Pricing energy spread options with variance gamma-driven Ornstein-Uhlenbeck dynamics

TL;DR

This paper develops a novel model for pricing energy spread options using variance gamma-driven Ornstein-Uhlenbeck processes, deriving analytical formulas and applying FFT for efficient computation.

Contribution

It introduces a new mean-reverting, infinite activity process model for energy prices and derives an analytical cumulant generating function for pricing.

Findings

Analytical pricing formulas for forwards and spread options

Effective calibration methods for real-world and market data

Numerical results demonstrating model accuracy and efficiency

Abstract

We consider the pricing of energy spread options for spot prices following an exponential Ornstein-Uhlenbeck process driven by a sum of independent multivariate variance gamma processes, which gives rise to mean-reverting, infinite activity price dynamics. Within this class of driving processes, the Esscher transform is used to obtain an equivalent martingale measure with a focus on the weak variance alpha-gamma process. By deriving an analytical formula for the cumulant generating function of the innovation term, we obtain a pricing formula for forwards and apply the FFT method of Hurd and Zhou to price spread options. Lastly, we demonstrate how the model should be both estimated on energy prices under the real world measure and calibrated on forward or call prices, and provide numerical results for the pricing of spread options.