Work detail

Extreme value theory: Empirical analysis of tail behaviour of GARCH models

Author: Bc. Jan Šiml
Year: 2012 - summer
Leaders: PhDr. Boril Šopov, MSc., LL.M.
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.
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


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