Extremal forex returns in extremely large data sets (Q1848525)

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.