Modeling and pricing precipitation derivatives under weather forecasts

We propose a pure jump precipitation model embedded in an enlarged filtration framework accounting for weather forecasts. Under different anticipative approaches, we define precipitation swap/futures prices and also introduce the notion of an "information premium". In contrast to some other models in the literature, our forward-looking swap price representations admit time-varying stochastic dynamics. In these setups, swap price processes under the physical and risk-neutral measure turn out to be indistinguishable. We also consider an extended multi-location model measuring precipitation in several locations. In order to price options on precipitation derivatives under weather forecasts modeled by enlarged filtrations, we develop customized approximation procedures involving complex power series expansions and wavelet transform techniques.