Extreme value theory: Empirical analysis of tail behaviour of GARCH models
| Author: | Bc. Jan Šiml |
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| Year: | 2012 - summer |
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| Work type: | Bachelors |
| Language: | English |
| Pages: | 130 |
| Awards and prizes: | B.A. with distinction from the Dean of the Faculty of Social Sciences for an extraordinarily good bachelors diploma thesis. |
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| Abstract: | This thesis investigates the capability of GARCH-family models to capture the tail properties using Monte Carlo simulation in framework of Conditional Extreme Value Theory. Analysis is carried out for three different GARCH-type models: GARCH, EGARCH, GJR-GARCH using Normal and Student’s t-distributed innovations on four well-known stock market indices: S&P 500, FTSE 100, DAX and Nikkei 225. After conducting 3000 simulations of every estimated model, the Hill estimate of shape parameter implied by the GARCH-type models will be calculated and the models’ performance will be assessed based on histograms, descriptive statistics and Root Mean Squared Error of simulated Hill estimates. Interesting results and implications for further research have been identified. Firstly, we highlight the Normal distribution’s inappropriate nature in this case and its inability to capture the tail properties. Furthermore, GJR-GARCHT with t-distributed innovations is identified to be the best model, closely followed by other t-distributed GARCH-type models. Finally, a pattern in all Q-Q plots forecasting the simulation study results is apparent, with the exception of the DAX. This anomalous behaviour therefore necessitated further analysis and a significant right tail influence was recorded. Even though Hill estimates utilise only the lowest order statistics, upper quantiles of DAX are found to play an important role in performance in the simulation study, and to significantly offset the asymmetric GARCH models. Considering these findings, it is possible to conclude that t-distributed GARCH-type models are able, for the most part, to capture tail properties, in comparison to Normal distributed GARCH-type models, whose maximal outcomes of simulation fail to even reach the original values of the Hill estimates. |
| Downloadable: | Bachelor Theses of Siml |
