Pricing in new markets

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.