A computational study of a quasi-PORT methodology for VaR based on second-order reduced-bias estimation

• Type: Article in International Scientific Journal
• Date: 2012

Authors

figueiredo, f (Author) FEP; gomes, mi (Author) Other; henriques-rodrigues, l (Author) Other; miranda, mc (Author) Other

Journal

Title: Journal of Statistical Computation and Simulation

Vol. 82 No. 4

Pages: 587-602

ISSN: 0094-9655

Publisher: Taylor & Francis

Indexing

ISI Web of Knowledge - 8 Citations

ISI Web of Science

Scopus - 12 Citations

Scientific classification

FOS: Natural sciences > Computer and information sciences

Other information

Authenticus ID: P-002-GJ6

DOI: 10.1080/00949655.2010.547196

Abstract (EN): In this paper, we deal with the estimation, under a semi-parametric framework, of the Value-at-Risk (VaR) at a level p, the size of the loss occurred with a small probability p. Under such a context, the classical VaR estimators are the Weissman-Hill estimators, based on any intermediate number k of top-order statistics. But these VaR estimators do not enjoy the adequate linear property of quantiles, contrarily to the PORT VaR estimators, which depend on an extra tuning parameter q, with 0 <= q < 1. We shall here consider 'quasi-PORT' reduced-bias VaR estimators, for which such a linear property is obtained approximately. They are based on a partially shifted version of a minimum-variance reduced-bias (MVRB) estimator of the extreme value index (EVI), the primary parameter in Statistics of Extremes. Due to the stability on k of the MVRB EVI and associated VaR estimates, we propose the use of a heuristic stability criterion for the choice of k and q, providing applications of the methodology to simulated data and to log-returns of financial stocks.

Language: English

Type (Professor's evaluation): Scientific

No. of pages: 16