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Equity-linked life insurance - a model with stochastic interest rates

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  • Nielsen, J. Aase
  • Klaus Sandmann

Abstract

Assuming constant interest rates Brennan and Schwartz (1976, 1979) obtained the rational insurance premium on an equity-linked insurance contract through the application of the theory of contingent claims pricing. Further considerations with deterministic interest rates have been discussed in Aase and Persson (1992) and in Persson (1993). Analysing the single premium case Bacinello and Ortu (1993b) allow for the short term interest rate to develop in accordance to an Ornstein-Uhlenbeck process. In a paper from 1994 they consider extensions to both the single and the periodic premium model. This paper presents a model similar to the one by Bacinello and Ortu (1994) for the periodic premium case with a stochastic interest rate dynamic. It is shown that the insurance contract includes an Asian-like option contract. Sufficient conditions on the guaranteed amount for the existence of a solution are derived. As no closed form solution will be obtained, we discuss different numerical approaches and apply Monte Carlo simulations with a variance reduction technique.

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Bibliographic Info

Paper provided by University of Bonn, Germany in its series Discussion Paper Serie B with number 291.

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Length: pages
Date of creation: Jan 1995
Date of revision: Mar 1995
Handle: RePEc:bon:bonsfb:291

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Postal: Bonn Graduate School of Economics, University of Bonn, Adenauerallee 24 - 26, 53113 Bonn, Germany
Fax: +49 228 73 6884
Web page: http://www.bgse.uni-bonn.de

Related research

Keywords: Asian option; forward risk adjusted measure; Monte Carlo simulations;

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References

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  1. Brennan, Michael J. & Schwartz, Eduardo S., 1976. "The pricing of equity-linked life insurance policies with an asset value guarantee," Journal of Financial Economics, Elsevier, vol. 3(3), pages 195-213, June.
  2. Persson, Svein-Arne, 1993. "Valuation of a multistate life insurance contract with random benefits," Scandinavian Journal of Management, Elsevier, vol. 9(Supplemen), pages S73-S86.
  3. Turnbull, Stuart M. & Wakeman, Lee Macdonald, 1991. "A Quick Algorithm for Pricing European Average Options," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 26(03), pages 377-389, September.
  4. Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
  5. Kemna, A. G. Z. & Vorst, A. C. F., 1990. "A pricing method for options based on average asset values," Journal of Banking & Finance, Elsevier, vol. 14(1), pages 113-129, March.
  6. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees : A corrigendum," Insurance: Mathematics and Economics, Elsevier, vol. 13(3), pages 303-304, December.
  7. Bacinello, Anna Rita & Ortu, Fulvio, 1993. "Pricing equity-linked life insurance with endogenous minimum guarantees," Insurance: Mathematics and Economics, Elsevier, vol. 12(3), pages 245-257, June.
  8. Vorst, Ton, 1992. "Prices and hedge ratios of average exchange rate options," International Review of Financial Analysis, Elsevier, vol. 1(3), pages 179-193.
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