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

Chu‐Hsiung Lin · Shan‐Shan Shen

36 citations0/0 files storedThe Journal of Risk Finance

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Financial Risk and Volatility Modeling Stochastic processes and financial applications Risk and Portfolio Optimization

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.

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References

1965The Behavior of Stock-Market Prices 1995Techniques for Verifying the Accuracy of Risk Measurement Models 2000Estimation of tail-related risk measures for heteroscedastic financial time series: an extreme value approach 1974A Comparison of the Stable and Student Distributions as Statistical Models for Stock Prices 1972The Distribution of Share Price Changes 1998Distributional Characteristics of Emerging Market Returns and Asset Allocation 2001Tail-Index Estimates in Small Samples 1994Alternative Models for the Conditional Heteroscedasticity of Stock Returns

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