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Joined: August 20th, 2019, 12:40 pm

Moments Matching: G2++

February 16th, 2021, 11:34 am

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? 

thank you,