Pricing Energy Derivatives in Markets Driven by Tempered Stable and CGMY Processes of Ornstein–Uhlenbeck Type

Abstract

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 nonarbitrage conditions such that the spot dynamics is consistent with the forward curve. Moreover, 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 pricing different contracts, namely strips of daily call options, Asian options with European style and swing options.

Keywords

• Lévy-driven Ornstein–Uhlenbeck processes
• CGMY process
• tempered stable distributions
• exact simulation
• energy markets
• derivative pricing