Academic journal article Journal of Risk and Insurance

Pricing and Capital Allocation for Multiline Insurance Firms

Academic journal article Journal of Risk and Insurance

Pricing and Capital Allocation for Multiline Insurance Firms

Article excerpt


We study multiline insurance companies with limited liability. Insurance premiums are determined by no-arbitrage principles. The results are developed under the realistic assumption that the losses created by insurer default are allocated among policyholders following an ex post, pro rata, sharing rule. In general, the ratio of default costs to expected claims, and thus the ratio of premiums to expected claims, vary across insurance lines. Moreover, capital and related costs are allocated across lines in proportion to each line's share of a digital default option on the insurer. Our results expand and generalize those derived elsewhere in the literature.


In a friction-free setting, an insurance company covering multiple insurance lines can hold sufficient capital to guarantee payments of all claims since there is no lost opportunity cost to holding additional capital. In practice, however, limited liability and limited capital imply that insurers may fail to make the required payments to policyholders. Thus, in practice policyholders face a counterparty risk, leading to the following questions: For an insurance company offering insurance in multiple insurance lines under the assumptions of limited liability and limited capital, what will be the price structure across lines and how should the firm allocate its capital and associated costs between these lines?

The main contribution of this article is to introduce a parsimonious model to answer these questions. Our results extend the analyses in earlier articles (e.g., Phillips, Cummins, and Allen, 1998; Myers and Read, 2001), but our results are quite different from theirs. The main source of the difference is that we assume that in the case of insurer default, the insurer's available assets are distributed to the policyholders following what we call the ex post pro rata rule. Under this rule, the available assets are allocated to policyholder claims based on each claimant's share of the total claims. This rule has sensible properties and generally reflects the actual practice, as discussed below.

The risk of default by insurance firms has recently been highlighted by the precarious position of the so-called "monoline" bond and mortgage security insurers as a result of the subprime mortgage crisis. These insurers are monoline in that insurance laws prohibit them from offering various consumer lines such as homeowner and auto insurance. (1) The insurers are "multiline," however, in the sense that they provide coverage against the default risk of a wide range of debt issues, including individual mortgages, securitizations such as mortgage-backed securities and collateralized debt obligations, and debt issued by entities such as state and local governments. Given the potentially high default rates on these debt issues and the limited capital of the insurers, it is quite possible that these insurers will be unable to pay all of the claims they face.

A similar issue of insurer default risk arises with investment banks that function as the counterparties on derivative securities for a wide range of underlying instruments, including foreign exchange, interest rate swaps and options, and credit default swaps. Our results for pricing and capital allocations can be interpreted as applying to such security insurers and derivative counterparties, as well as more traditional insurance firms.

Most of our analysis can be carried out and understood under the simplifying assumption that there is no (excess) cost associated with holding capital within the firm. This is in the same spirit as Phillips, Cummins, and Allen (1998). In practice, costs of internal capital appear to be important. For example, Froot, Scharsfstein, and Stein (1993) emphasize the importance of capital market imperfections for understanding a variety of corporate risk management decisions: the tax disadvantages to holding capital within a firm is an especially common and important factor. …

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