It has been suggested that I try building a trinomial tree to model the discount curve based upon some given par swap rates. However, I can only find literature on implementing a trinomial tree for the Hull-White. Even though the vasicek is taken to be a 'special case' of the Hull-White, all procedures I've found involve matching the current term structure - but this is not possible in my case as I am trying to estimate this from the par swap rates. If anyone can help clear up my current confusion, it would be most appreciated!

For the HW you need the current yield curve as input. You estimate the current yield curve out of swap rates.

I see your problem.Traditionally, trinomial trees are not used to find the discount curve from swap rates (afaik) although there is no reason why you cant I suppose...you'd need to back out the vol parameters in the usual way (using caps) , then choose the constant drift that best matches your swap rates (this might be non trivial), and then find the prices of the Arrow Debreu securitiesInstead, invert the formula for par swap rates and "bootstrap" them inductively. If you want to find the Vasicek parameters that best match a given set of swap rates, I think its best to try to minimise the total sum of squares comparing the swap rates under vasicek vs the observed swap rates.Ive been doing something very similar recently.Millhouse, mind me asking where (i.e. which city) youre from?

I've been looking at Trinomial trees quite extensively and want to share some experiences:"If you want to find the Vasicek parameters that best match a given set of swap rates, I think its best to try to minimise the total sum of squares comparing the swap rates under vasicek vs the observed swap rates."dr = (a - br)dt + sig.dzThe trinomial tree is not a very good discretisation. There is no point calibrating the parameters of the vasicek model because, usually, once you get to the tree contruction stage those values go out the window. This is because the HW constrcution only weakly captures the original dynamics. To combat this, you have to perform the calibration in situ with the construction... So what you should do (I sugest) is to pick a vol for the model (calculate historically), and make the mean reversion rate b equal to its historical value. Then calibrate the dynamics using the parameter a while you build the tree. If you calibrate to the yield curve then you only need one calibration paramter. If you decide to calibrate to Caps as well then you need to do some optimisation to work out a. More relevant to the original question:My memory of Swaps etc is a bit rusty, but surely if you have the swap rates, then those imply the zero coupon bond prices term structure. Then you can use these ZCBs to calculate/bootstrap a piece wise constant function for a? Would that work? I think this is what Dreamer is also sugegsting, I am adding that you need to do the calibration while you construct the tree, as opposed to calibrate then construct.Regards,Samy