Gaussian process regression for pricing variable annuities with stochastic volatility and interest rate

Taxation of a GMWB Variable Annuity in a Stochastic Interest Rate Model

“…This analysis combines the effects of taxation and of the variable interest rate which, as already shown separately in other research work, can have a significant impact on the withdrawal choices and thus on the hedging costs. This analysis has been possible thanks to the use of an efficient numerical method based on a tree approach (Goudenège et al, 2019). Numerical results show many interesting facts.…”

“…We stress out that the coefficients 2.5 and 30 are determined empirically in order to give accurate results and their small variations do not produce impacts on the numerical results. Finally, the construction of the set G Y relies on the trinomial tree proposed by Goudenège et al in (2019). Such a tree defines a discrete Markov chainȲ t that matched the first two moments of the process Y .…”

“…Shevchenko and Luo (2017) employ high-order Gauss-Hermite quadrature to evaluate the GMWB contract under the Vasicek interest rate model. Recently, Goudenège et al (2019) exploit a hybrid tree-PDE method together with Machine Learning techniques to efficiently evaluate the GMWB contract in a model that considers both stochastic interest rate and stochastic volatility. More generally, as far as pricing of Variable Annuities in a stochastic interest rate framework is considered, it is worth mentioning the work of Bacinello and Zoccolan (2019) that develops a Monte Carlo flexible approach to study the impact of threshold fee on the optimal surrender strategy about a product including accumulation and death guaranteed benefits under a model which considers stochastic interest rate, volatility and mortality.…”

“…This model has already been employed in other research works concerning GMWB Variable Annuities (e.g. Donnelly et al, 2014;Dai et al, 2015;Goudenège et al, 2018Goudenège et al, , 2019. We stress out that considering both taxation and stochastic interest rate is a challenging task because of the computational effort required to consider many factors together.…”

“…In order to manage such a computational effort, we use a backward dynamic approach that exploits a tree approach to compute the fair contract price. In particular, we employ a trinomial tree to approximate the stochastic interest rate process through a Markov chain, which represents an efficient numerical solution already used by Goudenège et al (2019). It is worth noting that tree methods have already been used to study the GMWB contract.…”