Value at Risk, Outliers and Chaotic Dynamics

Financial returns series typically exhibit excess kurtosis and volatility clustering. GARCH models are often applied to describe these two stylised facts. Nevertheless, applications of these processes to stock returns have shown that they cannot capture all excess kurtosis, high Jarque-Bera and inherent non-linearity. The aim of this work is to suggest a new non-linear framework for the calculation of the Value-at-Risk. As it has been demonstrated in Kyrtsou and Terraza V. (2004) the use of a mixed non-linear model in the estimation of VaR can improve the obtained results. In this paper we apply the traditional VaR-GARCH and the VaR-Mackey-Glass-GARCH models both to the initial and the filtered Nikkei returns series without outliers.