# how to get 3 month Forward rates from Hull white model simulation?

I implemented the Hull White one factor model in Monte Carlo simulation, and got the short rate on each node (time step =1month). my question is how to get the forward rate from the short rate? I am using the formula for zero coupon bond P(t,T)=A(t,T)*EXP(−B(t,T)*rt) (J.Hull's book), P(t,T) can be the discount factor between t and t+ 1month and then can be converted into a 1 month forward rate. To get a 3 month forward rate, I integrated those three 1month forward rate and then added a 1month-3month spread to obtain the simulated 3 month forward rate. can anyone advice if this approach is reasonable? The claims in contingent on 3month libor, for now I am just assume single curve. Thanks!

• What exactly do you mean by $P(t,T)$ can be the 1 month discount factor? Is there a reason why you assume $T=t + 3m$ is not possible/permitted? – KevinT Jan 14 at 17:07
• the model is for CVA, majority of the portfolio reset 1month, a few indexed to 3moth, – marietta Jan 14 at 17:13