Tid: 9 juni 2014 kl 16.15-17.00.

Föredragshållare: Fredrik Giertz

Titel: Analysis and optimization of a portfolio of catastrophe bonds

Abstract This master's thesis in mathematical statistics has the two major purposes; (i) to model risk associated with a special type of reinsurance contract, the catastrophe bond, and to investigate how to measure risk associated with the latter and (ii) to analyze and develop methods of obtaining an optimal portfolio consisting of several catastrophe bonds in terms of risk. Two pathways of modeling potential catastrophe bond losses are analyzed; one method directly modeling potential contract losses and one method modeling the underlying contract loss governing variables. The first method is simple in its structure but with the disadvantage of the inability to, in a simple and flexible way, introduce a dependence structure between the losses of different contracts. The second modeling method uses a stochastic number of stochastic events representation connected into a multivariate dependence structure using the theory of copulas.

Results show that the choice of risk measure is of great importance when analyzing catastrophe bonds and their related risks. As an example, the measure Value at Risk may fail to capture the essence of catastrophe bond risk, which in turn means that portfolio optimization with respect to the same might lead to a systematic obscurity of risk. Two coherent risk measures were found to be satisfactory at measuring catastrophe bond risk, expected shortfall and through a spectral risk measure.

This thesis extends a well-known optimization method of Conditional Value at Risk to achieve a method of optimizing any spectral risk measure. The optimization results show that expected shortfall optimization leads to portfolios being, possibly only slightly, advantageous at the specific point at which it is optimized but that their characteristics may be disadvantageous at other parts of the loss distribution. The optimized spectral risk measure portfolios were proven to possess good characteristics through all parts of the loss distribution. Optimization results were compared to the popular mean-variance portfolio optimization approach. The comparison shows that the mean-variance approach handles the special distribution of catastrophe bond losses in an over-simplistic way, and that it has a severe lack of flexibility towards focusing on different aspects of risk. In contrast, the spectral risk measure optimization procedure was proven to be the most flexible and possibly the most appropriate way to optimize a portfolio of catastrophe bonds.

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