Journal Article

Which Extreme Values Are Really Extreme?

Jesús Gonzalo and José Olmo

in Journal of Financial Econometrics

Volume 2, issue 3, pages 349-369
Published in print June 2004 | ISSN: 1479-8409
Published online June 2004 | e-ISSN: 1479-8417 | DOI: https://dx.doi.org/10.1093/jjfinec/nbh014
Which Extreme Values Are Really Extreme?

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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

Journal Article.  9416 words. 

Subjects: Financial Markets ; Econometrics and Mathematical Economics

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