Paper: arXiv 2509.17236

Authors: Thomas K. Kloster

Abstract

This paper considers the often overlooked fact that electricity spot prices in individual European generation zones evolve as a high dimensional panel structure. A general continuous time framework is developed by formulating the panel as an ambit field indexed by a cylinder surface, where the cross sectional dimension is represented by a circle. This requires a treatment of ambit fields on manifolds, but the departure from Euclidean space allows for embedding intrinsic dependence structures into the index set in a flexible and parameter-free way, where the daily delivery periods have a canonical mapping onto the circle. The model is a natural space-time extension of volatility modulated Lévy-driven Volterra processes, which have previously been studied in the context of energy markets, and the pricing of electricity derivatives turns out to be essentially as analytically tractable as in the null-spatial setting. The space-time framework extends the scope of possible derivatives to products written on individual delivery periods, where spreads between these constitute an interesting example. We establish useful formulas for the pricing of various derivatives along with a simulation scheme, and study specifications of the dependence structure in detail.

Complexity vs Empirical Score

  • Math Complexity: 8.5/10
  • Empirical Rigor: 5.0/10
  • Quadrant: Holy Grail — high math complexity, high empirical rigor

Why this score: The paper presents a highly original continuous-time theoretical framework, mapping electricity panel data onto ambit fields on manifolds (a cylinder surface). While it provides strong analytical derivations for derivative pricing, simulation schemes, and a Whittle likelihood estimation exercise, the empirical component serves primarily as an illustrative application rather than a exhaustive multi-dataset backtest.

Research Flowchart

  flowchart TD
    A[Research Goal: Model high-dimensional panel structure of day-ahead electricity prices] --> B[Data & Inputs: European spot prices & daily delivery periods]
    B --> C[Methodology: Map panel to cylinder surface via manifold Ambit Fields]
    C --> D[Model Formulation: Space-time extension of volatility-modulated Lévy-driven Volterra processes]
    D --> E[Computational Processes: Analytical pricing derivation & simulation scheme]
    E --> F[Key Outcomes: Tractable pricing formulas for multi-period derivatives & spread options]