This paper aims to provide a dynamic analysis of the insurance linked securities index. We are discussing the behaviour of the index for three years and pointing out the consequences of some major events like Katrina or the last and current financial crisis. Some stylized facts of the index, like the non-Gaussianity, the asymmetry or the clusters of volatility, are highlighted. We are using some GARCH-type models and the generalized hyperbolic distributions in order to capture these elements. The GARCH in Mean model with a Normal Inverse Gaussian distribution seems to be very efficient to fit the log-returns of the insurance linked securities index.
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