Modeling EUA price dynamics: A multistage PDE framework with Market Stability Reserve mechanisms

This study develops an MSR-adjusted multistage EUA pricing (MMEP) model, a novel pricing framework for analyzing EUA price dynamics under the Market Stability Reserve (MSR) in the EU Emissions Trading System (EU ETS). The model incorporates intertemporal linkages among the Total Number of Allowances in Circulation (TNAC), MSR adjustments, auction volumes, and regulatory interventions across multiple compliance periods. It explicitly considers MSR absorption, release, and cancellation mechanisms, allowing regulatory adjustments to affect continuation values and generate price adjustments at compliance-period boundaries. The analysis evaluates the model against observed EUA market data using annual EEX auction prices and EEX December EUA futures term structures. The empirical validation indicates that the model captures broad annual price and term-structure patterns more closely in the recent Phase IV period than in earlier transition-year observations. The numerical analysis further shows that supply-side assumptions, especially supply volatility and supply-drift assumptions linked to allowance-supply reduction, generate the largest changes in model-implied price paths under the calibrated baseline. By contrast, MSR intake rates and threshold levels have more state-dependent effects, becoming most relevant when TNAC approaches the relevant trigger regions. The MMEP framework therefore provides a structured annual pricing and scenario-analysis tool for evaluating MSR design, allowance-supply adjustments, and the policy trade-offs associated with EU ETS market stabilization.