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

Paper: arXiv 2507.11480

Authors: Tim Leung, Kevin W. Lu

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.

Complexity vs Empirical Score

• Math Complexity: 8.5/10
• Empirical Rigor: 7.5/10
• Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper provides a rigorous mathematical framework deriving analytical expressions for multivariate VG-driven Ornstein-Uhlenbeck processes applied to energy spread options. It combines sophisticated probability theory (Esscher transform, dilogarithm expressions) with a solid empirical workflow involving real Australian electricity data and full P/Q joint estimation-calibration methods.

Research Flowchart

  flowchart TD
    A[Goal: Price Energy Spread Options via VG-driven OU Dynamics] --> B[Data: Spot & Forward/Call Prices]
    B --> C[Model & Risk Neutral Measure: Weak Var Alpha-Gamma + Esscher Transform]
    C --> D[Analytical Derivation: CGF of Innovation Term & Forward Prices]
    D --> E[Option Pricing: Apply Hurd & Zhou FFT Method]
    E --> F[Estimation & Calibration: Real-world Fit + Numerical Results]