Fast and general simulation of Lévy-driven Ornstein-Uhlenbeck processes for energy derivatives

Lévy-driven Ornstein-Uhlenbeck (OU) processes represent a versatile class of stochastic processes that have garnered interest in the energy sector for their ability to capture typical features of market dynamics. However, in the current state of play, their Monte Carlo simulation is not straightforward for two main reasons: i) algorithms are only available for some specific processes within this class, and ii) they are often computationally expensive. In this paper, we introduce a new simulation technique designed to address both challenges. It relies on the numerical inversion of the characteristic function, offering a general methodology applicable to all Lévy-driven OU processes. Moreover, leveraging FFT, the proposed methodology ensures fast and accurate simulations, providing a solid basis for the widespread adoption of these processes in the energy sector. Lastly, the algorithm allows explicit control of the numerical error. We apply the proposed technique to the pricing of energy derivatives, comparing the results with the existing benchmarks. Our findings indicate that the proposed methodology is at least one order of magnitude faster than the existing algorithms, while maintaining an equivalent level of accuracy.