Hi all,I am in the process of implementing Hull-White consistent with both time-dependent yield and volatility (dr = [Theta(t)-Alpha(t)*r]*dt + Sigma(t)dz ). I am using two different sources:Book: Implementing Derivatives Models, by Clewlow and Strickland (page 278)Paper: Using Hull-WHite Interest Rate Trees, By Hull and White, Journal of Derivatives - Winter 1996 (page 9)These sources use different tree geometries. Clewlow uses a binomial root node while the rest of the nodes are trinomial. On the other hand, the paper does not mention anything about switching to binomial in the root node.Is anybody familiar with these two different approaches that understands the differece? Is there an advantage of one versus the other?Thanks for any help!!!!

I can't answer your question on which is best but the paper:The General Hull-White Model and Super Calibration, Hull and White, August 2000(available on Hull's web page) gives a good description of the HW model in which mean reversion andvolatility are time-varying. I recently implemented a trinomial tree version of this model but I found the calibration was too slow. There are no analytic formulae for swaptions oreven bonds so everything has to be priced on the tree during the least-squares optimisationphase. I have since then derived semi-analytic formulae for bonds and swaps which involve integrals in alpha(t) and sigma(t). This should significantly speed-upthe pricing during the calibration phase but I have not got round to implementingit yet. cg