Impact of Climate transition on Credit portfolio's loss with stochastic collateral

Abstract: 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 intensities processes. We thus derive the dynamics of macroeconomic variables for each 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). We consider two types of collateral. First, if it is a financial asset (invoices, cash, or investments), we model the later by the continuous time version of the discounted cash flows methodology, where the cash flows growth is driven by the instantaneous output growth, the instantaneous growth of a carbon price function, and an arithmetic Brownian motion. Secondly, for physical asset (real estate, business equipment, or inventory), we focus on the example of a property in housing market. As in (Sopgoui 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 of a portfolio of collateralized loans as a function of key climate transition parameters, such as carbon pricing and building energy efficiency. Banks will use these risk measures , depending on the climate transition scenarios, to define operating expenses, client fees, economic, and regulatory capital.