Which Extreme Values are Really Extreme?

Posted: 29 Feb 2008

See all articles by Jesús Gonzalo

Jesús Gonzalo

Universidad Carlos III de Madrid - Department of Statistics and Econometrics; Aarhus University - Department of Economics and Business Economics

Jose Olmo

Universidad de Zaragoza; University of Southampton

Date Written: 2004

Abstract

We define the extreme values of any random sample of size n from a distribution function F as the observations exceeding a threshold and following a type of generalized Pareto distribution (GPD) involving the tail index of F. The threshold is the order statistic that minimizes a Kolmogorov-Smirnov statistic between the empirical distribution of the corresponding largest observations and the corresponding GPD. To formalize the definition we use a semiparametric bootstrap to test the corresponding GPD approximation. Finally, we use our methodology to estimate the tail index and value at risk (VaR) of some financial indexes of major stock markets.

Keywords: bootstrap, extreme values, goodness-of-fit test, Hill estimator, Pickands theorem, VaR

Suggested Citation

Gonzalo Muñoz, Jesús and Olmo, Jose, Which Extreme Values are Really Extreme? ( 2004). Journal of Financial Econometrics, Vol. 2, No. 3, pp. 349-369, 2004, Available at SSRN: https://ssrn.com/abstract=821725

Jesús Gonzalo Muñoz (Contact Author)

Universidad Carlos III de Madrid - Department of Statistics and Econometrics ( email )

c/ Madrid 126
Getafe (Madrid), 28903
Spain
34 + 91 624 9853 (Phone)
34 + 91 624 9849 (Fax)

Aarhus University - Department of Economics and Business Economics

Fuglesangs Allé 4
Aarhus V
Denmark

Jose Olmo

Universidad de Zaragoza ( email )

Gran Via, 2
50005 Zaragoza, Zaragoza 50005
Spain

University of Southampton ( email )

Southampton
United Kingdom

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