A fuzzy-and-fair framework for solar irradiance modeling and derivative pricing: Bridging photovoltaic production risk and climate-linked finance

The variability of solar irradiance is a critical source of risk for photovoltaic (PV) producers, directly affecting energy output, project valuation, and financial stability. As solar penetration grows, existing hedging tools that primarily address price risk are insufficient, since they do not protect against the volumetric risk arising from fluctuations in solar production. This paper introduces a novel fuzzy-and-fair modeling framework that simultaneously addresses the physical characterization of solar radiation and its market valuation through derivative pricing. Our approach leverages a bounded transformation and a bimodal representation (clear and cloudy conditions) model calibrated on extraterrestrial horizontal radiation to produce smooth, seasonal, and realistic clear-sky profiles, accounting for daily and inter-annual variability. The innovation lies in directly integrating these irradiance estimates into the fair pricing of solar radiation derivatives, financial instruments designed to hedge volumetric production risk in PV projects. By translating irradiance uncertainty into market-consistent risk premiums, the model enables more robust PV project valuations, providing forward-looking signals for PV plant design, investment appraisal, and energy portfolio management by structuring hedging contracts in incomplete markets where solar radiation is a non-tradable underlying. In this work, we propose a two-step pricing methodology: first, fair values are obtained via replication-based strategies adapted to incomplete markets; second, a fuzzy extension accounts for ambiguity in data quality and heterogeneous expectations, generating bid–ask corridors for solar radiation derivatives. An empirical analysis using data from eight European locations demonstrates the model’s accuracy, flexibility, and applicability across different climatic regimes. The proposed approach offers both methodological innovation in stochastic modeling and practical tools for integrating renewable resource variability into financial decision-making, thereby supporting a more resilient and stable renewable energy transition.