Precautionary Measures for Credit Risk Management in Jump Models

TL;DR

This paper models optimal capital raising timing for banks under jump risk using Levy processes, balancing delay costs and regulatory compliance to enhance risk management strategies.

Contribution

It introduces a novel optimal stopping framework for bank capital management incorporating jump processes, providing explicit solutions for specific Levy models.

Findings

Explicit solutions for double exponential jump diffusion

Analysis of capital raising timing under jump risk

Enhanced understanding of default risk modeling

Abstract

Sustaining efficiency and stability by properly controlling the equity to asset ratio is one of the most important and difficult challenges in bank management. Due to unexpected and abrupt decline of asset values, a bank must closely monitor its net worth as well as market conditions, and one of its important concerns is when to raise more capital so as not to violate capital adequacy requirements. In this paper, we model the tradeoff between avoiding costs of delay and premature capital raising, and solve the corresponding optimal stopping problem. In order to model defaults in a bank's loan/credit business portfolios, we represent its net worth by Levy processes, and solve explicitly for the double exponential jump diffusion process and for a general spectrally negative Levy process.