🤖 AI Summary
This study addresses the joint risk arising from electricity prices and renewable generation volumes in green pay-as-you-produce power purchase agreements by developing a model-free pricing and semi-static hedging framework. The approach integrates dynamically traded electricity futures with statically held renewable-linked securities to decompose and manage risks associated with price, volume, and their covariance. A novel triple decomposition of the fair strike price is introduced, explicitly capturing the suppressive effect of renewable generation on electricity prices. The framework is implemented using a Lévy-driven bivariate MCARMA state-space model featuring state-dependent price spikes and calibrated to hourly German market data from 2023–2024. Empirical results demonstrate that the method effectively separates deterministic generation profiles from stochastic covariance risk, and that a sparse static hedge portfolio substantially reduces residual risk unaddressed by conventional fixed-volume futures contracts.
📝 Abstract
Pay-as-produced power purchase agreements (PPAs) expose buyers and sellers to the joint risk of power prices and renewable production. This paper develops a theoretical framework for hedging this exposure using a semi-static strategy: liquid futures hedge traded price risk dynamically, while a fixed portfolio of renewable-linked claims targets residual volume and covariance risk. The pricing and hedging decomposition is model-free, whereas the empirical implementation for German wind and solar generation uses a calibrated stochastic model. Conditional on a valuation measure, the fair strike is a production-weighted expected spot price. We show that it decomposes exactly into the baseload forward level, a deterministic production-profile correction, and a stochastic price-volume covariance correction, where the covariance term measures the pricing effect of renewable cannibalisation. The static hedge is selected through a finite-dimensional variance projection onto claims linked to renewable volume, delivery-period average prices, and price-volume covariance. We estimate a Lévy-driven bivariate MCARMA state-space model with state-dependent price spikes using hourly German data for 2023-2024 and apply it to monthly PPAs over the January-December 2025 delivery horizon. The results distinguish deterministic profile risk from stochastic covariance risk and show how sparse static overlays reduce residual exposures that fixed-volume futures cannot hedge. The selected portfolios also indicate which claim types are most effective for hedging residual renewable shape risk.