【论文精读】Bridging socioeconomic pathways of CO2 emission and credit risk

1 Introduction

The context of CO2 emission scenario.

Unless采取积极措施减少这些CO₂和其他温室气体（GHG）排放，在未来两个世纪内全球气温预计将继续上升3至4摄氏度（甚至更多）。如果不采取相应的减排和适应措施，则当前正在发生的全球变暖将对环境、地理分布和经济结构产生深远影响。在第21届联合国气候变化大会上通过的巴黎协定成为一项具有里程碑意义的国际气候政策——它建立了到2030年实现碳中和的主要框架，并为全球气温稳定在1.5摄氏度以下奠定了基础。这种理想化的情形建立在到2050年碳中和的目标之上，并根据各国的具体情况而有所不同。实际上存在许多其他的可能性——这些可能性取决于国家按照各自的《国家自主贡献方案》（NDC）所选择的发展路径（ecological transition trajectory）。最近的科学文献中将这些情景称为“共享社会经济 pathways”（SSPs）。

Refer to Figure 1 for a comprehensive analysis of global carbon dioxide emissions across various industrial and service sectors within the Organization for Economic Co-operation and Development (OECD). Based on selected scenarios, the relevant data can be accessed through the SSP Public Database at https://tntcat.iiasa.ac.at/SspDb.

Climate risks in finance

Climate change creates additional risk sources, referred to as climate risks, particularly notable physical and transitional risks as outlined in the significant resounding speech by Mark Carney.

This study primarily addresses transition risks and seeks to incorporate scenario projections from CMIP6 Phase 6 into credit risk assessments for firms. The research endeavors to develop a quantitative framework that examines how various production scenarios influenced by CO2 emission pathways can affect corporate credit risk. Specifically, this framework employs input variables such as targeted CO2 emission trajectories ((et)t_0), company-specific operational characteristics, sensitivity to climate-related factors, and hypothetical climate-neutral credit spreads. The model's outputs include probabilistic estimates of how these factors will influence corporate credit spreads under conditions of uncertain economic demand.

We examine a company striving to maximize its production profit while also accounting for the CO2 reduction plans outlined by SSPs. Exceeding emissions beyond the target could result in penalties. From the firm’s perspective, their goal is to identify an optimal strategy for achieving effective emissions by solving a penalized optimization problem. Such carbon emission transitions can influence a firm’s credit quality through its cash flow dynamics. In models like Merton or Black-Cox within structural credit approaches, default occurs when a company’s value falls below its debt obligations.

The optimal production problem, aimed at maximizing a company's expected profit, has been extensively studied. We assume that a firm's production is influenced by its energy consumption, particularly concerning its carbon emission level. Additionally, we examine overemission penalties under specific probabilistic risk measures, where a loss function is considered. Subsequently, following classic structural models in credit risk theory, we calculate the climate-related default probability of the firm and demonstrate through numerical examples how different relevant parameters and SSP scenarios affect default probabilities and intensities.

2 Model and results

2.1 Production and carbon emission constraint

a probability space ( Ω _,_A,P)

This firm's production level, denoted as P(t) , is determined by its energy consumption and is particularly influenced by its effective CO2-emission volume, \gamma(t) . The firm aims to solve the subsequent stochastic differential equation (SDE).

where γt denotes the current emission rate at time t, fractional Brownian motion Wt, which models uncertainty arising from fluctuating demand and supply dynamics in production processes, along with a positive constant volatility parameter σ. The parameter μ defines the baseline production rate and must meet stringent requirements of a Lipschitz condition with respect to variable x, ensuring stability through an independent positive constant K.

Empirical research indicates that overproduction often results in a decline in production efficiency, as evidenced by an oversupply situation. Meanwhile, while the impact of emissions on production growth is positive. Therefore, we posit that μ decreases as production P increases and rises as emission γ grows.

In reaction to their commitment towards reducing greenhouse gases, this company has implemented a structured approach denoted as e(t) = e_t; t ≥ 0, which signifies either a set value (if deterministic) or a range (if stochastic), ensuring compliance with regulatory standards.

This paper addresses effective emissions, which are generally assumed to be positive. However, in contexts such as carbon sequestration or within the European Emission Trading System (ETS), where emission allowance compensation is involved, specific statistical parameters known as standardised scenario projections (SSPs) could result in negative values, as illustrated in Figure 1 Energy sector. The implication is that the objective emission et could potentially become negative, necessitating its consideration as net emissions once all processes related to compensation and carbon capture are accounted for.

