Fast Pricing of Energy Derivatives with Mean-reverting Jump Processes
The law of a mean-reverting (Ornstein-Uhlenbeck) process driven by a compound Poisson with exponential jumps is investigated in the context of the energy derivatives pricing. The said distribution turns out to be related to the self-decomposable gamma laws, and its density and characteristic function are here given in closed-form. Algorithms for the exact simulation of such a process are accordingly derived with the advantage of being significantly faster (at least 30 times) than those available in the literature. They are also extended to more general cases (bilateral exponential jumps, and time-dependent intensity of the Poisson process). These results are finally applied to the pricing of gas storages and swings under jump-diffusion market models, and the apparent computational advantages of the proposed procedures are emphasized