Pricing of catastrophe insurance options written on a loss index with reestimation

We propose a valuation model for catastrophe insurance options written on a loss index. This kind of options distinguishes between a loss period [ 0 , T 1 ] , during which the catastrophes may happen, and a development period [ T 1 , T 2 ] , during which losses entered before T 1 are reestimated. Here we suppose that the underlying loss index is given by a time inhomogeneous compound Poisson process before T 1 and that losses are reestimated by a common factor given by an exponential time inhomogeneous Lévy process after T 1 . In this setting, using Fourier transform techniques, we are able to provide analytical pricing formulas for catastrophe options written on this kind of index.