Normal Tempered Stable Processes and the Pricing of Energy Derivatives

TL;DR

This paper models energy spot prices using normal tempered stable driven Ornstein-Uhlenbeck processes, deriving their properties, establishing no-arbitrage conditions, and developing exact simulation algorithms for pricing various energy derivatives.

Contribution

It introduces a novel modeling framework with closed-form characteristic functions, exact simulation algorithms, and applies these to price multiple energy derivatives.

Findings

Closed-form characteristic function for the process

Efficient exact simulation algorithm developed

Successful application to pricing diverse energy derivatives

Abstract

In this study we consider the pricing of energy derivatives when the evolution of spot prices is modeled with a normal tempered stable driven Ornstein-Uhlenbeck process. Such processes are the generalization of normal inverse Gaussian processes that are widely used in energy finance applications. We first specify their statistical properties calculating their characteristic function 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 without relying on numerical approximations or on numerical integration. Moreover, we conceive an efficient algorithm for the exact generation of the trajectories which gives the possibility to implement Monte Carlo simulations without approximations or bias. We illustrate the applicability of the theoretical findings and the simulation algorithms in the context of the pricing of different contracts, namely, strips of daily call options, Asian options with European style and swing options. Finally, we present an extension to future markets.