Extremal forex returns in extremely large data sets
type: Item
instance of: scholarly article
title: Extremal forex returns in extremely large data sets
zbMATH Open document ID: 1008.62054
DOI: 10.1023/A:1013917009089
author: Michel M. Dacorogna
author: Ulrich A. Müller
author: Olivier V. Pictet
author: Casper C. de Vries
published in: Extremes
publication date: 2002-11-21T00:00:00Z
review text: This paper is devoted to the statistical analysis of forex log-returns using heavy-tailed distribution models. The authors use the d.f.s \(F(x)=1+ax^{-\alpha}(1+bx^{-\beta}+o(x^{-\beta}))\) as \(x\to\infty\), \(a,\alpha,\beta>0\), and analyze the role of the second order parameters \(b\) and \(\beta\). Te aim of the paper is to provide a suitable technique of the Value-at-Risk (VaR) analysis in this case. It is shown that the analysis based on normal models underestimates the VaR for a single period for heavy-tailed data and overestimates effects of increasing time horizon. The Hill estimator for \(1/\alpha\) and the De Haan estimator for the VaR are discussed. The described technique is applied to data on USD/DM returns of 1987-1996.
Mathematics Subject Classification ID: 62G32
Mathematics Subject Classification ID: 62P05
Mathematics Subject Classification ID: 62G20
zbMATH DE Number: 1833861
zbMATH Keywords: regular variation
zbMATH Keywords: Poisson limit
zbMATH Keywords: foreign exchange rates
zbMATH Keywords: value at risk
MaRDI profile type: Publication
full work available at URL: a:1013917009089
OpenAlex ID: W1767956281
description: scientific article; zbMATH DE number 1833861