Hostname: page-component-586b7cd67f-rdxmf Total loading time: 0 Render date: 2024-11-27T19:46:30.588Z Has data issue: false hasContentIssue false
  • English
  • Français

The Valuation of Multiple Claim Insurance Contracts

Published online by Cambridge University Press:  06 April 2009

David C. Shimko
Get access Rights & Permissions [Opens in a new window]

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.

Type
Research Article
Information
Journal of Financial and Quantitative Analysis , Volume 27 , Issue 2 , June 1992 , pp. 229 - 246
Copyright
Copyright © School of Business Administration, University of Washington 1992

Access options

Get access to the full version of this content by using one of the access options below. (Log in options will check for institutional or personal access. Content may require purchase if you do not have access.)

References

Abramowitz, M., and Stegun, I. A.. Handbook of Mathematical Functions. New York, NY: Dover Publ. Inc. (1972)Google Scholar
Black, F., and Scholes, M.. “The Pricing of Options and Corporate Liabilities.” Journal of Political Economy, 81 (05/06 1973), 637–659.CrossRefGoogle Scholar
Brennan, M., and Schwartz, E.. “Consistent Regulatory Policy under Uncertainty.” Bell Journal of Economics, 13 (Autumn 1982), 506–521.CrossRefGoogle Scholar
Buser, S. “LaPlace Transforms as Present Value Rules: A Note.” Journal of Finance, 41 (03 1986), 243–247.CrossRefGoogle Scholar
Carr, P. P., and Jarrow, R. A.. “The Stop-Loss Start-Gain Paradox and Option Valuation: A New Decomposition into Intrinsic and Time Value.” Review of Financial Studies, 3 (No. 3, 1990), 469–492.CrossRefGoogle Scholar
Carr, P. P.; Jarrow, R. A.; and Myneni, R.. ”Alternative Characterizations of American Put Options.” Working Paper, Cornell Univ., Johnson Graduate School of Management, Ithaca, NY (1990).Google Scholar
Constantinides, G. M. “Market Risk Adjustment in Project Valuation.” Journal of Finance, 33 (05 1978), 603–616.CrossRefGoogle Scholar
Cox, J. C; Ingersoll, J. E.; and Ross, S. A.. “An Intertemporal General Equilibrium Model of Asset Prices.” Econometrica, 53 (03 1985), 363–384.CrossRefGoogle Scholar
Cummins, J. D. “Risk-Based Premiums for Insurance Guaranty Funds.” Journal of Finance, 43 (09 1988), 823–840.Google Scholar
Doherty, N. A., and Garven, J. R.. “Price Regulation in Property-Liability Insurance: A Contingent Claims Approach.” Journal of Finance, 41 (12 1986), 1031–1050.Google Scholar
Friedman, A.Partial Differential Equations of Parabolic Type. Englewood Cliffs, NJ: Prentice-Hall, Inc. (1964).Google Scholar
Goovaerts, M. J.; deVylder, F.; and Haezendonck, J.. Insurance Premiums. Amsterdam: North Holland-Elsevier Science Publ. B. V. (1984), 16–94.Google Scholar
Ingersoll, J. E. Jr, Notes on the Theory of Financial Decisions: Class Lecture Notes (#16). Unpubl. manuscript (1982).Google Scholar
Kraus, A., and Ross, S.. “The Determination of Fair Profits for the Property-Liability Insurance Firm.” Journal of Finance, 37 (09 1982), 1015–1028.Google Scholar
McDonald, R., and Siegel, D.. “Option Pricing when the Underlying Asset Earns a Below Equilibrium Rate of Return: A Note.” Journal of Finance, 39 (03 1984), 261–265.Google Scholar
Merton, R. C. “An Intertemporal Capital Asset Pricing Model.” Econometrica, 41 (09 1973), 867–887.CrossRefGoogle Scholar
Merton, R. C. “Option Pricing when Underlying Stock Returns are Discontinuous.” Journal of Financial Economics, 3 (01–03 1976), 125–144.CrossRefGoogle Scholar
Merton, R. C “An Analytic Derivation of the Cost of Deposit Insurance and Loan Guarantees: An Application of Modern Option Pricing Theory.” Journal of Banking and Finance, 1 (06 1977), 3–11.CrossRefGoogle Scholar
Samuelson, P. A., and McKean, H. P. Jr “Rational Theory of Warrant Pricing.” Industrial Management Review. Reprinted in The Collected Scientific Papers of Paul A. Samuelson, R. C. Merton, ed. Boston: M.I.T. Press (1972), 791–871.Google Scholar
Shimko, D. “The Equilibrium Valuation of Risky Discrete Cash Flows in Continuous Time.” Journal of Finance, 44 (12 1989), 1373–1383.CrossRefGoogle Scholar
Smith, C. “Applications of Option Pricing Analysis.” In Handbook of Financial Economics, Bicksler, J. L., ed. Amsterdam; North Holland Publ. Co. (1979), Chapter 4.Google Scholar