Variable Annuities with State-Dependent Fees: Valuation, Numerical Implementation, Comparative Static Analysis and Model Risk

In this paper we consider a variable annuity which provides guarantees at death and maturity financed through the application of a state-dependent fee structure, as defined first in Bae and Ko (2013) and extensively analysed in Bernard et al. (2014) and MacKay et al. (2017). We propose a quite general valuation model for such guarantees, along the lines of Bacinello et al. (2011). We then analyse numerically the interaction between fee rates, death/maturity guarantees, fee thresholds and surrender penalties under alternative model assumptions and policyholder behaviours. This allows us to get also some interesting insights into the model risk. Since the assumptions adopted in the numerical analysis are not at all trivial, we resort to Monte Carlo and Least Squares Monte Carlo methods (LSMC) for the numerical implementation of the valuation model. In particular, special care is needed in the application of LSMC, due to the shape of the surrender region. We are able to stem the numerical errors arising in the regression step by using suitable arrangements of the LSMC valuation algorithm.