Continuous Monitoring Does Credit Risk Vanish?

We present a model for pricing credit risk protection for a limited liability non-life insurance company. The protection is typically provided by a guarantee fund. In the case of continuous monitoring, i.e., where the market values of the company's assets and liabilities are continuously observable, and where the market values of assests and liabilities follow continuous processes, regulators can liquidate the insurance company at the instant the market value of its assets equals the market liability of its liabilities, implying that the credit protection is worthless. When jumps are included in the claims process, the protection provided by the guarantee fund has a strictly positive market value. The ability to continuously monitor asset prices with continuous sample paths eliminates economic losses from default. Our analysis suggests that economic losses from default stem from jumps in continuously observed asset prices and/or that asset prices are not continuously observed.

Keywords: Credit risk for non-life insurers, guarantee fund, continuous monitoring, barrier options.