferenz (DE-588)4648118-7 s GARCH-Prozess (DE-588)4346436-1 s DE-604 Lecture notes in economics and mathematical systems 612 (DE-604)BV000000036 612 Digitalisierung UB Regensburg application/pdf http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016440983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA Inhaltsverzeichnis |
| spellingShingle | Ardia, David Financial risk management with Bayesian estimation of GARCH models theory and applications Lecture notes in economics and mathematical systems Gestion du risque - Modèles mathématiques Statistique bayésienne Mathematisches Modell Bayesian statistical decision theory Risk management Mathematical models Bayes-Inferenz (DE-588)4648118-7 gnd Risikomanagement (DE-588)4121590-4 gnd GARCH-Prozess (DE-588)4346436-1 gnd Volatilität (DE-588)4268390-7 gnd |
| subject_GND | (DE-588)4648118-7 (DE-588)4121590-4 (DE-588)4346436-1 (DE-588)4268390-7 |
| title | Financial risk management with Bayesian estimation of GARCH models theory and applications |
| title_auth | Financial risk management with Bayesian estimation of GARCH models theory and applications |
| title_exact_search | Financial risk management with Bayesian estimation of GARCH models theory and applications |
| title_exact_search_txtP | Financial risk management with Bayesian estimation of GARCH models theory and applications |
| title_full | Financial risk management with Bayesian estimation of GARCH models theory and applications David Ardia |
| title_fullStr | Financial risk management with Bayesian estimation of GARCH models theory and applications David Ardia |
| title_full_unstemmed | Financial risk management with Bayesian estimation of GARCH models theory and applications David Ardia |
| title_short | Financial risk management with Bayesian estimation of GARCH models |
| title_sort | financial risk management with bayesian estimation of garch models theory and applications |
| title_sub | theory and applications |
| topic | Gestion du risque - Modèles mathématiques Statistique bayésienne Mathematisches Modell Bayesian statistical decision theory Risk management Mathematical models Bayes-Inferenz (DE-588)4648118-7 gnd Risikomanagement (DE-588)4121590-4 gnd GARCH-Prozess (DE-588)4346436-1 gnd Volatilität (DE-588)4268390-7 gnd |
| topic_facet | Gestion du risque - Modèles mathématiques Statistique bayésienne Mathematisches Modell Bayesian statistical decision theory Risk management Mathematical models Bayes-Inferenz Risikomanagement GARCH-Prozess Volatilität |
| url | http://bvbr.bib-bvb.de:8991/F?func=service&doc_library=BVB01&local_base=BVB01&doc_number=016440983&sequence=000002&line_number=0001&func_code=DB_RECORDS&service_type=MEDIA |
| volume_link | (DE-604)BV000000036 |
| work_keys_str_mv | AT ardiadavid financialriskmanagementwithbayesianestimationofgarchmodelstheoryandapplications |