Pricing and Semi-static Hedging of Green Pay-as-produced Power Purchase Agreements

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 L\'evy-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.