Fair Valuation of Participating Life Insurance Contracts with Jump Risk

Olivier Le Courtois () and François Quittard-Pinon ()
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Olivier Le Courtois: Department of Economics and Finance, EM Lyon Business School, 23 Avenue Guy de Collongue, Ecully 69134, France.
François Quittard-Pinon: [1] aDepartment of Economics and Finance, EM Lyon Business School, 23 Avenue Guy de Collongue, Ecully 69134, France.

The Geneva Risk and Insurance Review, 2008, vol. 33, issue 2, 106-136

Abstract: The purpose of this article is to value participating life insurance contracts when the linked portfolio is modeled by a jump-diffusion. More precisely, this process has a Brownian component and a compound Poisson one, where the jump size is driven by a double exponential distribution. Specifically here, the bankruptcy risk of the insurance company is considered. Thus, market and credit risks are taken into account. A quasi-closed-form formula is obtained in fair value for the price of the considered life insurance contract. This allows us to investigate the impact of strategic parameters as well as structural ones, as is shown in the numerical section of this paper. In particular, we study the impact on the contract of the volatility, jump intensity, jump asymmetry, company leverage, guaranteed rate, participation rate and level of the default barrier, and comment on how they are likely to increase the probability of early default of the issuer. The Geneva Risk and Insurance Review (2008) 33, 106–136. doi:10.1057/grir.2008.11

Date: 2008
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