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Pricing and capital requirements for with profit contracts: modelling considerations. (English) Zbl 1180.91160

Summary: 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 R. C. Merton process [J. Financ. Econ. 3, No. 1-2, 125–144 (1976; Zbl 1131.91344)], which is given by the sum of an arithmetic Brownian motion and a compound Poisson process, and the variance gamma (VG) process introduced by D. B. Madan and E. Seneta [“The variance gamma (VG) model for share market returns”, J. Bus. 63, 511–524 (1990)], and further refined by D. B. Madan and F. Milne [Math. Finance 1, No.4, 39–55 (1991; Zbl 0900.90105)] and D. B. Madan, P. Carr and E. C. Chang [Eur. Finance Rev. 2, No.1, 79–105 (1998; Zbl 0937.91052)]. 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.

MSC:

91B30 Risk theory, insurance (MSC2010)
91B25 Asset pricing models (MSC2010)
91G80 Financial applications of other theories
91G60 Numerical methods (including Monte Carlo methods)

Software:

Cephes
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