Exact Simulation of Variance Gamma-Related OU Processes: Application to the Pricing of Energy Derivatives

Abstract

ABSTRACT In this study we use a three-step procedure that relates the self-decomposability of the stationary law of a generalized Ornstein-Uhlenbeck process to the transition law of such processes. Based on this procedure and the results of Qu, Dassios, and Zhao (2019), we derive the exact simulation, without numerical inversion, of the skeleton of a Variance Gamma and of a symmetric Variance Gamma driven Ornstein-Uhlenbeck process. Extensive numerical experiments are reported to demonstrate the accuracy and efficiency of our algorithms. These results are instrumental to simulate the spot price dynamics in energy markets and to price Asian options and gas storages by Monte Carlo simulations in a framework similar to the one discussed in Cummins, Kiely and Murphy (2017, 2018).