Pricing and hedging variable annuities

Abstract

The aim of this paper is to present a general method to value, hedge and assess risk for a subclass of VA contracts in a Lévy market. This subclass contains Guaranteed Minimum Maturity Benefit (GMMB), Guaranteed Minimum Death Benefit (GMDB), and Guaranteed Minimum Accumulation Benefit (GMAB) that has a cliquet-style option in its design. The suggested unifying method is based on the generalized Fourier transform and gives general quasi-closed form solutions for a large class of Lévy processes. A numerical analysis that uses a Kou process illustrates the whole procedure.