Enhancing Least Squares Monte Carlo with Diffusion Bridges : An Application to Energy Facilities

The aim of this study is to present an efficient and easy framework for the application of the Least Squares Monte Carlo methodology to the pricing of gas or power facilities as detailed in Boogert and de Jong. As mentioned in the seminal paper by Longstaff and Schwartz, the convergence of the Least Squares Monte Carlo depends on the convergence of the optimization combined with the convergence of the pure Monte Carlo method. In the context of the energy facilities, the convergence of the algorithm is more challenging in particular for the computation of sensitivities and optimal dispatched quantities. To our knowledge, an extensive study of the convergence and hence, of the reliability of the algorithm has not been performed yet, in our opinion because of the apparent infeasibility and complexity to use a very high number of simulations. We present then an easy way to simulate random trajectories by means of diffusion bridges similar to the one proposed by Kutt and Welke that is equivalent to generate a time reversal Itō diffusion. Our approach permits to perform a backward dynamic programming strategy based on a huge number of simulations without storing the whole simulated trajectory.Generally, in the valuation of energy facilities one is also interested in the forward recursion. We then design the backward and forward recursions algorithm such that one can produce the same random trajectories by the use of multiple independent random streams without storing at intermediate time steps. Finally, we show the advantages of our methodology for the valuation of virtual hydro power plants and gas storages