Corrected-Hill versus partially reduced-bias value-at-risk estimation

Abstract

The value-at-risk (VaR) at a small level q, $0<q<1$, is the size of the loss that occurs with a probability q. Semi-parametric partially reduced-bias (PRB) VaR-estimation procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p any real number, are put forward. After the study of their asymptotic behavior, these PRB VaR-estimators are altogether compared with the classical ones for finite samples, through a large-scale Monte-Carlo simulation study. A brief application to financial log-returns is provided, as well as some final remarks.

KEYWORDS AND PHRASES:

• Heavy right tails
• Heuristic sample fraction selection; Monte-Carlo simulation; Semi-parametric estimation; Statistics of extremes; Value-at-risk estimation

AMS 2000 subject classification::

• Primary 62G32; Secondary 65C05

Additional information

Funding

Research partially supported by FLAD, Fundação Luso-Americana para o Desenvolvimento, COST Action IC1408—CroNos, and National Funds through FCT—Fundação para a Ciência e a Tecnologia, projects UID/MAT/UI0006/2013 (CEAUL) and UID/MAT/0297/2013 (CMA/UNL).