Banks, financial institutions, and insurers are required to assess and disclose their exposure to risks that may have a material impact on their performance. This requirement is driven by the regulatory and financial reporting environments. Recently, these risks include climate-related financial risks and the credit portfolios of banks have been identified as being subject to climate-related risks. Existing approaches to incorporate climate risk into portfolio credit risk models includes the Climate Extended Risk Model (CERM). This method adds additional climate factors to the systematic risk component and requires adjustments to factor loadings and correlations to reflect climate variables, which is not straightforward. UNEP FI and BoC-OSFI proposed a combination bottom-up and top-down approach in which climate risk impact is specified at the subsector level (top-down) and this combines with account-level balance sheet projections (bottom-up) for different climate scenarios. Recently, the Bank for International Settlements (BIS) suggested a methodology for incorporating physical climate risk into existing credit risk models by adjusting obligors' correlation with the systematic risk factor.

Banks have devoted significant resources into the development and implementation of their existing or legacy portfolio credit risk (PCR) models. We propose a method to integrate climate risk into legacy credit risk models that i) provides simple modification(s) of legacy PCR models, making implementation straightforward; ii) results in intuitive, interpretable adjustment(s) to existing models, which can be viewed as optimal in a relative-entropic sense; iii) uses the original legacy PCR model parameters (e.g., factor loadings and default correlation) in contrast to other approaches of incorporating climate risk; iv) enables model calibration in an easily-communicated fashion; v) facilitates sensitivity analysis to climate risk factors, allowing for risk attribution; and vi) allows for a wide variety of adjustments.

Our proposed methodology provides a novel and flexible theoretical framework for adjusting existing PCR models for climate risk. At the core of the approach are probability distortion functions: non-linear operators that re-weight the objective probability distribution, a technique widely used in risk management, portfolio optimization, and actuarial science. Distortion functions are applied to the distribution of some components of the account-level model --- either the systematic factor distribution or the credit quality distributions. This allows for tailoring of climate impacts to individuals or subsectors, including a detailed analysis of the climate impact on obligor-level quantities (e.g., probability of default and pairwise correlation of default indicators). It also offers the flexibility to incorporate an additional climate-based segmentation dimension into portfolio credit risk quantification—one that does not necessarily align with the segmentation structure of legacy credit models. The portfolio-level characteristics (e.g., expected loss, economic capital) are determined by aggregation and it is straightforward to measure the climate risk impact on these quantities. Our approach is an alternative to those that introduce climate variables as an additional systematic factor (e.g., CERM) and it includes the UNEP FI/BoC-OSFI and BIS methodologies as special cases. Using the 1-factor threshold model as an example, we explore the distorted models' properties at both the account and portfolio levels and calibrate a distorted model to a set of climate scenarios.

This is joint work with M. Drmac, W. Mnif, and A. Zeldenrijk.