Capital Allocation for Insurance Companies

This study shows how option pricing methods can be used to allocate re- quired capital (surplus) across lines of insurance. The capital allocations depend on the uncertainty about each line‘s losses and also on correlations with other lines‘ losses and with asset returns. The allocations depend on the marginal contribution of each line to default value-that is, to the present value of the insurance company‘s option to default. The authors show that marginal default values add up to the total default value for the company, so that the capital allocations are unique and not arbitrary. They therefore disagree with prior literature arguing that capital should not be allocated to lines of business or should be allocated uniformly. The study presents sev- eral examples based on standard option pricing methods. However, the "adding up" result justifying unique capital allocations holds for any joint probability distribution of losses and asset returns. The study concludes with implications for insurance pricing and regulation.