Variable Annuities with State-Dependent Fees

In this paper we consider a variable annuity with guarantees at death and maturity financed through the application of state-dependent fees. We define a general valuation model for them, and propose to apply the LSMC approach in order to analyse the interaction between fee rates, death/maturity guarantees, fee thresholds and surrender penalties under alternative model assumptions and policyholder behaviours. However, special care is needed in the numerical implementation of this approach, due to the shape of the surrender region.We can stem the numerical errors arising in the regression step by using suitable arrangements of the LSMC valuation algorithm.