Impact of Counterparty Risk on the Reinsurance Market

Abstract

We investigate the impact of counterparty risk on contract design in the reinsurance market. We study a multiplicative default risk model, with partial recovery and where the probability of the reinsurer's default depends on the loss incurred by the insurer. The seller is assumed to be risk-neutral while the buyer is risk-averse and uses either expected utility or conditional tail expectation risk criteria. We show that generally the buyer wishes to over-insure above a deductible level and that many of the standard comparative statics cease to hold. We also derive the properties of stop-loss insurance in our model and consider the possibility of divergent beliefs about the default probability. Classical results are recovered when default risk is loss-independent, or there is zero recovery rate. Results are illustrated with numerical examples.

Keywords: Optimal Insurance Design, Multiplicative background risk, Counterparty risk, Reinsurance market, Stop-loss Insurance

JEL Classification: G22, D81, D82