Loss function

The firm aims to achieve increased profitability while effectively controlling emissions by accounting for the constraints outlined in the advertisement.

Under a baseline emission projection, the company determines its optimal effective emissions to maximize expected profits while managing production, cost, and emission constraints. The mathematical optimization problem is formulated below: We consider profit maximization over all future times under pathwise emission constraints as an optimization problem with an objective function.

where r > 0 is a constant2discount rate. We aim to solve

2.2 Optimal emission strategy

Profit maximization in an explicit model

2.3 Credit risk under emission transition

In this section, we investigate the credit risk of a firm resulting from its shift to a low-carbon emission and production pattern. By deriving effective production levels established in our earlier optimization problem, we establish a firm value process and subsequently calculate its default probability through structural modeling.

Structural credit model and default probability

Within the framework of a structural credit model, this firm is deemed to have defaulted when its asset value falls below a specified threshold.

We define the default barrier as being governed by a deterministic function L(t), where its value evolves over time to represent the minimum level of liability payments required for debt repayment, labor costs, operational expenses (OPEX), and capital expenditure (CAPEX) at any given time t. Should a company's value exceed this threshold, it will find itself in a financially sustainable position capable of operating normally. In contrast, if a company faces financial difficulties below this threshold, it may encounter fiscal challenges leading to potential default events that could arise from such circumstances.

3 Numerical illustrations

3.1 SSPs scenarios and optimal emission

We focus on several CO₂ emission scenarios that align with different socioeconomic reference pathways offered by CMIP6: including SSP1-2.6, SSP2-4.5, SSP3-LowNTCF, SSP4-6.0, and SSP5-3.4-OS. These scenarios represent illustrative pathways outlined by the IPCC in their sixth Assessment Report, which depict atmospheric CO₂ concentrations ranging from the lowest (SSP1) to the highest (SSP5).

In other words, SSP1 and SSP5 describe respectively economic growth pattern via sustainable and fossil-fuel pathways. We choose two sectors: Transportation (Figure 2 ) and Industrial (Figure 3 ) sectors for which the year 2015 is our starting point. For each sector, we consider the above five SSPs including two baseline scenarios: SSP1-2.6 which is the most mitigated scenario corresponding approximately to the previous scenario generation Representative Concentration Pathway (RCP) 2.6, and SSP2-4.5 with is a moderate scenario similar to RCP-4.5. We also consider three (Tier 2) supplementary scenarios: SSP3-LowNTCF (Near-Term Climate Forcing) which provides a comparison scenarios with high NTCF emissions (notably SOx and methane), SSP4-6.0 focusing on a socio-economic context of inequality, and SSP5-34-OS (OverShoot) which allows for large overshoot by mid-century followed by substantive policy tools in the latter half of the century.

3.2 Default probability for different sectors

In this study, we examine the emission-related default probability within an explicit framework and evaluate carbon emission reductions under various SSP benchmarks. We adopt an explicit framework as outlined in Proposition 1 and employ an alternative formulation for constructing the value process linked to optimal outcomes.

As expected the initial value of the intensity coincides with the prefixed value λ 0=3%. When time evolves, the more constrained scenarios are associated to larger default probabilities and higher intensities. The SSP1-2.6 scenario is the most impacted one, which is quite natural given its immediate and hard reduction strategy. The scenario which follows is SSP5-3.4-OS: although this benchmark allows for a large overshoot up to 2060, the relatively strict mitigation during the latter period makes the default probability and intensity increase significantly. Observe that SSP4-6.0 corresponds to a fixed intensity of λ 0=3% in the Transportation sector and the same phenomenon appears for the SSP3-LowNTCF scenario in the Industrial sector, as the optimal emission is unconstrained in these two cases. We note that in this study we only investigate the transition risk related to the firm’s mitigation strategy and ignore the possible physical risks under each scenario for example the more frequent damage and natural catastrophes under scenarios with higher temperature increase such as a SSP5 scenario.

Figure 7 demonstrates the baseline intensity for the Industrial sector under the influence of parameter c, which quantifies the firm's reliance on CO2 emissions, and ω, representing the penalty strength. The analysis focuses on two extreme scenarios: SSP1-2.6, which denotes stringent policy measures, and SSP4-6.0, a more moderate approach. For both scenarios, an increase in either parameter leads to a rise in baseline intensity. Notably, when c is large, indicating high dependence on emissions, this increase is particularly pronounced in cases of severe mitigation efforts such as SSP1-2.6 (left panel). A combination of strong penalty policies with stringent mitigation strategies significantly impacts the likelihood of default for firms with high CO2 emission dependency.