Hi everyone,I am a newbie to interest rate models and I have tonnes of questions in this area. Hope you guys can lend a hand to me My first question (to this forum) is about calibrating the LIBOR market model. The data I have now are1) Daily swap rates of maturities 0.5 years (spot LIBOR indeed), 1 year, 2 years, 3 years and so other integer years (the tenor is 0.5 years, though)2) Daily Black's volatilities of ATM caps and floors of maturities 1 year, 2 years, and other integer years (the tenor is 0.5 years again)3) Daily Black's volatilities of ATM swaptions of maturities in integer years (which may not be the same as the caps and floors above), tenor is also 0.5 yearsFor 2 and 3, the maturities are fixed in the sense that I cannot see how the Black's volatility of, say, 1 year cap, changes over time. What I have is the Black's volatility of 1 year cap with maturity date 1/1/2006 when the observation date is 1/1/2005; maturity 1/2/2006 when the observation date is 1/2/2005, etc.These data are given by my professors, who said they are from Datastream (there are even no forward rates?!). Yet, to my understanding, they are not enough for calibration of the BGM model... (I read Interest rate models: theory and practice by Brigo and Mercurio, 2001)In the worst case, if I can't find any more data, how could I do the calibration, with some extra assumptions maybe?

I think you have more data than you need already. You can calculate forward rates from the swap rates that you have. Then if you're building a 1-factor model, choose one set of instruments (probably caps or floors) for the volatility calibration. You'll have to do some interpolation of both rates and volatilities if you want to use a time step shorter than 1 year, but that's no big deal. As long as the rates and vols you put in the model result in correct market prices at the data points you have, you're all set.

Sorry for replying late... as there are many other things to tackle...Now I've got the weekly Eurodollar futures quotes, implying I could get the forward rates. I carried out principal components analysis after catergorizing the rates according to their accrual periods (like the one described in P 584, J. Hull Options, Futures and Other Derivatives, 5th edition). So how can I determine whether the caps/swaptions (as in my first post) are under-/over-valued compared with the volatilities I have got from PCA?