How do we apply moments matching-variance reduction technique to the G2++ model? In a one-factor short rate model, it is achieved by adding instantaneous forward rate from the market and subtracting the same obtained from the empirical distribution.
r_corrected = r_simulated + f(0,t) - \bar f(0,t), for each path,
r_simulated is obtained from the short-rate process, f(0,t) from bond data and \bar f(0,t) from empirical distribution.
In the G2++ model, we have got two factors, x(t) and y(t) and in the bond pricing formula, they are weighed by functions of parameters a and b, respectively. I tried some maths and found that I need to subtract the mean of x(t), y(t) and V(0,t)/2t from the short rate process in order to achieve exact bond prices from simulations. I am getting an error of 3% at 30 Y maturity and it diverging for longer maturities.
Any insights into this?
Also, how do we apply moment matching in displaced diffusion models?