ABSTRACT
Contents 6.1 Introduction . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88 6.2 Computational Kernels in Participating Life Insurance Policies . . . . . . 89 6.3 Numerical Methods for the Computational Kernels . . . . . . . . . . . . . . . . . . 91
6.3.1 Numerical Methods for High-Dimensional Integration. . . . . . . 92 6.3.2 Numerical Solution of Stochastic Differential Equations . . . . . . 93
6.4 A Benchmark Mathematical Model . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95 6.5 Numerical Experiments . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 99 6.6 Conclusions. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109 Acknowledgment . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .109 References . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .110
Abstract: In this work we focus on the numerical issues involved in evaluating an important class of financial derivatives: participating life insurance contracts. We investigate the impact of different numerical methods on accuracy and efficiency in the solution of main computational kernels generally arising from mathematical models describing the financial problem. The main kernels involved in the evaluation of these financial derivatives are multidimensional integrals and stochastic differential equations. For this
reason we consider different Monte Carlo simulations and various stochasticdifferential-equation discretization schemes. We have established that a combination of the Monte Carlo method with the antithetic variates (AV) variancereduction technique and the fully implicit Euler scheme developed by Brigo and Alfonsi (2005) provides high efficiency and good accuracy.
