Debora Daniela Escobar (University of Vienna)
Title:聽The distortion premium: properties, robustness and applications in energy markets.
Abstract:聽This talk focuses on pricing insurance contracts with the distortion premium under model ambiguity. In most of the cases real distributions of a random losses are unknown and premiums are calculated using the best models we have, called baseline models. For the calculation of a robust premium, we calculate the distortion premium over a set of distributions, called ambiguity sets. In this talk we define them as balls around the baseline model where the radii are measured with the Wasserstein distance. Exact values of the robust distortion premium are calculated and worst case solutions are found under some assumptions, when this is not possible approximations of the worst case solution are presented. In addition, we propose a procedure for the identification of the distortion premium from observed prices. We use this methodology in the framework of futures in energy markets. Given that electricity is a non-storable commodity, futures in this market do not have a clear valuation. We assume these prices are calculated following the distortion premium. More precisely, we also add a shift parameter and ambiguity premium for model misspecifications, i.e., futures here are priced with robust shifted distortion premiums. Distortion densities together with the shift parameters and ambiguity radii are successfully recovered. From these results we can interpret the positions of different participants in the market as well as the dynamics of the risk premia in this market.