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Statistical methods to expect extreme values: Application of POT approach to CAC40 return index

A. Zoglat, S. El Adlouni, E. Ezzahid, A. Amar, C. G. Okou, F. Badaoui

Abstract


In the past twenty years a new development in the extreme value theory has been done, especially for the “Peaks Over Threshold (POT) approach”. This approach, based on the analysis of the data exceeding a sufficiently high threshold, aims to improve the efficiency of the extreme quantile estimators. The selection of an appropriate threshold is one of the
important concerns of the POT approach. Various threshold selection methods, namely Square Error Method (SEM), Automated Threshold Selection Method (ATSM), and Multiple Threshold Method (MTM), has been developed. Such approaches allow avoiding subjective drawbacks of empirical and graphical methods for optimal thresholds selection.

The main objective of the present study is to compare the performances of these methods in the case of financial risk estimations related to the market turmoil. The main focus of this paper is to assess the performance of the POT approach, combined to the maximum likelihood and moment methods for parameter estimations.

Results show that the MTM outperforms ATSM and SEM. It is confirmed that the inverse of CAC40 return index has a Frechet distribution tail behavior, and the parameters are better estimated by the moments method.

Keywords


Peaks Over Thresholds, Generalized Pareto Distribution, Square Error Method, Automated Threshold Selection Method, Multiple Threshold Method.

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