Nelson and Siegel derive their famous functional-form model for the spot & forward rates under (or rather, on-top-of)the assumption that the (instantaneous) forward rate satisfies a 2nd order non-homogeneous linear ODE. That is,if f(t) denotes the forward rate at future time t, (now equals zero), then a f'' +b f' +c f +d =0 for some constants a,b,c,d.They point out that in order to avoid over-parametrization, they also assume that the characteristic equation a x^2+b x +c = 0has a unique root, which is equivalent to assuming b^2-4ac=0.I couldn't find any argument supporting the basic assumption. That is, why assume, apart from being easy to solve, a linear ODE?What emipirical observations might support this?

my observation is that N&S is confined to undergraduate textbooks or old-school guys who spline the treasury curve for LTCM-style rich/cheap analysis.

This is curious, I've come across a not so old paper discussing the NS model : http://ideas.repec.org/p/uts/rpaper/226.htmlGmike, maybe u could give more details on ur observationThanks

"my observation is that N&S is confined to undergraduate textbooks or old-school guys who spline the treasury curve for LTCM-style rich/cheap analysis"Gmike: We just about had a trifle too much and a little too many of the pompous new school guys whohave no clue as to what the letters C,D,O, M ,B & S really stand for. This haughty approach, by which a mathematicalmodel is deemed irrelevant because it is not sexy, or because reddish tie nerds who yesterday got out of some MBS programenhanced by an extra course on stochastic analysis (!) are sneering at it, may look good at poolsides with rich customerswho appreciate the jazz band but have no clue as to what they are buying, but when push comes to shove it was the central banks, those sensible people who work with NS, who gave all the money. Now, can you answer my original question, or is it just more of the same meta-meta-finance?

NB, It seems Diebold and others tried to reconcile both views, so-called macroeconomic and financial...Did they succeed ? I mean are these models of practical use ? I don't know and that was the purpose of my first post.Well this doesn't answer ur question but it helps narrow the gap...

I don't know to what extent they are of practical use. I do know that lots of folks use NS on a daily basis. Regardless, myquestion can be treated as purely theoretical: it is really interesting to know how come you decide that something obeysthis differential equation or that; it certainly suggests a manifestation of the zeroth principle of physics: I have a solution, now let's look for problems.

You can label me however you want and I apologize if my language upsets you.But I have also had just about enough of pseudo fixed income academia. I have worked in fixed income all my life (buy side, sell side, modelling, research, trading, you name it) and really the only places I have encountered Nelson and Siegel was (1) in graduate school (2) when an ex-salomon dude showed me the LTCM rich/cheap approach for govies and (3) when I had to help my little brother with his undergrad homework.I just dont see the point of the nelson and siegel model from a practitioner's point of view. If there is one, I am more than happy to learn about it.

Thank you for the link and the paper is very intersting. But my point is, this model has been beaten to death by academics while I dont see anybody using it anymore "on the street". Or do you? I mean I understand it is a nice way to fit a line through a whole bunch of govies that are all over the curve. But that is it, there is no deeper meaning.

I two would like an answer to the OPs original question.Also Gmike2000 which paper are you referring to?ThanksBaz

hey gmike2000, your statement is really quite inaccurate. Had you made that statement before 2006 (I am not going to tell you more than that), it might have received somewhat more respect, but since then things have changed a lot, trust me. BTW, what is wrong with LTCM rich-cheap analysis?newbanker, I don't think that N&S motivate the model either geometrically (~kinematically), physically (~dynamically) or economically. The solutions of linear second order odes are just known and very well studied. For example you can discuss the various dynamic regimes of the "linear forced and damped harmonic oscillator", which is a prototypical physical systemm in terms of the coefficients of the equation you wrote down. If you don't like to think in terms of physics, just think that the equation you wrote down is the simplest possible combination of a function (i.e. the instantaneous forward rate), its first derivative (the slope) and its second derivative (the curvature). It is a very parsimonious model for a continuous line with some differentiability properties. I don't find it natural to think this way, but mathematicians probably do.You can probably fairly easily interpret each term in the equation as a physicist would, i.e. in terms of a force and you would probably find that the second order term is relatively unimportant in the balance etc... But I don't think that this is going to get you very far. We all know that YC dynamics is much more complex than a simple oscillator especially with QE3 and stuff, huh?