In this paper we investigate price and Greeks computation of a Guaranteed Minimum With-drawal Benefit (GMWB) Variable Annuity (VA) when both stochastic volatility and stochasticinterest rate are considered together in the Heston Hull-White model. We consider a nu-merical method the solves the dynamic control problem due to the computing of the optimalwithdrawal. Moreover, in order to speed up the computation, we employ Gaussian ProcessRegression (GPR). Starting from observed prices previously computed for some known combi-nations of model parameters, it is possible to approximate the whole price function on a defineddomain. The regression algorithm consists of algorithm training and evaluation. The first stepis the most time demanding, but it needs to be performed only once, while the latter is veryfast and it requires to be performed only when predicting the target function. The developedmethod, as well as for the calculation of prices and Greeks, can also be employed to computethe no-arbitrage fee, which is a common practice in the Variable Annuities sector. Numericalexperiments show that the accuracy of the values estimated by GPR is high with very lowcomputational cost. Finally, we stress out that the analysis is carried out for a GMWB annuitybut it could be generalized to other insurance products.