Parametric Value-at-Risk in Leptokurtic Distributions

Abstract: Value-at-risk offers a quick estimate of the market risk exposure inherent in an asset or portfolio. A wide range of value-at-risk methods exist, which differ slightly in the estimation procedures and their assumptions. The most widely used methods belong to the parametric value-at-risk family, which attempts to fit a probability distribution to the underlying data. In the majority of cases the assumed distribution is normal. However, most financial data have been shown to follow leptokurtic distributions, yielding the assumption of normality void. In fact, it would lead to severe underestimation of the tail risk. This study explores the usage of the leptokurtic Student's t-distribution as an alternative to the normal distribution. Five different volatility estimation techniques are used on monthly data from two currencies and two commodity futures contracts. The estimated conditional volatilities are then applied to both distributions in order to assess the performance of each distribution and volatility estimation technique. The performance is gauged by backtesting the computed VaR levels through a proportion of failures test, an independence test as well as a joint test. The results only imply minor improvements when using the t-distribution. These results are due to the poor estimations of the tail distributions stemming from skewness in the sample distributions. Moreover, the implied volatility could potentially be a strong candidate for accurate VaR estimations if the underlying options are liquid, thus reflecting an efficient market.