Can the student‐tdistribution provide accurate value at risk?

Purpose - This paper aims to investigate how effectively the value at risk (VaR) estimated using the student‐tdistribution 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‐tdistribution as a fit to the empirical distribution for estimating the VaR measure, namely, VaR‐t method. Since the Student‐tdistribution 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‐tdistribution in VaR estimation are introduced. Findings - The main finding of the study is that using the student‐tdistribution 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‐tdistribution 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.