Topological Conditioning via Natural Visibility Graphs for Monte Carlo Simulation of Power Prices

A locally parametric framework is proposed for Monte Carlo simulation of electricity prices that jointly reproduces the key stylized facts of power markets: mean-reversion, fat tails, asymmetry, and volatility clustering. Following a two-stage pipeline in which mean-reversion is estimated separately from the innovation distribution, the paper focuses on the second stage: simulating the residual innovations via topological conditioning on Natural Visibility Graphs (NVG) built on the observed innovation sequence. At each simulation step, the local structure of the graph is used to identify historically similar market states and to draw the next innovation from a locally fitted distribution. The key methodological contribution is that this topological conditioning mechanism simultaneously determines the local scale, skewness, and tail weight of the innovation distribution — three properties that parametric models such as GARCH must address through separate equations — without any assumption on regime dynamics or transitions. The framework is locally parametric: the number of model parameters grows with the sample size rather than being fixed in advance, and the specific distributional family used as a local working model can be replaced without altering the conditioning mechanism. Applied to two power markets with contrasting distributional characteristics — the Italian Power Exchange (PUN) and PJM West Hub (US) — the framework achieves simultaneous coverage of three distributional statistics (\( \hat\sigma \), \( \hat\gamma, \hat\kappa \)) and the first-order autocorrelation of squared innovations \( \hat\rho_1(\varepsilon_t^2) \) for both markets, with a single neighbourhood size k=10 and no market-specific re-calibration; more generally, k serves as the natural adaptation parameter for markets with substantially different distributional characteristics.