Development and Pricing of a New Participating Contract

Abstract

The purpose of this article is to design and price a new type of participating life insurance contract. Participating contracts are popular in the US and in European countries; they satisfy various covenants and obey various regulations depending on the country where they are issued. The standard literature is Briys and de Varenne [1994, 1997a] and Grosen and Jorgensen [2000], to quote only a few. Bernard, Le Courtois and Quittard-Pinon [2005] studied a particular type of participating contract, where a Vasicek model of interest rates is assumed and where the potential default of the issuing company is taken into account. In this paper, we design a new type of participating contract very similar to the one considered in the above-mentioned study, but where the guaranteed rate corresponds to the return of a portfolio of Government bonds. We show that this new type of contract can be valued in closed-form, even when the interest rates are stochastic and default of the company is taken into account.

Keywords: Participating Life Insurance Policies, Contingent Claims Valuation, Default Risk, Stochastic Interest Rates, Dubins-Schwarz theorem

JEL Classification: G13, G22