Value-at-risk forecasting with the ARMA-GARCH family of models during the recent financial crisis

• Thesis title in Czech: Odhadování value-at-risk s využitím ARMA-GARCH modelů během poslední finanční krize
• Thesis title in English: Value-at-risk forecasting with the ARMA-GARCH family of models during the recent financial crisis
• Key words: VaR, analýza rizika, finanční krize, podmíněná volatilita, conditional coverage, odhad modelů, akciový index, garch, egarch, tarch, moving average proces, autoregresivní proces
• English key words: VaR, risk analysis, financial crisis, conditional volatility, conditional coverage, stock index, garch, egarch, tarch, moving average process, autoregressive process
• Academic year of topic announcement: 2011/2012
• Thesis type: rigorosum thesis
• Thesis language: angličtina
• Department: Institute of Economic Studies (23-IES)
• Supervisor: PhDr. Mgr. Milan Rippel
• Author: hidden - assigned by the advisor
• Date of registration: 16.09.2011
• Date of assignment: 16.09.2011
• Date and time of defence: 19.10.2011 00:00
• Venue of defence: IES
• Date of electronic submission: 20.09.2011
• Date of proceeded defence: 19.10.2011
• Opponents: PhDr. Jakub Seidler, Ph.D.

References

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Christoffersen, P. F. (1998): „Evaluating interval forecasts." International Economic Review 39(4): pp. 841-862.

Engle, R. F. (1982): „Autogregressive conditional heteroscedasticity with estimates of the variance of united kingdom inflation." Econometrica 50: pp. 987-1008.

Holton, G. A. (2003): „Value at Risk : theory and practice. Amsterdam : Academic Press, 405 s. ISBN 0123540100.

Huang, A. Y. (2010): „An optimization process in value-at-risk estimation." Review of Financial Economics 19(3): pp. 109-116.

Jorion, P. (2007): Value at risk: The New Benchmark for Managing Financial Risk. New York, NY [u.a.]: McGraw-Hill, 3. ed. edition.

Kupiec, P. H. (1995): „Techniques for verifying the accuracy of risk measurement models." Finance and Economics Discussion Series 95-24, Board of Governors of the Federal Reserve System (U.S.).

Lopez, J. A. (2001): „Evaluating the predictive accuracy of volatility models." Journal of Forecasting 20(2): pp. 87-109.

Terasvirta, T. (2006): „An introduction to univariate garch models." Working papers in Economics and Finance 646: p. 30.

Zakoian, J.-M. (1994): „Threshold heteroskedastic models." Journal of Economic Dynamics and Control 18(5): pp. 931-955.

Preliminary scope of work

Práce se zabývá analýzou volatility šesti akciových indexů (DJI, GSPC, IXIC, FTSE, GDAXI a N225) mezi léty 2004 až 2009. Uvedené období spadá do periody s relativně vyšší volatilitou, než je u uvedených indexů obvyklé. Data z akciových indexů jsou analyzována pomocí ARMA, ARCH, GARCH, TARCH a GARCH modelů s různými parametry nastavení a za předpokladů rozdělení logaritmizovaných výnosů jedním ze statistických rozdělení – normální, Student-t a GED.
Všechny modely jsou periodicky přepočítávané v přibližně půlroční periodě následně porovnány co do přesnosti pomocí méně známé metody conditional coverage, která je schopná porovnat jak procentuální shodu aplikovaného modelu, tak jeho negativní vlastnosti jako například clusterování chyb.

Preliminary scope of work in English

The work analysis volatility of six stock indices (DJI, GSPC, IXIC, FTSE, GDAXI a N225) between the years 2004 and 2009. The selected period is a preiod with relatively high volatility than usual for the mentioned indices. Data from stock indices are analyzed using ARMA, ARCH, GARCH, TARCH and GARCH models with various parameters and under the premise of log-returns modeled using one of the Normal, Student-t and GED distributions. All models are periodically reestimated in approximately six months long periods and their predictive accuracy is tested using a less known method called conditional coverage, which is able to compare the models not only based on the failure rates but also takes into account clustering of violations.