Hi all,May I ask a question on the calibration of a shifted BGM model? To keep it simple, the model is assumed to be the following (which is equivalent to Dr. Piterbarg's when ignoring the stoc-vol component)dF(t)=(...)dt+vol*(F+shift)dW, where F is the forward rate, and the volatility is decomposed as vol(t)=h(t)*g(T-t)The dW is a multidimenstional independent Brownian motion [dW1, dW2, ..., dWn], and vol is thus [vol1, vol2, ..., voln]So the question is, how "bad" if we allow some component of [h(t)*h(t)] (e.g. h2(t)*h2(t)) to be negative while I still make sure the forward rate variance vol*vol to be positive through the time even if it becomes slightly negative in some circumstances. Or in practice, is it really normal to let the model parameter h(t)*h(t) be negative for some of its components?The reason I am asking is, when I tried to calibrate a 3F factor shifted-BGM to 3 columns of the swaption matrix (USD 2Y, 10Y, and 30Y) under the condition of shift~1/dt (i.e. reducing to a Gaussian HJM model), some components of h(t)*h(t) turn out to be negative...Thank you
Last edited by kelang
on May 22nd, 2014, 10:00 pm, edited 1 time in total.