Value at risk, outliers and chaotic dynamics

Abstract

Financial returns series typically exhibit excess kurtosis and volatility clustering. The GARCH is often applied to describe these two stylized facts. Nevertheless, all excess kurtosis in stock returns cannot be captured by this model. In presence of such dynamics, a non-linear model in variance cannot take into account all the non-linearity in returns. The aim of this work is the study of relationships between chaotic dynamics, and outliers as well as their impact on Value at Risk. In this paper, our empirical study is based on the daily Nikkei returns series from 06/01/1987 to 14/03/2001. We apply the traditional GARCH and the Mackey-Glass-GARCH (Kyrtsou and Terraza (2003)) both to the initial and the filtered Nikkei returns series without outliers. The performance test of Lopez (1988) for Value at Risk models is then applied to determine the best model. We show that during the period of estimation, the GARCH and the Mackey-Glass-GARCH VaR models with (without) outliers at 95% overestimate (underestimate) risks. The filtering of outliers lead to underestimation of risk more accentuated during the Asian crisis period confirming the presence of severe distortions in the underlying structure of the series when removing extreme events. During this period, the Mackey-Glass-GARCH is better than the GARCH comparing the hedging rates.