Tractable Simulation and Estimation of Climate-Linked Financial Variables using Extended OU Processes

This paper presents a stochastic modelling framework for climate-sensitive and policy-relevant variables crucial to Australia’s clean energy transition. Traditional Ornstein–Uhlenbeck (OU) processes capture mean-reversion but cannot represent the state-dependent volatility and extreme-event behavior observed in temperature anomalies, carbon prices and energy market indices. To address these limitations, we introduce constant, linear and quadratic diffusion specifications and apply Lamperti transformations to obtain unit-diffusion processes that preserve mean-reversion while enabling stable simulation and efficient estimation. The framework offers a unified and extensible approach for modelling variables across different volatility regimes. Illustrative applications show that the transformed drift terms reproduce nonlinearities and tail-risk features, allowing the model to capture stable climate processes, moderately volatile carbon markets and highly volatile energy indices within a coherent structure. This provides a flexible and numerically robust foundation for analyzing climate–finance interactions under uncertainty. By enabling transparent scenario generation and improved representation of volatility amplification under shocks, the model supports evidence-based planning relevant to Australia’s national priorities, including emissions reduction, energy security and climate risk assessment. The framework directly aligns with SDGFormula: see text7 (Affordable and Clean Energy), SDGFormula: see text9 (Industry, Innovation and Infrastructure) and SDGFormula: see text13 (Climate Action). Future work includes multivariate extensions, regime-switching dynamics, and data-driven calibration to capture complex environmental–financial interactions.