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A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities

  • Grosen, Anders

    ()

    (Department of Finance, Aarhus School of Business)

  • Jensen, Bjarke

    ()

    (SEB Fixed Income Research)

  • Løchte Jørgensen, Peter

    (Department of Management)

This paper sets up a model for the valuation of traditional participating life insurance policies. These claims are characterized by their explicit interest rate guarantees and by various embedded option elements, such as bonus and surrender options. Owing to the structure of these contracts, the theory of contingent claims pricing is a particularly well-suited framework for the analysis of their valuation. The eventual benefits (or pay-offs) from the contracts onsidered crucially depend on the history of returns on the insurance company’s assets during the contract period. This path-dependence prohibits the derivation of closed-form valuation formulas but we demonstrate that the dimensionality of the problem can be reduced to allow for the development and implementation of a finite difference algorithm for fast and accurate numerical evaluation of the contracts. We also demonstrate how the fundamental financial model can be extended to allow for mortality risk and we provide a wide range of numerical pricing results.

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Paper provided by University of Aarhus, Aarhus School of Business, Department of Business Studies in its series Finance Working Papers with number 01-5.

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Length: 34 pages
Date of creation: 27 Feb 2001
Date of revision:
Handle: RePEc:hhb:aarfin:2001_005
Note: Later published in The Geneva Papers on Risk and Insurance Theory, vol. 26, 2001, p. 57-84.
Contact details of provider: Postal: The Aarhus School of Business, Fuglesangs Allé 4, DK-8210 Aarhus V, Denmark
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  1. Steinar Ekern & Svein-Arne Persson, 1996. "Exotic Unit-Linked Life Insurance Contracts," The Geneva Risk and Insurance Review, Palgrave Macmillan, vol. 21(1), pages 35-63, June.
  2. Aase Nielsen, J. & Sandmann, Klaus, 1995. "Equity-linked life insurance: A model with stochastic interest rates," Insurance: Mathematics and Economics, Elsevier, vol. 16(3), pages 225-253, July.
  3. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  4. 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.
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