A New Approach for Using Lévy Processes for Determining High-Frequency Value-at-Risk Predictions

22 Pages Posted: 27 Apr 2009

See all articles by Wei Sun

Wei Sun

affiliation not provided to SSRN

Svetlozar Rachev

Texas Tech University

Frank J. Fabozzi

EDHEC Business School

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.

Suggested Citation

Sun, Wei and Rachev, Svetlozar and Fabozzi, Frank J., A New Approach for Using Lévy Processes for Determining High-Frequency Value-at-Risk Predictions. European Financial Management, Vol. 15, Issue 2, pp. 340-361, March 2009, Available at SSRN: https://ssrn.com/abstract=1376566 or http://dx.doi.org/10.1111/j.1468-036X.2008.00467.x

Wei Sun

affiliation not provided to SSRN ( email )

Svetlozar Rachev

Texas Tech University ( email )

Dept of Mathematics and Statistics
Lubbock, TX 79409
United States
631-662-6516 (Phone)

Frank J. Fabozzi

EDHEC Business School ( email )

France
215 598-8924 (Phone)

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