Why does the HJM-Model start with the Forward-dynamic instead of the Bond-Dynamic
The formula f(t,T)=-D/DT(log(P(t,T))) provides us a 1-1-correspondence between the FOrward-curve and the Bondprices and also an equivalence between the dynamics.
The mainprinciple is to duplicate interest rate sensitive derivatives by bonds and hence to valuate them by the Bondprices.
So, why do we go the way: f(0,T)->f(t,T) -> P(t,T)-> interest rate derivatives instead of directly start with P(0,T) -> modelling the Bondprice-Dynamic->....
What is the purpose of starting with the forward curve ?
In a few papers I read that it facilitates the mathematical analysis and empirical evaluation. But what exactly does that mean? In these papers it remained unanswered.
I would be very pleased, if anybody could explain it to me.