An Ambit Field Framework for the Full Panel of Day-ahead Electricity Prices

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.

💡 Research Summary

The paper tackles a fundamental yet often ignored feature of European electricity markets: day‑ahead spot prices are revealed simultaneously for a large number of delivery periods (hourly, half‑hourly, or quarter‑hourly), forming a high‑dimensional panel. Traditional modelling approaches either collapse this panel to an average price or treat each delivery period as an independent univariate time series, leading to either loss of information or an explosion of parameters.

To overcome these limitations the authors introduce a continuous‑time random field framework based on ambit fields defined on a cylindrical surface. The time axis (t) runs along the cylinder’s axis while the cross‑sectional dimension (delivery period) is mapped onto a circle parameterised by an angle (\theta). For each pair ((t,h)) (where (h) denotes the delivery period) an ambit set (A_t(h)) is defined as a truncated cylinder surface that contains all past times (s\le t) and the whole circle. This geometric construction automatically embeds two stylised facts observed in the data: (i) strong correlation between adjacent periods (adjacency) and (ii) a “cyclicality” linking the last period of day (t) with the first period of day (t+1). The distance on the circle provides a parameter‑free notion of proximity between periods, reflecting the actual chronological closeness of the underlying physical market.

The spot price field is modelled as
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