Hello,I was reading Hua He's 1990 paper and trying to use two trinomial trees to price an American spread option on two assets. It looks to me that the tree would be recombining, but not in the traditional sense. Hence, I am not able to obtain a general form for finding the underlying asset price based on the time step and node location. This means that one would either have to store the entire stock price lattice (since it is an American option), which is obviously very inefficient, or run the stock price lattice once, get to maturity, and then use backward induction at every time step to obtain the underlying asset prices. One would only have to store the current and previous time steps in the second option.Am I missing something here? Has anyone attempted to use a trinomial tree where m!= 1 for the middle node? I feel like I am making this more complicated than it should be. Thanks!

It looks like trinomial trees for which m!=1 are considered nonrecombining, even though some nodes do recombine but in a non-systematic fashion. I am not aware of a general form for calculating node values based on the time step and node location for such trees. In that case, I cannot fathom why anyone would want to use a tree that grows at a rate of 3^n.

QuoteOriginally posted by: GTIIt looks like trinomial trees for which m!=1 are considered nonrecombining, even though some nodes do recombine but in a non-systematic fashion. I am not aware of a general form for calculating node values based on the time step and node location for such trees. In that case, I cannot fathom why anyone would want to use a tree that grows at a rate of 3^n.I don't know of this method for 2-factor but I have done finite difference for 2-asset and it's not so dificult. Of course, it is a different kind of approach and may not be what you are looking for.

I thought about using FDM, but doesn't that require knowing the PDE that discribes the option value? Can you elaborate on this approach further?

QuoteOriginally posted by: GTII thought about using FDM, but doesn't that require knowing the PDE that discribes the option value? Can you elaborate on this approach further?The PDE is in Zhang's book and is OK (he uses Ito). Then we can use FDM stuff. I presume you have a 'normal' 2-asset spread with correlation? Just out of curiosity, have you a source for 2-factor tri?

Yes, we have two correlated lognormal processes, first being GBM and the second with an added term sigma2*sqrt(1-row)*s2*dw2. S2 is the price of the second asset, row is the corelation coeff, and dw2 is the second BM.Hua He's 1990 paper basically shows that n-variate (n+1)-nomial trees would approximate an n-dimensional diffusion process. I'm not sure if this is the type of source you were referring to.In my case, I have 2 assets, so I would need two separate non-recombining trinomial trees. I'm going to try implemeting this but it will be computationally demanding.

> In my case, I have 2 assets, so I would need two separate non-recombining trinomial trees. I'm going to try > implemeting this but it will be computationally demanding. I agree, and it's a bit of non-trivial datastructure (C++?). FDM is just a matrix at every level.