wilmott.com

Based on a given numeraire I want to determine the drift of the forward rates in the LMM.Does anyone have a good reference for me?

QuoteOriginally posted by: DutchQuantBased on a given numeraire I want to determine the drift of the forward rates in the LMM.Does anyone have a good reference for me?"Interest Rate Models, Theory and Practice", D. Brigo, F. Mercurio"Stochastic Calculus for Finance II, Continuous-Time Models", S. S. Shreve

if you know the dynamics of the forward rate under the usual martingale measure, then you should be able to compute the explicit dynamics under the new measure a la girsonov. The R-N derivative for the new numeraire should be dP*/dP = N(T)/(N(0)*Beta(T)) where N(t) is the new numeraire. State price density is eta(t) = N(t)/(N(0)*Beta(t)), a martingale under the usual RN measure. d eta(t) = sig.eta.dW. If X(t) is a process with dX = mu_X.dt+sigma_X.dW then mu under the new measure should be mu_X-sigma_X.sig. (At least that's the basic story, as long as there are no complications that it is the *forward* rate you are modelling.) Note that sigma_X is here the diffusion coefficient (I did not assume the diffusuion term was of the form sig.X.dW. Shreve's notes (available on the internet) are a good primer/review.Hope this helps. Maybe you knew all that already.

Thanks,I've been looking around for Shreve's documents and that helps.