Value‐at‐risk: Techniques to account for leptokurtosis and asymmetric behavior in returns distributions

Abstract

Purpose

The last few years in the financial markets have shown great instability and high volatility. In order to capture the amount of risk a financial firm takes on in a single trading day, risk managers use a technology known as value‐at‐risk (VaR). There are many methodologies available to calculate VaR, and each has its limitations. Many past methods have included a normality assumption, which can often produce misleading figures as most financial returns are characterized by skewness (asymmetry) and leptokurtosis (fat‐tails). The purpose of this paper is to provide an overview of VaR and describe some of the most recent computational approaches.

Design/methodology/approach

This paper compares the Student‐t, autoregressive conditional heteroskedastic (ARCH) family of models, and extreme value theory (EVT) as a means of capturing the fat‐tailed nature of a returns distribution.

Findings

Recent research has utilized the third and fourth moments to estimate the shape index parameter of the tail. Other approaches, such as extreme value theory, focus on the extreme values to calculate the tail ends of a distribution. By highlighting benefits and limitations of the Student‐t, autoregressive conditional heteroskedastic (ARCH) family of models, and the extreme value theory, one can see that there is no one particular model that is best for computing VaR (although all of the models have proven to capture the fat‐tailed nature better than a normal distribution).

Originality/value

This paper details the basic advantages, disadvantages, and mathematics of current parametric methodologies used to assess value‐at‐risk (VaR), since accurate VaR measures reduce a firm's capital requirement and reassure creditors and investors of the firm's risk level.

Citation

Lechner, L.A. and Ovaert, T.C. (2010), "Value‐at‐risk: Techniques to account for leptokurtosis and asymmetric behavior in returns distributions", Journal of Risk Finance, Vol. 11 No. 5, pp. 464-480. https://doi.org/10.1108/15265941011092059