Hedging against Black Swans in Day-Ahead Energy Markets
Liviu Aolaritei, Boubacar Bangoura, Saverio Bolognani, Nicolas Lanzetti, Florian Dörfler
TL;DR
This study tackles hedging day-ahead wind nominations against black swan price spikes in energy markets. It introduces an optimal transport-based distributionally robust optimization (OT-DRO) framework that defines a Wasserstein-like ambiguity set around an empirical forecast-driven distribution via a transport cost $c$ and radius $ε$, yielding a convex decision rule for nominations. Using four years of Finnish wind-generation and market data, the authors carefully construct a reference distribution, a bounded uncertainty set, and tail-aware robustness, obtaining a tractable linear program that outperforms forecast-based nominations during extreme events while remaining competitive otherwise. Empirically, OT-DRO reduces large losses and stabilizes profits, with notable gains (≈21–22%) during spike periods like Spring 2020, demonstrating practical value for wind producers facing volatile regulation prices.
Abstract
Renewable generators must commit to day-ahead market bids despite uncertainty in both production and real-time prices. While forecasts provide valuable guidance, rare and unpredictable extreme events (so-called black swans) can cause substantial financial losses. This paper models the nomination problem as an instance of optimal transport-based distributionally robust optimization (OT-DRO), a principled framework that balances risk and performance by accounting not only for the severity of deviations but also for their likelihood. The resulting formulation yields a tractable, data-driven strategy that remains competitive under normal conditions while providing effective protection against extreme price spikes. Using four years of Finnish wind farm and market data, we demonstrate that OT-DRO consistently outperforms forecast-based nominations and significantly mitigates losses during black swan events.