A new approach for using lévy processes for determining high-frequency value-at-risk predictions

Wei Sun, Svetlozar Rachev, Frank J. Fabozzi

Research output: Contribution to journalArticlepeer-review

12 Scopus citations

Abstract

A new approach for using Lévy processes to compute value-at-risk (VaR) using high-frequency data is presented in this paper. The approach is a parametric model using an ARMA(1,1)-GARCH(1,1) model where the tail events are modelled using fractional Lévy stable noise and Lévy stable distribution. Using high-frequency data for the German DAX Index, the VaR estimates from this approach are compared to those of a standard nonparametric estimation method that captures the empirical distribution function, and with models where tail events are modelled using Gaussian distribution and fractional Gaussian noise. The results suggest that the proposed parametric approach yields superior predictive performance.

Original languageEnglish
Pages (from-to)340-361
Number of pages22
JournalEuropean Financial Management
Volume15
Issue number2
DOIs
StatePublished - Mar 2009

Keywords

  • Fractional Gaussian noise
  • Fractional Lévy stable noise
  • High-frequency data
  • Lévy stable distribution
  • Value-at-risk

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