We propose a modular decomposition of energy price dynamics, based on the observation that the apparent complexity of energy markets arises from the aggregation of structurally distinct phenomena rather than from intrinsic model complexity. Mean reversion, heavy-tailed innovations, and volatility clustering originate from different economic mechanisms and act on distinct dimensions of the stochastic process; each admits a separate, minimal treatment. We formalise this decomposition as a two-stage, distribution-free framework for Monte Carlo simulation of energy prices, in which each stage addresses one structural layer of the process. In Stage I, the mean-reversion speed is estimated from the observed price path using a Temporal Convolutional Network. The estimator exploits the spectral invariance of the AR(1) autocorrelation function, ensuring robustness to heavy tails and volatility clustering. In Stage II, the innovation process is characterised through three dedicated sub-components. (IIa) A compact Gated Recurrent Unit-based Conditional Flow Matching model generates bulk innovations non-parametrically; this is the minimal default within a modular family of admissible bulk generators (e.g. asymmetric normalizing flows or skew parametric models). (IIb) A Generalised Pareto Distribution overlay handles extreme tail events, justified as the universal limiting distribution for threshold exceedances by the Pickands–Balkema–de Haan theorem. (IIc) A Gaussian AR(1) copula introduces volatility clustering without altering the marginal distribution, in full accordance with Sklar’s theorem; this copula is the minimal default within a modular family of admissible temporal-dependence components (e.g. ARFIMA-driven or regime-switching specifications), with its persistence parameter calibrated directly from the empirical autocorrelation of squared innovations. Applied to PJM West Hub electricity, Henry Hub natural gas, and WTI crude oil over 2016–2025, the empirical distributional and temporal statistics of all three markets fall within the inter-path bands of the simulated paths on the four primary metrics considered. Robust diagnostics complement the validation: they highlight the rare-event sensitivity of higher-order moments as a structural caveat of the validation strategy, and identify long-memory volatility and pronounced bulk asymmetry as cases where the default AR(1) and the default GRU-CFM Mini, respectively, would naturally be replaced by richer admissible specifications. An out-of-sample analysis further confirms that the framework is broadly well calibrated at the unconditional, long-run scale at which its parameters are estimated.

A distribution-free framework for energy price modelling via modular decomposition

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发表日期：

2026年7月13日

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Carlo Mari,
Emiliano Mari

摘要

We propose a modular decomposition of energy price dynamics, based on the observation that the apparent complexity of energy markets arises from the aggregation of structurally distinct phenomena rather than from intrinsic model complexity. Mean reversion, heavy-tailed innovations, and volatility clustering originate from different economic mechanisms and act on distinct dimensions of the stochastic process; each admits a separate, minimal treatment. We formalise this decomposition as a two-stage, distribution-free framework for Monte Carlo simulation of energy prices, in which each stage addresses one structural layer of the process. In Stage I, the mean-reversion speed is estimated from the observed price path using a Temporal Convolutional Network. The estimator exploits the spectral invariance of the AR(1) autocorrelation function, ensuring robustness to heavy tails and volatility clustering. In Stage II, the innovation process is characterised through three dedicated sub-components. (IIa) A compact Gated Recurrent Unit-based Conditional Flow Matching model generates bulk innovations non-parametrically; this is the minimal default within a modular family of admissible bulk generators (e.g. asymmetric normalizing flows or skew parametric models). (IIb) A Generalised Pareto Distribution overlay handles extreme tail events, justified as the universal limiting distribution for threshold exceedances by the Pickands–Balkema–de Haan theorem. (IIc) A Gaussian AR(1) copula introduces volatility clustering without altering the marginal distribution, in full accordance with Sklar’s theorem; this copula is the minimal default within a modular family of admissible temporal-dependence components (e.g. ARFIMA-driven or regime-switching specifications), with its persistence parameter calibrated directly from the empirical autocorrelation of squared innovations. Applied to PJM West Hub electricity, Henry Hub natural gas, and WTI crude oil over 2016–2025, the empirical distributional and temporal statistics of all three markets fall within the inter-path bands of the simulated paths on the four primary metrics considered. Robust diagnostics complement the validation: they highlight the rare-event sensitivity of higher-order moments as a structural caveat of the validation strategy, and identify long-memory volatility and pronounced bulk asymmetry as cases where the default AR(1) and the default GRU-CFM Mini, respectively, would naturally be replaced by richer admissible specifications. An out-of-sample analysis further confirms that the framework is broadly well calibrated at the unconditional, long-run scale at which its parameters are estimated.