Statistical estimation errors of VaR under ARCH returns

Hiroyuki Taniai, Masanobu Taniguchi

Research output: Contribution to journalArticle

3 Citations (Scopus)

Abstract

In this paper we discuss some problems of existing methods for calculating the Value-at-Risk (VaR) in ARCH setting. It should be noted that the commonly used approaches often confuse the true innovations with the empirical residuals, i.e., estimation errors for unknown ARCH parameters are ignored. We adjust this by using the asymptotics of the residual empirical process, and propose a feasible VaR which, according to the spirit of VaR, keeps the assets away from a specified risk with high confidence level. Its meaningfulness in comparison with the usual VaR will be illustrated clearly by numerical studies.

Original languageEnglish
Pages (from-to)3568-3577
Number of pages10
JournalJournal of Statistical Planning and Inference
Volume138
Issue number11
DOIs
Publication statusPublished - 2008 Nov 1

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Keywords

  • ARCH model
  • Discretized estimator
  • Functional delta method
  • Residual empirical process
  • Value-at-risk

ASJC Scopus subject areas

  • Statistics and Probability
  • Statistics, Probability and Uncertainty
  • Applied Mathematics

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