Capital allocation in insurance: Economic capital and the allocation of the default option value

Abstract

The determination and allocation of economic capital is important for pricing, risk management and related insurer financial decision making. This paper considers the allocation of economic capital to lines of business in insurance. We show how to derive closed form results for the complete markets, arbitrage-free allocation of the insurer default option value, also referred to as the insolvency exchange option, to lines of business. We assume that individual lines of business and the surplus ratio are joint log-normal although the method we adopt allows other assumptions. The allocation of the default option value is required for fair pricing in the multi-line insurer. We illustrate some other methods of capital allocation and give numerical examples for the capital allocation of the default option value based on explicit payoffs by line.