Imagine you want to model interest rate fluctuations. You have to have a decent model for fluctuations at all maturities. Are there any reasonable constraints? How far can the curve invert? How likely is that? What are the self-consistency constraints? How do we incorporate current option prices into the analysis? A well-known practitioner once told me that modeling the yield curve is to modeling equity prices as quantum field theory is to ordinary quantum mechanics!
See here for Derman's explanation of the BDT (Black, Derman, Toy) yield curve model. I discussed a nice bio of Fischer Black here, and Derman's book here.
