Bootstrap methods in statistics of extremes
Ivette Gomes – University of Lisbon
Frederico Caeiro – Nova University of Lisbon
Lígia Henriques-Rodrigues – University of São Paulo
B G Manjunath – Dell

Extreme events in finance

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In this chapter we provide an overview of the bootstrap methodology together with its possible use in the reliable estimation of any parameter of extreme events. For an asymptotically consistent choice of the threshold to use in the estimation of the extreme value index (EVI), we suggest and discuss the so-called double-bootstrap algorithm, where in each run two bootstrap samples of related sizes are generated. Such a threshold is used for the adaptive estimation of a positive EVI, also called tail index, the primary parameter in statistics of extremes.

Apart from the classical Hill and peaks over random threshold (PORT)-Hill EVI estimators, we consider a class of minimum-variance reduced-bias (MVRB) EVI estimators and associated PORT-MVRB EVI estimators. The algorithm is described for the EVI estimation, but it can work similarly for the estimation of other parameters of extreme events, like a high quantile, the probability of exceedance, or the return period of a high level.

Extreme events in finance Extreme events in finance

Jan Beirlant, University of Lisbon

Ivette Gomes

University of Lisbon

Klaus Herrmann, Nova University of Lisbon

Frederico Caeiro

Nova University of Lisbon

Ligia Henriques-Rodrigues, University of Sao Paulo

Lígia Henriques-Rodrigues

University of São Paulo

B G Manjunath, Dell

B G Manjunath

Dell