Journal of Risk

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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 Ángel Sánchez-Granero

  • The skewness and fat tail distributions outperform the normal one in forecasting VaR.
  • The skewed generalised-t distribution of Theodossiou seems to be the best in fitting the data.
  • According to a regulator loss function, t-Student distribution is the best in forecasting VaR.
  • According to a firm loss function, the skewed distributions outperform the t-Student distribution.

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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