An Excursion-Theoretic Approach to Regulator's Bank Reorganization Problem

The importance of the global financial system cannot be exaggerated. When a large financial institution becomes problematic and is bailed out, that bank is often claimed as “too big to fail”. On the other hand, to prevent bank’s failure, regulatory authorities adopt the Prompt Corrective Action (PCA) against a bank that violates certain criteria, often measured by its leverage ratio. In this article, we provide a framework where one can analyze the cost and effect of PCA’s. We model a large bank that has deteriorating assets and regulatory actions attempting to prevent the bank’s failure. The model uses the excursion theory of Lévy processes and finds an optimal leverage ratio that triggers a PCA. A nice feature includes that it incorporates the fact that social cost associated with PCA’s are greatly affected by the size of banks subject to PCA’s. In other words, one can see the cost of rescuing a bank which is “too big to fail”.