Valuation of participating contracts and risk capital assessment: the importance of market modelling

The aim of this paper is to provide an assessment of alternative frameworks for the valuation of participating contracts with minimum guarantee, in terms of impact on the market consistent price of the contracts and the options embedded therein, and on 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 process (Merton, 1976), 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), and further refined by Madan and Milne (1991) and Madan et al. (1998). Although with the Merton process closed analytical formulae can be obtained for certain smoothing mechanisms (see Ballotta (2005) for example), the same does not apply when the VG process is adopted. Hence, we consider suitable simulation procedures based on stratified Monte Carlo/Quasi Monte Carlo with bridges, as proposed by Ribeiro and Webber (2004) and Avramidis and L’Ecuyer (2006), and adapt them to the specifics of the chosen participating policy, and to the calculation not only of the contract fair value, but also of some relevant risk measures, such as VaR and TVaR.