GARCH dependence in extreme value models with Bayesian inference
Extreme value methods are widely used in financial applications such as risk analysis, forecasting and pricing models. One of the challenges with their application in finance is accounting for the temporal dependence between the observations, for example the stylised fact that financial time series...
| Main Authors: | , , , |
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| Format: | Journal Article |
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Elsevier Science
2011
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| Online Access: | http://hdl.handle.net/20.500.11937/21796 |
| _version_ | 1848750690320515072 |
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| author | Zhao, X. Scarrott, C. Oxley, Leslie Reale, M. |
| author_facet | Zhao, X. Scarrott, C. Oxley, Leslie Reale, M. |
| author_sort | Zhao, X. |
| building | Curtin Institutional Repository |
| collection | Online Access |
| description | Extreme value methods are widely used in financial applications such as risk analysis, forecasting and pricing models. One of the challenges with their application in finance is accounting for the temporal dependence between the observations, for example the stylised fact that financial time series exhibit volatility clustering. Various approaches have been proposed to capture the dependence. Commonly a two-stage approach is taken, where the volatility dependence is removed using a volatility model like a GARCH (or one of its many incarnations) followed by application of standard extreme value models to the assumed independent residual innovations. This study examines an alternative one stage approach, which makes parameter estimation and accounting for the associated uncertainties more straightforward than the two-stage approach. The location and scale parameters of the extreme value distribution are defined to follow a conditional autoregressive heteroscedasticity process. Essentially, the model implements GARCH volatility via the extreme value model parameters. Bayesian inference is used and implemented via Markov chain Monte Carlo, to permit all sources of uncertainty to be accounted for. The model is applied to both simulated and empirical data to demonstrate performance in extrapolating the extreme quantiles and quantifying the associated uncertainty. |
| first_indexed | 2025-11-14T07:40:50Z |
| format | Journal Article |
| id | curtin-20.500.11937-21796 |
| institution | Curtin University Malaysia |
| institution_category | Local University |
| last_indexed | 2025-11-14T07:40:50Z |
| publishDate | 2011 |
| publisher | Elsevier Science |
| recordtype | eprints |
| repository_type | Digital Repository |
| spelling | curtin-20.500.11937-217962019-05-03T02:47:34Z GARCH dependence in extreme value models with Bayesian inference Zhao, X. Scarrott, C. Oxley, Leslie Reale, M. GARCH Dependence Bayesian inference Extreme values Extreme value methods are widely used in financial applications such as risk analysis, forecasting and pricing models. One of the challenges with their application in finance is accounting for the temporal dependence between the observations, for example the stylised fact that financial time series exhibit volatility clustering. Various approaches have been proposed to capture the dependence. Commonly a two-stage approach is taken, where the volatility dependence is removed using a volatility model like a GARCH (or one of its many incarnations) followed by application of standard extreme value models to the assumed independent residual innovations. This study examines an alternative one stage approach, which makes parameter estimation and accounting for the associated uncertainties more straightforward than the two-stage approach. The location and scale parameters of the extreme value distribution are defined to follow a conditional autoregressive heteroscedasticity process. Essentially, the model implements GARCH volatility via the extreme value model parameters. Bayesian inference is used and implemented via Markov chain Monte Carlo, to permit all sources of uncertainty to be accounted for. The model is applied to both simulated and empirical data to demonstrate performance in extrapolating the extreme quantiles and quantifying the associated uncertainty. 2011 Journal Article http://hdl.handle.net/20.500.11937/21796 10.1016/j.matcom.2010.08.002 Elsevier Science restricted |
| spellingShingle | GARCH Dependence Bayesian inference Extreme values Zhao, X. Scarrott, C. Oxley, Leslie Reale, M. GARCH dependence in extreme value models with Bayesian inference |
| title | GARCH dependence in extreme value models with Bayesian inference |
| title_full | GARCH dependence in extreme value models with Bayesian inference |
| title_fullStr | GARCH dependence in extreme value models with Bayesian inference |
| title_full_unstemmed | GARCH dependence in extreme value models with Bayesian inference |
| title_short | GARCH dependence in extreme value models with Bayesian inference |
| title_sort | garch dependence in extreme value models with bayesian inference |
| topic | GARCH Dependence Bayesian inference Extreme values |
| url | http://hdl.handle.net/20.500.11937/21796 |