A Loan Portfolio Model Subject to Random Liabilities and Systemic Jump Risk

TL;DR

This paper extends the Vasiček loan portfolio model to include random liabilities and systemic jump risk, analyzing their effects on loss distribution and risk measures like VaR and expected shortfall.

Contribution

It introduces a model incorporating stochastic liabilities and systemic jumps, providing new insights into their impact on portfolio loss distribution and risk assessment.

Findings

Liability risk impact depends on correlation and default intensity.

Systemic jump risk significantly affects loss distribution upper percentiles.

The model offers a more comprehensive risk analysis framework.

Abstract

We extend the Vasi\v{c}ek loan portfolio model to a setting where liabilities fluctuate randomly and asset values may be subject to systemic jump risk. We derive the probability distribution of the percentage loss of a uniform portfolio and analyze its properties. We find that the impact of liability risk is ambiguous and depends on the correlation between the continuous aggregate factor and the asset-liability ratio as well as on the default intensity. We also find that systemic jump risk has a significant impact on the upper percentiles of the loss distribution and, therefore, on both the VaR-measure as well as on the expected shortfall.