Impact of the carbon price on credit portfolio's loss with stochastic collateral
构建了一个端到端模型框架，评估气候转型下银行抵押贷款组合的风险指标，推导了碳价格和建筑能效等参数对违约损失率、预期和非预期损失的影响。
The aim of this work is to propose an end-by-end modeling framework to evaluate the risk measures of a bank's portfolio of collateralized loans in an economy subject to the climate transition. The economy, organized in sectors, is driven by a multidimensional Ornstein–Uhlenbeck (OU) productivity process, while the climate transition is declined thanks to continuous deterministic carbon price and intensity processes. Thus we derive the dynamics of macroeconomic variables for each climate transition scenario. By considering that a firm defaults if it is over-indebted, we define each loan's loss at default as the difference between exposure at default (EAD) and the liquidated collateral, which will help us to define the loss given default (LGD), the expected, and unexpected losses (EL/UL). We consider two types of collateral. First, if it is a financial asset (invoices, cash, or investments), we model the latter using the continuous-time version of the discounted cash flow methodology, where cash flow growth is driven by instantaneous output growth, instantaneous growth of a carbon price function, and an arithmetic Brownian motion. Second, for physical asset (real estate, business equipment, or inventory), we focus on the example of a property in the housing market. As in Sopgoui [Modeling the impact of Climate transition on real estate prices. arXiv preprint arXiv:2408.02339, 2024.], a building price is the difference between the price of an equivalent efficient building following an exponential OU as well as the actualized renovation costs and the actualized future energy costs due to the inefficiency of the building, optimally determined by the carbon price process. Finally, we obtain expressions for risk measures (LGD, EL, and UL) of a portfolio of collateralized loans as a function of key climate transition parameters, such as carbon pricing and energy efficiency of buildings. Banks will use these risk measures, depending on climate transition scenarios, to define operating expenses, client fees, economic, and regulatory capital.