Risk measures for variable annuities: A hermite series expansion approach

Abstract

In this study, we propose an efficient approach to the calculation of risk measures for an insurer's liability from writing a variable annuity with guaranteed benefits. Our approach is based on a novel application of the Hermite series expansions on the transition density of a diffusion process to the insurance setting. We compare our method with existing methods in the literature, including the analytical method, spectral method and Green's function method, and illustrate its substantial advantages in calculating risk measures for variable annuities with different guarantee structures. The improved efficiency makes our method flexible to practical implementation in reporting risk measures on a daily basis. We also conduct a sensitivity analysis of the risk measures with respect to key parameters. Keywords: Variable annuity, Guaranteed minimum maturity benefit, Guaranteed minimum death benefit, Value-at-Risk, Conditional-tail-expectation, JEL classification: G22, G32