Abstract

In this thesis we consider recent developments in insurance and electricity financial products. In particular, we investigate the interplay between insurance and finance, and therein the problem of pricing catastrophe insurance options written on a loss index as well as electricity products. Catastrophe insurance options are standardized exchange-traded financial securities based on an underlying index, e.g. a PCS index, that encompasses insurance losses due to natural catastrophes. The PCS index is provided by the Property Claim Services (PCS), a US independent industry authority which estimates catastrophic property damage. The advantages of the catastrophe options in comparison to other capital market insurance solutions are lower transaction costs relative to the re-insurance and minimal credit risk, because of the guarantee of the exchange. The main results of the thesis are fairly realistic models for catastrophe loss indexes and electricity futures markets, where by employing Fourier transform techniques we are able to provide analytical pricing formulas for European type options traded in the markets. For the catastrophe loss index we specify a model, where the initial estimate of each catastrophe loss is re-estimated immediately by a positive martingale starting from the random time of loss occurrence. Significant advantage of this methodology is that it can be applied to loss distributions with heavy tails -- the appropriate tail behavior for catastrophe modeling. The case when the re-estimation factors are given by positive affine martingales is also discussed and a characterization of positive affine local martingales is provided. For electricity futures markets we derive a model, where we can simultaneously model evolution of futures and spot prices. At the same time we have an explicit connection between electricity futures and spot price processes. Furthermore, an important achievement is that the spot price dynamics in this model becomes multi-dimensional Markovian. The Markovian structure is crucial for pricing of path dependent electricity options.