Hello everyone, How could someone get the instantaneous forward rates? for instance in bloomberg, or how is that done in practise?i need them to calibrate the Hoo Lee model (as Explained in Paul Glasserman - Monte Carlo Methods in Financial Engineering)Thank you in advance!!Regards

Instantaneous rates aren't really found in the wild. The way to manufacture them is to fit a functional form that relates discount factors to time to maturity, say as a function P(t). The corresponding forward rate function is then f(t)=-d ln(P(t)) / dt.

Hey! thank you for the replyin this case, why using the instantaneous forward rates in the formula letting the Hoo Lee model fit the term structure? it would have been easier to keep discount factor from the very beginingtaking the derivative d ln(P(t)) / dt comes to just get out the instanteous forward rate under the integral, isn't it? Or let me put it this way, how do you compute numerically the d ln(P(t)) / dt ?Thank you again

First of all, it is Ho, not Hoo. Second, given that you get to choose the functional form for the discount factors, you may cleverly choose one that is analytically differentiable. In fact, come to think of it, it would be hard not to. Third, yes, you are right. Instantaneous forward rate dynamics turned out to be a bit of a side track for interest rate modeling, and both the math and finance get easier if you focus your modeling on discount factors (aka zero coupon bond prices). That being said, HJM made pretty serious strides in this framework, and their work is important on several levels. The '86 Ho Lee paper is only interesting from the perspective of the history of interest rate modeling, and as squarely set in a discrete time binomial setting did not in fact address instantaneous forward rates.

Thanks for the correction.Yeah i just get confused on the form of the discount factor to be derived. For me it is just exp(-integral [r(0,t] dt) and there's no other form unless we consider the discrete version.I'm not familiar with the HJM yet. If you have any practical papers/references regarding all the this discussion i'll be glad to have themMany thanks again

Hi,this paper:www.yetanotherquant.de/libor/tutorial.pdfbrings you from zero to HJM in 9 pages.Hope it helps.

Many thanks!!