I am working on Hull-White 2Factor model, I have to simulate it to generate zero curves for the next 50 years (at yearly frequency). I have EIOPA curve (zero rate curve at t =0, up to T=100 Years) and a matrix of swaption volatility.
Could anyone guide me on how I can achieve it? I see that there exists an analytical formula for P(t, T) to price a bond at time t, and expiring at time = T. However, I don't see Weiner increment in the formula, wondering if this can be used to simulate yield curves, what about the two sources of randomness in that case?
Thank you very much.