Anyone has any suggestions/experience of pricing instrument on multiple trees. Say, if I have a callable floater. The reference rate might be Libor 6 month rate but the discount rate might be treasury rate. I may have to build two separate trees to generate cash flows and discount. Is this the right way of doing things?I am quite confused on this cos I need to match each node on reference rate tree to the discount tree. The one-to-one mapping relationship seems to make no sense.

Before getting too caught up in details of the numerical implementation (e.g. matching nodes on trees), you should think about what aspects of the joint stochastic process are most important to model for your purpose. If you are going to restrict yourself to a univariate process, then it would seem that you want to get the volatility structure of the reference rate right (it will generate the cash flows) and make sure the discount rate paths will match the current present value of known future cash flows. You are in this case left with the modeling choice of whether to model the discount rate as a deterministic process, or as a deterministic spread to the reference rate. If you allow yourself a second dimension, you can use this to model a stochastic spread process between the two rates. Rather than thinking of your model as represented by two trees, it may be conceptually easier to think of it as one tree with each node having multiple attributes. This way you ensure that one-to-one mapping, which is really just to say that each node represents a single state of the world.

Thank you very much, Bearish! I like your idea of adding a spread (deterministic or stochastic) to the single tree. It will resolve the mapping issue. Also, it basically use single state to represent multiple attributes as you mentioned. That makes perfect sense. I am a little bit confused about your saying: make sure the discount rate paths will match the current present value of known future cash flowsAre you saying that in this step, I am trying to match the initial term structure of the discount curve by finding the deterministic spread (assume using univariate process) against the reference rate on each node? Then, the rate level on the node will represent the reference rate and the rate - spread will basically represent the discount curve. And the whole process will be driven by the reference rate vol structure. If by incorporating stochastic spread, the vol structure of the discount curve would be included. Am I correct?