Modeling Electricity Prices with Stochastic Langevin Equations

Abstract In this paper, we present an arithmetic electricity spot price model based on generalized Langevin equations. In this setup, we investigate electricity forward pricing under future information modeled by initially enlarged filtrations. Hence, our model not only accounts for memory effects via the involved retarded Langevin equations, but also incorporates forward-looking information on future price behavior via the appearing enlarged filtrations. We also treat the pricing of options written on anticipative electricity forwards. We finally derive the optimal mean variance hedging portfolio for an electricity market insider having knowledge of future price behavior.