Evaluating the performance of the skewed distributions to forecast value-at-risk in the global financial crisis

Pilar Abad, Sonia Benito, Carmen López Martín and Miguel à ngel Sánchez-Granero

Journal of Risk

Abstract: ABSTRACT This paper evaluates the performance of several skewed and symmetric distributions;by modeling the tail behavior of daily returns and forecasting value-at-risk (VaR).;First, we use some goodness-of-fit tests to analyze which distribution best fits the;data. The comparisons in terms of VaR are carried out by examining the accuracy;of the VaR estimate and minimizing the loss function from the points of view of the;regulator and the firm. The results show that the skewed distributions outperform;the normal and Student t (ST) distributions in fitting portfolio returns. Following a;two-stage selection process, whereby we initially ensure that the distributions provide;accurateVaR estimates, and focusing on the firm's loss function, we can conclude that;skewed distributions outperform the normal and ST distributions in forecasting VaR.;From the point of view of the regulator, the superiority of the skewed distributions;related to ST is not evident. As the firms are free to choose the model they use to;forecast VaR, in practice, skewed distributions will be used more frequently.

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