How would you price an American option using term structure vol. using a tree method? Using the basic binomial tree model leads to non recombining nodes. Any suggestions on how to produce a tree with combining nodes?

<t>The parameterization is suppose to be fit to variance (the square of vols) since it is the variances which are theoretically asymptotically linear in log-moneyness. It is not gauarenteed to be arb free. There are parameter restrictions to ensure this but they may have to be built into a fitting a...

has anyone tried to fit Gatheral's SVI parameterization? If so, have you implemented an algorithm which constrains the implied variacne surface to be a) positive and/or b)arbitrage free

Stochastic Calculus is essential.

<t>The original paper is:Robbins, H. and Monro, S. (1951). A stochastic approximation method. Ann. Math. Stat. 22, 400-407. I'm sure there are more recent and refined version of this algorithm that apply to different situations. In fact, there are entire text books on stochastic approximation and it...

There are several procedures for handling this. One of the most primative (yet most effective) is the "Robins-Monro" stochastic approximation algorithm.

<r>Here is an interesting approach to that problem in the context of multivariable Brownian motion and more generally diffusions.<URL url="http://www.stats.uwaterloo.ca/stats_navigation/techreports/06WorkingPapers/2006-12.pdf"><LINK_TEXT text="http://www.stats.uwaterloo.ca/stats_nav ... 006-12.pdf">...

<r>You wno't find any good answers to that question in a book. Simulating a conditioned (or tied-down ) diffusion is in general a very difficult problem which has only been very recently addressed in the literature in a satisfactory way. When the process is a Brownian motion (or a transformation of ...