Fitting heavy Tail distributions with mixture models

Basílio, Jorge; Oliveira, Amilcar

http://hdl.handle.net/10400.2/14666

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Authors

Basílio, Jorge

Oliveira, Amilcar

Abstract(s)

The normal probability distribution as assumption for financial returns have been recognized as inappropriate, and a source of inaccurate estimation of Value at Risk. Empirical evidence also have been shown that financial returns shows a more accentuated leptokurtic distribution when compared with a Normal distribution and also skewed. This is usually a cause of underestimated values of VaR, specially when the quantiles are very low. Therefore it is necessary to focus on the tail of the distribution and identify models to fit that behavior. We will highlight the differences between the quality of fitting in the tails of the distribution and the fitting for all the distribution. This work compares and interprets the results obtained by applying mixture models as a method to estimate the behavior on the extremes for heavy tail data distributions. This results will be then used to describe an analytical solution of VaR under mixture models.