Value at Risk: GARCH vs. Stochastic Volatility Models: Empirical Study

• Název práce v češtině: Value at Risk: GARCH vs. modely stochastické volatility: empirická studie
• Název v anglickém jazyce: Value at Risk: GARCH vs. Stochastic Volatility Models: Empirical Study
• Klíčová slova: VaR, GARCH, Stochastická volatilita, backtestové metódy, podmienený coverage, nepodmienený coverage
• Klíčová slova anglicky: VaR, GARCH, Stochastic Volatility, backtesting methods, conditional coverage, unconditional coverage
• Akademický rok vypsání: 2010/2011
• Typ práce: diplomová práce
• Jazyk práce: angličtina
• Ústav: Institut ekonomických studií (23-IES)
• Vedoucí / školitel: PhDr. Petr Gapko, Ph.D.
• Řešitel: skrytý - zadáno vedoucím/školitelem
• Datum přihlášení: 10.06.2011
• Datum zadání: 10.06.2011
• Datum a čas obhajoby: 13.09.2012 00:00
• Místo konání obhajoby: IES
• Datum odevzdání elektronické podoby: 31.07.2012
• Datum proběhlé obhajoby: 13.09.2012
• Oponenti: PhDr. Jakub Seidler, Ph.D.

Seznam odborné literatury

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Inc.
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Journal of Econometrics 31.
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A Review of the Theory and Empirical Evidence." Journal of Econometrics 52,
April.
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Value at Risk Measures." Working Papers - 03: CIRANO.
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Stochastic Volatility." Institut fr Mathematische Stochastik University of Freiburg.
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tice, Nobel Lecture." New York University, Department of Finance, December 8.
8. Engle, R. F., S. M. Focardi, & F. J. Fabozzi (2007): \ARCH/GARCH Models in
Applied Financial Econometrics.", http://pages.stern.nyu.edu/ rengle/ARCHGARCH.pdf.
Engle, R. F. & S. Manganelli (2001): \Value at Risk Models in Finance." European
Central Bank, Working Paper No. 75, ISSN 1651 1810.
Giot, P. & S. Laurent (2003): \Modelling Daily Value at Risk Using Realized
Volatility and ARCH Types Models." Journal of Empirical Finance, May.
9. Jimnez-Martn, J., M. McAleer, & T. Prez-Amaral (2009): \The Ten Com-
mandments for Managing Value-at-Risk Under the Basel II Accord." ECO2008-
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Předběžná náplň práce v anglickém jazyce

Value at Risk (VaR) has over time evolved to one of
the most popular comprehensive tools used to estimate exposure to market
risks. VaR claims the maximum loss of portfolio, expressed in its units, with
certain probability during given period. It works with the distribution of loss
and pro�t. With zero mean only standard deviation of the loss matters. A
time horizon and a con�dence level are chosen and a cumulative distribution
function is assumed.
Because volatility is a key input to VaR models, the characterization of
asset or portfolio volatility is of great importance when implementing and testing
VaR models. The correct choice of volatility model is one of the most
important factors in determining the e�ectiveness of VaR. Volatility modeling
is nowadays dominated by three families of models: the Conditional Volatility
ARCH/GARCH models developed by Engle (1982) and Bollerslev (1986),
respectively; Stochastic Volatility (SV) models, which speci�es a stochastic
process for volatility, �rst introduced by Taylor (1982); and Realized Volatility
(RV) models. This paper will consider �rst two methods of estimating volatility,
while GARCH and SV are two competing, well-known, often-used models
to explain volatility of �nancial series.
ARCH/GARCH models have subsequently led to a huge family of autoregressive
conditional volatility models. Its popularity is attributed to the fact
of easy to implement, bringing great results and having large ability to capture
several stylized facts of �nancial returns, such as time-varying volatility,
persistence and clustering of volatility, and asymmetric reactions to positive
and negative shocks of equal magnitude. The ARCH/GARCH family proved
to be a rich framework and many di�erent extensions and generalizations of
the initial ARCH/GARCH models have been proposed.
SV models have been until nowadays extremely time consuming to estimate.
But it is not longer a case since the strong evolution of simulation based
econometric methods in last years. Problem of di�cult estimation is handled
with lot of algorithms developed recently: Generalized Methods of Moments,
the Quasi Maximum Likelihood method, Simulated Maximum Likelihood technique,
the Markov Chain Monte Carlo method. The idea behind the family of
SV models is that the volatility is driven by a latent process representing the
flow of price relevant information
Both GARCH and SV models take account the important volatility clustering
of �nancial returns. But the main di�erence is that in SV model the volatility
is a latent variable with unexpected noise, while in the GARCH model, the
volatility one period ahead is observable given todays information.
However, VaR models are useful only if they predict future risks accurately.
In order to evaluate the quality of the VaR estimates, the models should always
be backtested with appropriate methods. Backtesting is a statistical procedure
where actual pro�ts and losses are systematically compared to corresponding
VaR estimates. The objective of this paper will be the theoretical and empirical
comparison and evaluation of GARCH and SV models for forecasting of VaR.
Empirical part will be applied on 4 di�erent western European stock indices.