Pricing and capital requirements for with profit contracts: modelling considerations

The aim of this paper is to provide an assessment of alternative frameworks for the fair valuation of life insurance contracts with a predominant financial component, in terms of impact on the market consistent price of the contracts, the embedded options, and the capital requirements for the insurer. In particular, we model the dynamics of the log-returns of the reference fund using the so-called Merton (1976 Merton, RC. 1976. Option pricing when underlying stock returns are discontinuous. J. Finan. Econ., : 125–144.  [Google Scholar]) process, which is given by the sum of an arithmetic Brownian motion and a compound Poisson process, and the Variance Gamma (VG) process introduced by Madan and Seneta (1990 Madan, DB and Seneta, E. 1990. The variance gamma (VG) model for share market returns. J. Bus., 63: 511–524. [Crossref], [Web of Science ®] , [Google Scholar]), and further refined by Madan and Milne (1991 Madan, DB and Milne, F. 1991. Option pricing with VG martingale components. Math. Finan., 1: 39–45. [Crossref] , [Google Scholar]) and Madan et al. (1998 Madan, DB, Carr, P and Chang, E. 1998. The variance gamma process and option pricing. Eur. Finan. Rev., 2: 79–105. [Crossref] , [Google Scholar]). We conclude that, although the choice of the market model does not affect significantly the market consistent price of the overall benefit due at maturity, the consequences of a model misspecification on the capital requirements are noticeable.