Reduced-bias and partially reduced-bias mean-of-order-p value-at-risk estimation: a Monte-Carlo comparison and an application

M. Ivette Gomes, Frederico Caeiro, Fernanda Figueiredo, Lígia Henriques-Rodrigues, Dinis Pestana

Research output: Contribution to journalArticlepeer-review

Abstract

On the basis of a sample of either independent, identically distributed or possibly weakly dependent and stationary random variables from an unknown model F with a heavy right-tail function, and for any small level q, the value-at-risk (VaR) at the level q, i.e. the size of the loss that occurs with a probability q, is estimated by new semi-parametric reduced-bias procedures based on the mean-of-order-p of a set of k quotients of upper order statistics, with p an adequate real number. After a brief reference to the asymptotic properties of these new VaR-estimators, we proceed to an overall comparison of alternative VaR-estimators, for finite samples, through large-scale Monte-Carlo simulation techniques. Possible algorithms for an adaptive VaR-estimation, an application to financial data and concluding remarks are also provided.

Original languageEnglish
Pages (from-to)1735-1752
Number of pages18
JournalJournal Of Statistical Computation And Simulation
Volume90
Issue number10
DOIs
Publication statusPublished - 2 Jul 2020

Keywords

  • Bias reduction
  • heavy right-tails
  • heuristic methods
  • Monte-Carlo simulation
  • Primary 62G32
  • Secondary 65C05
  • semi-parametric estimation
  • statistics of extremes
  • value-at-risk estimation

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