POT approach for estimation of extreme risk measures of EUR/USD returns
Abstract
Leadbeter et al. (M.R.,G.Leadbetter, G.Lindgren,and H.Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer Series in Statistics. Springer-Verlag: New York, 1983.) have generalized the extreme value theory of i.i.d. in the case of the stationary process, where it have defined an extremal index $\theta\in]0,1[$ for measuring the degree of dependence at the extremes, this parameter measures how the extremes cluster together and $1/\theta$ is interpreted as the average size of these clusters. Using this parameter and the Peak Over Threshold method which involves the Generalized Pareto Distribution we estimate in this work the extreme quantile and the conditional tail expectation for EUR/USD returns.References
P. Artzner, F. Delbaen, J. M. Eber, and D. Heath, Coherent Measures of Risk, Mathematical Finance, vol. 9, pp. 203–228, 1999.
A. A. Balkema, and L. De. Haan, Residual life time at great age, Annals of Probability, vol. 2, pp. 792–804, 1974.
S. Coles, An Introduction to Statistical Modeling of Extreme Values, Springer Series in Statistics. Springer-Verlag: London, 2001.
P. Embrechts, C. Kluppelberg, and T. Mikosch, Modelling Extremal Events for Insurance and Finance, Springer, Berlin, 1997.
R. A Fisher, and L.H.C. Tippett, Limiting Forms of the Frequency Distribution of the Largest or Smallest Member of a Sample, Proceedings of the Cambridge Philosophical Society, vol. 2, pp. 180– 190, 1928.
C. A. T. Ferro, and J. Segers, Inference for Clusters of Extreme Values, Journal of the Royal Statistical Society, Series B, vol.65, no.2, pp. 545-556, 2003.
M. R., G. Leadbetter, G. Lindgren, and H. Rootzen, Extremes and Related Properties of Random Sequences and Processes, Springer Series in Statistics. Springer-Verlag: New York, 1983.
S. T. Rachev, S. Stoyanov, and F. J Fabozzi, Advanced Stochastic Models, Risk Assessment, and Portfolio Optimization: The Ideal Risk, Uncertainty, and Performance Measures, New Jersey: John Wiley & Sons., 2007.
R. L Smith, and I. Weissman, Estimating the extremal index, Journal of the Royal Statistical Society, Series B, vol. 56, pp. 515–528, 1994.
M. Süveges, Likelihood estimation of the extremal index, Extremes, vol. 10, pp. 41–55, 2007.
I. Weissman, and S. Y. Novak, On blocks and runs estimators of the extremal index, J. Statist. Plann. Inference, vol. 66, pp. 281–288, 1998.
- Authors retain copyright and grant the journal right of first publication with the work simultaneously licensed under a Creative Commons Attribution License that allows others to share the work with an acknowledgement of the work's authorship and initial publication in this journal.
- Authors are able to enter into separate, additional contractual arrangements for the non-exclusive distribution of the journal's published version of the work (e.g., post it to an institutional repository or publish it in a book), with an acknowledgement of its initial publication in this journal.
- Authors are permitted and encouraged to post their work online (e.g., in institutional repositories or on their website) prior to and during the submission process, as it can lead to productive exchanges, as well as earlier and greater citation of published work (See The Effect of Open Access).
