Pricing and capital requirements for with profit contracts: modelling considerations

Abstract

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) 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), and further refined by Madan and Milne (1991) and Madan et al. (1998). 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.

Keywords:

• Fair valuation
• Incomplete markets
• Lévy processes
• Monte Carlo methods
• Participating contracts
• Solvency requirements

Acknowledgements

The author would like to thank Enrico Biffis for many useful discussions about many steps of the development of this project and Tamim Zamrik for his help with few Matlab implementations for the VG model. Further thanks go to Steven Haberman, Vladimir Kaishev and Jiwook Jang for reading previous drafts of this paper and making very helpful suggestions and comments. Earlier versions of this work have been presented at the 12th International Conference on Computing in Economics and Finance, the EURO XXI conference, the 10th International Congress in Insurance: Mathematics and Economics and the International AFIR 2007 Colloquium. The author would like to thank the participants of these conferences, in particular Farid AitSahlia, Mogens Steffensen and Ragnar Norberg. The author also thanks two anonymous referees for their valuable feedback. Usual caveat applies. This research was partially supported by the UK Actuarial Profession.