George H. Zanjani

Pricing and capital allocation in catastrophe insurance

Abstract This paper studies multi-line pricing and capital allocation by insurance companies when solvency matters to consumers, capital is costly to hold, and the average loss is uncertain. In this environment, product quality concerns lead firms to diversify across markets and charge high prices for risk that threatens company solvency, even if the risk is unrelated to other asset risk. Price differences across markets are traced to differences in capital required at the margin to maintain solvency. Finally, the paper shows that capital costs have significant effects on catastrophe insurance markets because of high marginal capital requirements.

Catastrophe Bonds, Reinsurance, and the Optimal Collateralization of Risk Transfer

Catastrophe bonds feature full collateralization of the underlying risk transfer, and thus abandon the insurance principle of economizing on collateral through diversification. We examine the theoretical foundations beneath this paradox, finding that fully collateralized instruments have important uses in a risk transfer market when insurers cannot contract completely over the division of assets in the event of insolvency, and, more generally, cannot write contracts with a full menu of state-contingent payments. In this environment, insureds have different levels of exposure to an insurers default. When contracting constraints limit the insurers ability to smooth out such differences, catastrophe bonds can be used to deliver coverage to those most exposed to default. We demonstrate how catastrophe bonds can improve welfare in this way by mitigating differences in default exposure, which arise with: (1) contractual incompleteness, and (2) heterogeneity among insureds, which undermines the efficiency of the mechanical pro rata division of assets that takes place in the event of insurer insolvency.

Federal Financial Exposure to Natural Catastrophe Risk

The objective of this paper is to estimate the expected annual costs to taxpayers of federal disaster-related expenditures to provide guidance to federal policymakers in budgeting and formulating disaster relief policy. Our estimates take into account recent trends in the generosity of federal disaster policy as well as statistical data on the frequency and severity of losses from natural catastrophes. Our estimates of the costs of disasters are based on two sources: (1) simulation analysis by Applied Insurance Research, a leading catastrophe modeling firm, and (2) historical data on insured catastrophe losses from Property Claims Services, an insurance industry statistical firm. We estimate the average expected federal expenditures for disaster assistance related to hurricanes, earthquakes, thunderstorms, and winter storms to be about

The marginal cost of risk, risk measures, and capital allocation

20 billion a year. In a bad year, corresponding to a catastrophic event of severity expected only once every century, the bill could exceed

Capital Allocation and Its Discontents

100 billion. Given the current approach to disaster relief funding, we project an unfunded liability for disaster assistance over the next 75 years comparable to that of Social Security. The magnitude of the projected liability strongly suggests that government should adopt a proactive, ex ante approach to disaster relief policy rather than the current ad hoc reactive approach.

Financial Pricing of Insurance

Financial institutions use risk measures to calculate the marginal capital cost when expanding the exposure to a certain risk within their portfolio. We reverse this approach by calculating the marginal cost based on economic fundamentals for a profit-maximizing firm and then by identifying the risk measure delivering the correct marginal cost. The resulting measure depends on context. Whereas familiar measures can be recovered in some circumstances, other circumstances yield unfamiliar forms. In all cases, the risk preferences of the institution’s claimants determine how the correct risk measure must weight various default states. Our results demonstrate that risk measures used for pricing and performance measurement should be chosen based on economic fundamentals and may not necessarily adhere to the mathematical properties typically imposed in the literature. This paper was accepted by Jerome B. Detemple, finance .

Bankruptcy in the Core and Periphery of Financial Groups: The Case of the Property-Casualty Insurance Industry

Capital allocation concerns an assignment of the capital of a financial institution to the various sources of risk within the firm. While the procedure is commonly applied within financial institutions for purposes of pricing and performance measurement, its necessity and feasibility are disputed within the academic literature. This chapter clarifies how incomplete markets and frictional costs can create conditions sufficient for capital allocation to play a role either as an input to or a by-product of the pricing process. It then reviews the various approaches to capital allocation, with particular attention paid to the theoretical foundations of the Euler (gradient) approach to capital allocation. Finally, the chapter illustrates the application of the Euler method using various popular risk measures in the context of an example from life insurance.

Mutuality and the Underwriting Cycle: Theory with Evidence from the Pennsylvania Fire Insurance Market, 1873-1909

The financial pricing of insurance refers to the application of asset pricing theory, empirical asset pricing, actuarial science, and mathematical finance to insurance pricing. In this chapter we unify different approaches that assign a value to insurance assets or liabilities in the setting of a securities market. By doing so we present the various approaches in a common framework that allows us to discuss differences and commonalities. The presentation is done as simply as possible while still communicating the important ideas with references pointing the reader to more details.

Market Discipline and Guaranty Funds in Life Insurance

This paper studies the survival outcomes experienced over a 14-year period by a comprehensive sample of group-affiliated U.S. property-casualty insurance companies from 1994. While it is generally assumed that affiliate support enhances the financial strength of a subsidiary within a group, this paper finds that claimants on non-core affiliates (i.e., those with less reinsurance support from and with looser ties to the flagship company) fared better, on average, than claimants on core and flagship subsidiaries.

Egalitarian Equivalent Capital Allocation

This paper studies the connection between risk-sharing and organizational form. It models the organizational form decision as a trade-off between the superior capital market access of the stock form and a regulatory or agency advantage held by the mutual form. When capital is expensive, consumers will substitute away from paying investors to supply risk-bearing capital and toward bearing more risk through mutual companies. The theory is supported with evidence from the Pennsylvania fire insurance market in 1874-1909. During this period, use of the mutual form moved in tandem with the insurance underwriting cycle.