What I am trying to do is to use Monte Carlo simulation on Hull-White tree. That is first of all construct a HW short rate tree based on term structure and yield volatility. Then I want to use Monte Carlo simulation to produce paths for different assets on the HW tree. There maybe some correlation between these assets as well.. I implemented first phase that is constructed the HW tree .. I have read all the comments in willmott related with this subject.. But I still have questions in my mind on how to proceed.. So, could somebody help me.. Thanks in advance for your helps.

I have found a paper which exactly does what I thought. It is "E.J. Dockner and H. Moritsch, 1999. Pricing Constant Maturity Floaters with Embedded Options Using Monte Carlo Simulation". What I will do is; a) starting from first node of HW trinomial tree generate a uniform random variate to decide the direction of MC path b) computing the underlying asset's price in the next time step by the following formula (r is the interest rate of node currently we are on) c) By applying a) and b) go to until the maturity of the option. d) So after c) we have a one path of underlying asset's price, discounts so we can easily find the price of the european or american options written on underlying asset e) repeat these steps 10000 times and take the average.. Note: Correlation can easily be included in step b).. Please give me some comments..

I have realized how much I am wrong in my view after communicating with Mr. Dockner. This kind of approach can only be applied for options that are only dependent on interest rates... All the best..

Why is this approach wrong?

mathfinlove just models the r with the HW tree, not the S. And, btw, the r is not necessarily the same as in the formula below.

mathfinlove, in general you can do MC on a tree if you want. It's rarely optimal to do so, but I've seen it used by colleagues. And Balmung is of course correct in pointing out that r in the B-S world is a completely different r than in the H-W world.

Can we just do MC in general just like the equity side, but now we have the dynamics to bedr = (alpha(t) - ar) dt + sigma * root(T) * W. ie, randomly generate W, based on the above formula to get dr, then r + dr is our next r. Is this correct?

thanks got it

I'm resurrecting this discussion because I want to know wheter the algorithm suggested by Mathfinlove coul be indeed applied if one has to price an interest rate derivative. I know that maybe it is not optimal but when the tree has many time steps and one needs the full forward curve for each node, maybe doing a montecarlo on the tree is a good solution.What do you think?