Can the student‐t distribution provide accurate value at risk?

Abstract

Purpose

This paper aims to investigate how effectively the value at risk (VaR) estimated using the student‐t distribution captures the market risk.

Design/methodology/approach

Two alternative VaR models, VaR‐t and VaR‐x models, are presented and compared with the benchmark model (VaR‐n model). In this study, we consider the Student‐t distribution as a fit to the empirical distribution for estimating the VaR measure, namely, VaR‐t method. Since the Student‐t distribution is criticized for its inability to capture the asymmetry of distribution of asset returns, we use the extreme value theory (EVT)‐based model, VaR‐x model, to take into account the asymmetry of distribution of asset returns. In addition, two different approaches, excess‐kurtosis and tail‐index techniques, for determining the degrees of freedom of the Student‐t distribution in VaR estimation are introduced.

Findings

The main finding of the study is that using the student‐t distribution for estimating VaR can improve the VaR estimation and offer accurate VaR estimates, particularly when tail index technique is used to determine the degrees of freedom and the confidence level exceeds 98.5 percent.

Originality/value

The main value is to demonstrate in detail how well the student‐t distribution behaves in estimating VaR measure for stock market index. Moreover, this study illustrates the easy process for determining the degrees of freedom of the student‐t, which is required in VaR estimation.

Citation

Lin, C. and Shen, S. (2006), "Can the student‐t distribution provide accurate value at risk?", Journal of Risk Finance, Vol. 7 No. 3, pp. 292-300. https://doi.org/10.1108/15265940610664960