Hi Kiri, The Cheyette model was explained extremely poorly in the "old times" (i.e. before this book). Don't be scared of it. It's a very slight generalization of the Hull-White model. Between buying the A&P book and the B&M one, I wouldn't hesitate one second (I have both, I lent B&M to a friend more than a year ago, and he keeps telling me he'll return it. I don't miss it that much. I wouldn't tolerate being away from the A&P book for more than a few days). It depends what you mean by implementation. If you want to implement it in Mathematica, you can probably do it in a day, even less. If you want to implement it in C++, even that wouldn't be too complicated, if what you have now is a Monte Carlo implementation. You just need to add one more state variable, and keep track of it. If currently you have a tree implementation, I don't know, it could take some time; essentially your tree becomes a local vol tree, and you have to be careful in the parts of the tree where the vol is high (you need to increase the step size in the short rate, or you'll get an instability). It would certainly be a more difficult project, and I would budget much more than just a few days. So, just to give you some peace of mind about the current state of the art in terms of models. There are 2 widespread ones, and another emerging one. - quasi-Guassian- Libor Market Models- quadratic GaussianThe affine class of models (CIR among them) is ok-ish, but you don't have the same flexibility with the smile. The quadratic Gaussian is quite new, and requries a lot of thinking until you become thouroughly familiar with it. It has the tremendous advantage of dimension reduction, so it certainly is worth a look. But don't start with it. The quasi-Gaussian is very convenient, being just a slight generalization of the Hull-White. It is very flexible, allows for all sorts of smiles and correlations, but may have some quirks, as the rates floor I mentioned. The LMM is the ultimate in flexibility, but having more factors is slow, and may not be very stable. These are all "honest" models. There are also some "hacks", where you start with some O.U. process, then get the short rate as a function of this process. You can run these only in trees. Their only advantage is dimension reduction, and therefore speed. Back to your observations on models: - CIR model: that's correct, you don't match the initial zero curve- CIR with time dependent parameters: you can match the initial zero curve. Again, a good description is in the A&P book. I don't think calibrating the vol is very hard. Whatever you use to calibrate Hull-White you can still use now- BK/BDT: correct, you need (recombining) trees to calculate both zero bonds and swaptions. Trees are suitable for constructing zero curve in the future, just pick a point in the future, and take the subtree that stems from that point. On that tree you can calculate whatever zero bonds you want. Best,V.