Hi every one,May be this is a silly question, but I'm a bit confused and would like to be sure.I'm trying to price a contract using Hull&White one factor model with Monte Carlo simulations. My contract is a strip of payoffs at fixed dates [$](T_i)_{i \in \{i,n\}}[$] . Each payoff is indexed on the 3 months libor rate and the 5 years bond yield at date [$]T_i[$].My question is how to compute the 3m libor rate withing a given short rate path.My first solution was to use the ZC formula [$]P(T_i,T_i+3m)=A(T_i,T_i+3m)e^{-B(T_i,T_i+3m)r(T_i)}[$] and then compute [$]L(T_i,T_i+3m)[$] that at each date.The prices I got was quite unexpected. I think that the formula I used is wrong, since it is based on the ZC [$]P(t,T)[$] which is an expectation. I should rather integrate the short rate for the given path from [$]T_i[$] to [$]T_i+3m[$] and then imply the libor rate from the result.Am I wrong in my analysis ?Thanks in advance

Your first solution is right (at least in principle). As of time T(i) you don't know the path from T(i) to T(i)+3m, so using that piece of forward looking information would not be right. Although, as long as you are not making any decisions at time T(i) based on that information, your alternative solution should be unbiased, but not very efficient.

Thanks bearish for your reply.Indeed, I came to the same conclusion (I had a hindsight bias).I'll try to investigate why I have these strange prices.Cheers

Why not diffusing directly the ZC bond ? Use the fact that P(t,T_i,T_i + 3m) is a martingale under the forward risk-neutral measure associated to T_i and that P(0,T_i,T_i + 3m)=P(0,T_i + 3m)/P(0,T_i). Then using P(T_i,T_i,T_i + 3m) = P(T_i,T_i + 3m) you can get the corresponding Libor fwd.Moreover you don't need to calibrate the short rate to the current Libor fwd curve.