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

We propose models to quantify the distortion the credit portfolio (expected and unexpected) losses, when the obligor companies as well as their guarantees belong to an economy subject to the climate transition. The economy's productivity is modeled as a multidimensional Ornstein-Uhlenbeck (O.-U.) process while the climate transition is represented by a continuous deterministic carbon price process. 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: financial asset (such as invoices, cash, or investments) or physical asset (such as real estate, business equipment, or inventory). For financial assets, we model them by the continuous time version of the discounted cash flows methodology, where the cash flows SDE is driven by the instantaneous output growth, the instantaneous growth of a carbon price function, and an arithmetic Brownian motion. For physical assets, we focus on property in the housing market. We define, as Sopgoui (2024), their value as the difference between the price of an equivalent efficient building following an exponential O.-U. as well as the actualized renovation costs and the actualized sum of the future additional energy costs due to the inefficiency of the building, before an optimal renovation date which depends on the carbon price process. Finally, we obtain how the loss' risk measures of a credit portfolio are skewed in the context of climate transition through carbon price and/or energy performance of buildings when both the obligors and their guarantees are affected. This work provides a methodology to calculate the (statistics of the) loss of a portfolio of secured loans, starting from a given climate transition scenario described by a carbon price.