Extreme Risk and Value-at-Risk in the German Stock Market

Abstract

Extreme Value Theory methods are used to investigate the distribution of the extreme minima in the German stock market over the period 1973 to 2001. Innovative aspects of this paper include (i) a wide set of distributions considered, (ii) L-moment diagrams employed to identify the most appropriate distribution/s, (iii) ‘probability weighted moments’ used to estimate the parameters of these distribution/s and (iv) the Anderson–Darling goodness of fit test employed to test the adequacy of fit. The ‘generalized logistic’ distribution is found to provide adequate descriptions of the extreme minima of the German stock market over the period studied. VaR analysis results show that the EVT methods used in this study can be particularly useful for market risk measurement since they produce estimates that outperform those derived by traditional methods at high confidence levels.

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