  This paper proposes a market consistent valuation framework for variable
annuities with guaranteed minimum accumulation benefit, death benefit and
surrender benefit features. The setup is based on a hybrid model for the
financial market and uses time-inhomogeneous L\'evy processes as risk drivers.
Further, we allow for dependence between financial and surrender risks. Our
model leads to explicit analytical formulas for the quantities of interest, and
practical and efficient numerical procedures for the evaluation of these
formulas. We illustrate the tractability of this approach by means of a
detailed sensitivity analysis of the price of the variable annuity and its
components with respect to the model parameters. The results highlight the role
played by the surrender behaviour and the importance of its appropriate
modelling.
