A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities
AbstractThis 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 considered 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. The Geneva Papers on Risk and Insurance Theory (2001) 26, 57–84. doi:10.1023/A:1011264408187
Download InfoIf you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
Bibliographic InfoArticle provided by Palgrave Macmillan in its journal The Geneva Papers on Risk and Insurance Theory.
Volume (Year): 26 (2001)
Issue (Month): 1 (June)
Contact details of provider:
Web page: http://www.palgrave-journals.com/
Postal: Palgrave Macmillan Journals, Subscription Department, Houndmills, Basingstoke, Hampshire RG21 6XS, UK
Other versions of this item:
- Grosen, Anders & Jensen, Bjarke & Løchte Jørgensen, Peter, 2001. "A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities," Finance Working Papers 01-5, University of Aarhus, Aarhus School of Business, Department of Business Studies.
- Bjarke Jensen & Peter Løchte Jørgensen & Anders Grosen, . "A Finite Difference Approach to the Valuation of Path Dependent Life Insurance Liabilities," Management Working Papers 1999-11, School of Economics and Management, University of Aarhus.
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- 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.
- Nielsen, J. Aase & Klaus Sandmann, 1995. "Equity-linked life insurance - a model with stochastic interest rates," Discussion Paper Serie B 291, University of Bonn, Germany, revised Mar 1995.
- 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.
- 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.
- Eling, Martin & Kochanski, Michael, 2012. "Research on Lapse in Life Insurance – What Has Been Done and What Needs to Be Done?," Working Papers on Finance 1224, University of St. Gallen, School of Finance.
- Bacinello, Anna Rita, 2005. "Endogenous model of surrender conditions in equity-linked life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 37(2), pages 270-296, October.
- Kling, Alexander & Richter, Andreas & Ru[ss], Jochen, 2007. "The interaction of guarantees, surplus distribution, and asset allocation in with-profit life insurance policies," Insurance: Mathematics and Economics, Elsevier, vol. 40(1), pages 164-178, January.
- Gerstner, Thomas & Griebel, Michael & Holtz, Markus, 2009. "Efficient deterministic numerical simulation of stochastic asset-liability management models in life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 44(3), pages 434-446, June.
- De Giovanni, Domenico, 2007. "Lapse Rate Modeling: A Rational Expectation Approach," Finance Research Group Working Papers F-2007-03, University of Aarhus, Aarhus School of Business, Department of Business Studies.
- Bauer, Daniel & Kiesel, Rudiger & Kling, Alexander & Ru[ss], Jochen, 2006. "Risk-neutral valuation of participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 39(2), pages 171-183, October.
- Tanskanen, Antti Juho & Lukkarinen, Jani, 2003. "Fair valuation of path-dependent participating life insurance contracts," Insurance: Mathematics and Economics, Elsevier, vol. 33(3), pages 595-609, December.
- Iwaki, Hideki & Yumae, Shoji, 2004. "An efficient frontier for participating policies in a continuous-time economy," Insurance: Mathematics and Economics, Elsevier, vol. 35(3), pages 611-625, December.
- Hainaut, Donatien, 2010. "Optimal design of profit sharing rates by FFT," Insurance: Mathematics and Economics, Elsevier, vol. 46(3), pages 470-478, June.
- Kling, Alexander & Richter, Andreas & Ruß, Jochen, 2006. "The Impact of Surplus Distribution on the Risk Exposure of With Profit Life Insurance Policies Including Interest Rate Guarantees," Discussion Papers in Business Administration 1220, University of Munich, Munich School of Management.
- Zemp, Alexandra, 2011. "Risk comparison of different bonus distribution approaches in participating life insurance," Insurance: Mathematics and Economics, Elsevier, vol. 49(2), pages 249-264, September.
- Bernard, Carole & Le Courtois, Olivier & Quittard-Pinon, Francois, 2005. "Market value of life insurance contracts under stochastic interest rates and default risk," Insurance: Mathematics and Economics, Elsevier, vol. 36(3), pages 499-516, June.
- Zaglauer, Katharina & Bauer, Daniel, 2008. "Risk-neutral valuation of participating life insurance contracts in a stochastic interest rate environment," Insurance: Mathematics and Economics, Elsevier, vol. 43(1), pages 29-40, August.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Elizabeth Gale).
If references are entirely missing, you can add them using this form.