How do u price CAP using hull and white short rate model. do we take caplet tenor as the delta t in the hull and white model?Secondly if u r generating a term structure using Hull and white model do we take unequal time steps similar to the term structure u aretaking??Thirdly if u are using a trinomial tree then we calculate the options price at the last node and do a backward induction of the same to reach the final option price. so while pricing caps we need to generate the tree for each caplet or can do with the entire cap with one tree. It wud be a gr8 help if somebody can explain the methodology for applying the trinomial tree for the calculation of CAP price.

There are analytic solutions available for caps and floors in the HW model. Is there any particular reason why you want to use a tree?

Yes!using a tree gives you the freedom to see what is going on,Write a Java code to show the tree. Change the tree parameters and see how the tree dances around (and you can sing along dance my baby dance, too) and do all that is possible with the rates and get the satisfaction that YOU ARE NOT PLAYING WITH A BLACK BOX. The termination of the tree can be delayed with large amount of computing power available at a cheaper price.Well, after doing it for a couple of hours you can still be shoked to find that the next day's rates are not part of the tree even if you worked out hundreds of scenarios. That is besides the point.What people are doing now-a-days are they are using the tree branches as building blocks for simulating scenarios etc.Cheers

An exact closed-form solution is a black box? Can I quote you on that? By definition you introduce numerical error as soon as you build a tree. I'll grant you that trees are useful for path dependent valuation requiring simulation, that is rather expanding on the original question starting this thread, isn't it? If you want to catch a mouse, build a mousetrap. If you want to rule the world, well then...

"you can sing along dance my baby dance"? Wish my models came with tranquilizers too!

Other reasons to price simple caps and floors on a tree might be:- you can compare the results with the closed-form solution in order to validate your tree implementation;- you can use them (together with the closed-form solution) as control variates for more exotic products.Luigi

Another problem rises with closed formula (at least when you use a black model) is the accuracy of the convexity adjustment for large maturities and/or high volatilities. However with the tree you don't have this problem.