[Paper Review] Decarbonization of financial markets: a mean-field game approach

P. Lavigne, Peter Tankov|arXiv (Cornell University)|Jan 22, 2023

Climate Change Policy and EconomicsEconomics, Econometrics and Finance3 citations

TL;DR

This paper models the decarbonization of large financial markets using a mean-field game framework, where firms optimize emission strategies under climate transition risk while interacting through a stochastic discount factor determined by investor portfolios. It shows that uncertainty about climate policies increases emissions and share price spreads, but green-minded investors reverse this effect by lowering emissions and narrowing price differentials.

ABSTRACT

We develop a financial market model in which a large population of firms chooses dynamic emission strategies under climate transition risk, interacting with both environmentally concerned and neutral investors. Firms face a trade-off between financial returns and environmental performance, while their decisions are coupled through an equilibrium stochastic discount factor determined by investors' portfolio allocations. The framework is formulated as a mean-field game, for which we establish existence and uniqueness of a Nash equilibrium among firms. We propose a convergent numerical scheme to compute the equilibrium and use it to study how climate transition risk and green-minded investors affect decarbonization dynamics and asset prices. Our results show that uncertainty about future climate risks and policies increases aggregate emissions and widens valuation spreads between green and brown firms. Although environmentally concerned investors can partially offset these effects by raising the cost of capital for high-emission firms and incentivizing emission reductions, policy uncertainty weakens their impact. Even a large share of green-minded investors is insufficient to reverse emission growth when future climate policies are unclear, highlighting the crucial role of credible and predictable climate policy in enabling financial markets to support decarbonization.

Motivation & Objective

• To model the dynamic decarbonization of large financial markets as a stochastic game involving firms and investors under climate transition risk.
• To analyze how uncertainty in climate policies and the presence of green-minded investors affect corporate emission strategies and asset pricing.
• To establish a theoretical and computational framework for equilibrium dynamics in large markets with heterogeneous investor preferences and stochastic emission schedules.
• To quantify the impact of environmental concern and policy uncertainty on aggregate emissions and share price differentials between green and brown firms.

Proposed method

• Formalizes the market as a mean-field game with a continuum of small, identical firms and two classes of large investors (regular and green-minded), using symmetric interactions and common noise.
• Models firms' emission decisions as stochastic control problems optimizing a trade-off between financial performance (share value) and environmental penalties (carbon costs) with a stochastic carbon penalty reflecting climate risk uncertainty.
• Derives the equilibrium stochastic discount factor from investor portfolios, which depends only on common noise and the mean-field, consistent with classical asset pricing theory.
• Proves existence and uniqueness of a Nash equilibrium in the mean-field limit using rigorous mean-field game theory, enabling analytical and numerical tractability.
• Develops a convergent numerical algorithm to compute the equilibrium, allowing simulation of market dynamics under various climate risk and investor composition scenarios.
• Employs Monte Carlo simulations to estimate the distribution of aggregate emissions and share prices, with sensitivity analysis on key parameters like climate risk (γ), green investor concern (λ), and proportion (ρ).

Experimental results

Research questions

• RQ1 How does uncertainty about future climate policies affect the equilibrium emission levels and share prices of firms in a large financial market?
• RQ2 What is the impact of green-minded investors on the decarbonization dynamics of firms and the relative pricing of green versus brown assets?
• RQ3 How does the stochastic nature of carbon penalties influence firms' optimal emission strategies and market-wide decarbonization outcomes?
• RQ4 To what extent do the presence and environmental stringency of green investors reduce aggregate emissions and narrow the price spread between green and brown firms?
• RQ5 How do changes in climate risk (γ), green investor concern (λ), and the proportion of green investors (ρ) affect the sensitivity of firm share prices to emission efficiency?

Key findings

• Higher uncertainty about climate policies (increased γ) leads to higher aggregate emissions and wider spreads between share prices of green and brown companies, even in the absence of green investors.
• The sensitivity of share prices to emission efficiency (P2) increases with climate risk (γ), as carbon-efficient firms become more valuable relative to carbon-intensive ones under uncertainty.
• Green-minded investors reduce emissions: increasing the environmental concern parameter λ leads to a 15%–20% reduction in average emissions compared to a market without green investors.
• The proportion of green investors (ρ) has a strong dampening effect on emission levels; increasing ρ from 0 to 1.0 reduces average emissions and lowers the price sensitivity to emission efficacy (P2) by approximately 5%–10%.
• The price sensitivity to firm value (P1) remains relatively stable across scenarios, indicating that firm fundamentals are less affected by climate risk and green investor presence than emission efficiency.
• The model predicts that in markets with high green investor participation, all firms emit less, pay lower dividends, and have lower share prices, but the relative advantage of green firms increases due to lower climate risk exposure.