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The Valuation of Multiple Claim Insurance Contracts

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  • Shimko, David C.

Abstract

This paper provides a closed form solution for the value of a multiple claim insurance contract that is subject to a deductible amount and/or an upper limit on claims. The solution is a time integral of European option prices. The model provides three important insights. First, systematic risk in insurance policies is altered in the presence of deductibles and maximum indemnity levels. Second, idiosyncratic risk affects policy valuation and the required rates of return on underwriting portfolios. Finally, contrary to traditional actuarial intuition, changes in the risk-free interest rate may either increase or reduce policy values.

Suggested Citation

  • Shimko, David C., 1992. "The Valuation of Multiple Claim Insurance Contracts," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 27(2), pages 229-246, June.
  • Handle: RePEc:cup:jfinqa:v:27:y:1992:i:02:p:229-246_00
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    Cited by:

    1. Gatzert, Nadine & Schmeiser, Hato, 2008. "The influence of corporate taxes on pricing and capital structure in property-liability insurance," Insurance: Mathematics and Economics, Elsevier, vol. 42(1), pages 50-58, February.
    2. Duan, Jin-Chuan & Yu, Min-Teh, 2005. "Fair insurance guaranty premia in the presence of risk-based capital regulations, stochastic interest rate and catastrophe risk," Journal of Banking & Finance, Elsevier, vol. 29(10), pages 2435-2454, October.
    3. Chao-Liang Chen, 2006. "The portable guarantee to exchange back an old defined benefit for a new defined contribution (DC) pension plan," Applied Economics, Taylor & Francis Journals, vol. 38(6), pages 699-706.
    4. Martin, J. Spencer & Santomero, Anthony M., 1997. "Investment opportunities and corporate demand for lines of credit," Journal of Banking & Finance, Elsevier, vol. 21(10), pages 1331-1350, October.
    5. Shen, Weixi & Xu, Huiping, 2005. "The valuation of unit-linked policies with or without surrender options," Insurance: Mathematics and Economics, Elsevier, vol. 36(1), pages 79-92, February.
    6. Lo, Chien-Ling & Chang, Carolyn W. & Lee, Jin-Ping & Yu, Min-Teh, 2021. "Pricing catastrophe swaps with default risk and stochastic interest rates," Pacific-Basin Finance Journal, Elsevier, vol. 68(C).
    7. Lin, Chung-Gee & Yang, Wei-Ning & Chen, Shu-Chuan, 2014. "Analyses of retirement benefits with options," Economic Modelling, Elsevier, vol. 36(C), pages 130-135.
    8. Chao-Liang Chen, 2005. "The funding for a Defined Benefit (DB) pension plan based on the fair valuation of the plan's insolvency risk," Applied Economics, Taylor & Francis Journals, vol. 37(14), pages 1623-1633.
    9. Geman, Helyette & Yor, Marc, 1997. "Stochastic time changes in catastrophe option pricing," Insurance: Mathematics and Economics, Elsevier, vol. 21(3), pages 185-193, December.
    10. Cynthia Van Hulle & Hans Degryse & Kristien Smedts, 2017. "Risk-sharing benefits and the capital structure of insurance companies," Working Papers Department of Accountancy, Finance and Insurance (AFI), Leuven 571404, KU Leuven, Faculty of Economics and Business (FEB), Department of Accountancy, Finance and Insurance (AFI), Leuven.
    11. J. David Cummins & Hèlyette Geman, 1993. "An Asian Option to the Valuation of Insurance Futures Contracts," Center for Financial Institutions Working Papers 94-03, Wharton School Center for Financial Institutions, University of Pennsylvania.
    12. Lo, Chien-Ling & Lee, Jin-Ping & Yu, Min-Teh, 2013. "Valuation of insurers’ contingent capital with counterparty risk and price endogeneity," Journal of Banking & Finance, Elsevier, vol. 37(12), pages 5025-5035.
    13. Lim, Terence & Lo, Andrew W. & Merton, Robert C. & Scholes, Myron S., 2006. "The Derivatives Sourcebook," Foundations and Trends(R) in Finance, now publishers, vol. 1(5–6), pages 365-572, April.

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