Concepts from Mathematical Finance for Assessing and Achieving Intergenerationally Equitable Climate Mitigation: Implied CO2-Price, Carbon Interest Rate, Fair Share of GDP, and the Extension of an Integrated Assessment Model with a Climate Transformation Fund

This paper applies concepts from mathematical finance to the analysis of climate change mitigation costs and policy design. We define three metrics: an implied CO2-price based on the total discounted cost of abatement and damages; a carbon interest rate, representing the internal rate of return of abatement actions; and a fair share of GDP to support effort-based climate funding. These metrics provide ex post evaluations of optimal emission pathways in integrated assessment models (IAMs), offering a descriptive framework for understanding the cost structure of climate policy. In addition, we extend an integrated assessment model by incorporating a climate transformation fund, funded by a fixed GDP share, a CO2-price, or a mix) and that finances climate-related costs over time. This extension improves intergenerational equity. We consider the general case of a stochastic model. Our numerical experiments on a classical (deterministic) DICE model show that the implied CO2-price is a factor of 10 larger than the classical social cost of carbon (a marginal price) and that the implied share of GDP is roughly 3 %. However, the model exhibits substantial intergenerational inequality. Introducing a climate transformation fund, our numerical result shows that roughly 2.4 % of the GDP is sufficient to cover all climate mitigation costs (including abatement and damage cost), equally distributing the burden among all generations. This intergenerational equitable climate change mitigation results in only a modest reduction of the GDP or consumption (significantly smaller than the funding rate). Analysing a stochastic extension of a DICE model, we see that the presence of a climate transformation fund significantly reduces the convexity and volatility of the cost structure.