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

TL;DR

This paper develops a framework for pricing energy derivatives using Ornstein-Uhlenbeck processes driven by tempered stable and CGMY models, providing closed-form characteristic functions, simulation algorithms, and applications to various energy contracts.

Contribution

It introduces new closed-form characteristic functions and efficient simulation algorithms for tempered stable and CGMY driven Ornstein-Uhlenbeck processes, with applications to energy derivative pricing.

Findings

Closed-form characteristic functions derived

Efficient simulation algorithms developed

Successful application to energy derivatives pricing

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 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.