  In this study we consider the pricing of energy derivatives when the
evolution of spot prices follows a tempered stable or a CGMY driven Ornstein-
Uhlenbeck process. To this end, we first calculate the characteristic function
of the transition law of such processes in closed form. This result is
instrumental for the derivation of non-arbitrage conditions such that the spot
dynamics is consistent with the forward curve. Moreover, based on the results
of Cufaro Petroni and Sabino (2020), we also conceive efficient algorithms for
the exact simulation of the skeleton of such processes and propose a novel
procedure when they coincide with compound Poisson processes of
Ornstein-Uhlenbeck type. We illustrate the applicability of the theoretical
findings and the simulation algorithms in the context of the pricing different
contracts namely, strips of daily call options, Asian options with European
style and swing options. Finally, we present an extension to future markets.
