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

We extend the Vasiček 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. ∗Turku School of Economics, Department of Accounting and Finance, FIN-20500 Turku, Finland, e-mail: [email protected] †Turku School of Economics, Department of Accounting and Finance, FIN-20500 Turku, Finland, e-mail: [email protected] ar X iv :1 00 6. 08 63 v1 [ qfi n. R M ] 4 J un 2 01 0