352259.Rozga.Arneric_-_Full_paper1.doc - REVISTA...

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REVISTA INVESTIGACIÓN OPERACIONAL _____ Vol., 30, No.N, pp-pp., 2009 DEPENDENCE BETWEEN VOLATILITY PERSISTENCE, KURTOSIS AND DEGREES OF FREEDOM Ante Rozga 1 and Josip Arnerić, 2 Faculty of Economics, University of Split, Croatia ABSTRACT In this paper the dependence between volatility persistence, kurtosis and degrees of freedom from Student’s t-distribution will be presented in estimation alternative risk measures on simulated returns. As the most used measure of market risk is standard deviation of returns, i.e. volatility. However, based on volatility alternative risk measures can be estimated, for example Value-at-Risk (VaR). There are many methodologies for calculating VaR, but for simplicity they can be classified into parametric and nonparametric models. In category of parametric models the GARCH(p,q) model is used for modeling time-varying variance of returns. KEY WORDS: Value-at-Risk, GARCH(p,q), T-Student MSC: 62H12, 62P20, 91B28, 91B28 RESUMEN En este trabajo la dependencia de la persistencia de la volatilidad, kurtosis y grados de liberad de una Distribución T-Student será presentada como una alternativa para la estimación de medidas de riesgo en la simulación de los retornos. La medida más usada de riesgo de mercado es la desviación estándar de los retornos, i.e. volatilidad. Sin embargo, medidas alternativas de la volatilidad pueden ser estimadas, por ejemplo el Valor-al-Riesgo (Value-at-Risk, VaR). Existen muchas metodologías para calcular VaR, pero por simplicidad estas pueden ser clasificadas en modelos paramétricos y no paramétricos . En la categoría de modelos paramétricos el modelo GARCH(p,q) es usado para modelar la varianza de retornos que varían en el tiempo. 1. INTRODUCTION It isn’t easy to estimate VaR when stochastic process which generates distribution of returns is not known. Unfortunately the assumption that the returns are independently and identically normally distributed is often unrealistic. Furthermore, empirical research about financial markets reveals following facts about financial time series: financial return distributions are leptokurtic, i.e. they have heavy and fat tails, equity returns are typically negatively skewed and squared return series shows significant autocorrelation, i.e. volatilities tend to cluster According to first two facts it is important to examine which probability density function capture heavy tails and asymmetry the best. According to the third fact it is important to correctly specify conditional mean and conditional variance equations from GARCH family models. Therefore, high kurtosis exists within financial time series of high frequencies (observed on daily or weekly basis). This confirms the fact that distribution of returns generated by GARCH(p,q) model is always leptokurtic, even when normality assumption is introduced.
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