April 21st, 2015, 1:25 pm
Hi,I have a question with regard to a forward rate based model (like the Libor Market Model). Say at time 0 I know the entire term structure and thus the forward rates[$]f(0, 0, T_1), f(0, T_1, T_2), ..., f(0, T_N, T_{N+1})[$]where the first forward rate has just expired. A forward rate model defines equations of motion for the remaining rates, i.e. for[$]f(0, T_1, T_2), ..., f(0, T_N, T_{N+1}).[$]If I evolve these rates, say to time [$]t = \Delta t[$] I have[$]f(\Delta t, T_1, T_2), ..., f(0, T_N, T_{N+1}).[$]What I do not have is[$]f(\Delta t, \Delta t, T_1).[$]Without this I cannot compute entire term structure as I would not know, e.g., [$]P(\Delta t, T_1)[$]. How would one generally proceed in this case? Simply extrapolate it from the evolved rates? Or assume that the rate did not change since [$]t = 0[$]?