Cointegrating Jumps: an Application to Energy Facilities

TL;DR

This paper introduces a model for dependent jump processes in energy markets, leveraging self-decomposability to capture cointegration among jumps, and provides closed-form solutions for spread option pricing.

Contribution

It develops a novel approach using self-decomposable random variables to model dependent jumps in energy assets, enabling analytical pricing of spread options.

Findings

Model captures dependence among energy asset jumps effectively.

Provides closed-form formulas for spread option prices.

Applicable to both Merton and mean-reverting energy price models.

Abstract

Based on the concept of self-decomposable random variables we discuss the application of a model for a pair of dependent Poisson processes to energy facilities. Due to the resulting structure of the jump events we can see the self-decomposability as a form of cointegration among jumps. In the context of energy facilities, the application of our approach to model power or gas dynamics and to evaluate transportation assets seen as spread options is straightforward. We study the applicability of our methodology first assuming a Merton market model with two underlying assets; in a second step we consider price dynamics driven by an exponential mean-reverting Geometric Ornstein-Uhlenbeck plus compound Poisson that are commonly used in the energy field. In this specific case we propose a price spot dynamics for each underlying that has the advantage of being treatable to find non-arbitrage conditions. In particular we can find close-form formulas for vanilla options so that the price and the Greeks of spread options can be calculated in close form using the Margrabe formula (if the strike is zero) or some other well known approximation.