Pricing in Incomplete Markets

Abstract

For life insurance companies and pension funds, it is always the case in practice that not all of the risks in their books can be hedged. Hence, the standard Black-Scholes methodology cannot be applied in this situation. This paper discusses and compares several methods that have been proposed in the literature in recent years: the Cost-of-Capital method (the current insurance-industry standard), Good Deal Bound pricing, and pricing under Model Ambiguity. Although each of these methods has a very different economic starting point, we show that all three converge for small time-steps to the same limit. This convergence provides a basis for comparing the different parameters used by the three methods. From this comparison we conclude that the current cost-of-capital of 6% used by the industry and the European insurance supervisor (EIOPA) is too low, since it is not in line with the values implied by the Good Deal Bound and Model Ambiguity methods. A cost-of-capital of 12% is needed to bring the method in line with the other two methods.

Keywords: incomplete market, cost-of-capital, good deal bound, model ambiguity

JEL Classification: D81, G12, G22, G23