Mathematical Modeling of Climate Risk in Banking: Optimizing Balance Sheets for a Sustainable Future

Date of Award

6-2025

Degree Name

Doctor of Philosophy

Department

Mathematics

First Advisor

Qiji J. Zhu Ph.D.

Second Advisor

Pedro Judice, Ph.D.

Third Advisor

Jay Treiman, Ph.D.

Fourth Advisor

Yuri Ledyaev, Ph.D.

Keywords

Bank balance sheet, climate risk, financial mathematics

Abstract

In 2020, a study by Pedro Júdice and Jim Zhu titled Bank Balance Sheet Risk Allocation analyzed the relationship between asset-liability structures and the pricing of risk faced by banks, with a focus on interest rate and credit risk. However, despite the growing recognition of climate risk as a major financial threat, existing balance sheet models have largely failed to incorporate it. This dissertation addresses that gap by proposing a linear programming framework that explicitly incorporates climate risk, alongside interest rate and credit risks. The model employs convex duality to derive financial interpretations of the optimality conditions, enhancing its theoretical and practical relevance.

To structure the analysis, we classify optimal solutions based on the number of general assets included, beginning with portfolios of bonds (subject to interest rate and climate risks) and then extending to those that include general assets (subject to all three risk types).

To calibrate the model’s parameters, we use a combination of the Advanced Internal Ratings-Based (IRB) approach and complementary methods, drawing on data from established sources such as Bloomberg and the Federal Reserve Economic Data (FRED). Climate risk is quantified primarily through sectoral carbon footprints, capturing transition risks; the inclusion of physical climate risks remains limited due to challenges in quantifying geographically heterogeneous exposures.

We further propose the potential use of the Extreme Value Theory (EVT) and the Merton Model to estimate rare climate-related credit events, leveraging historical equity data. While these techniques are not fully implemented in this version of the model, they represent promising directions for future research.

Once parameterized, the model is applied to real-world data to generate optimized balance sheet allocations under risk constraints. The results illustrate how banks can more effectively allocate capital under multiple regulatory and environmental stressors.

This research contributes a novel framework for managing balance sheet risk by integrating climate considerations, offering a path forward for banks seeking alignment with sustainability goals while preserving financial soundness.

Access Setting

Dissertation-Abstract Only

Restricted to Campus until

6-1-2027

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