Howdy,I'm looking at 'Back to Basics:...' (Huag, Huag, Lewis 2003) in relation to an American put with underlying geometric Brownian process. I'm wondering about the computational cost of this approach.For American puts it seems to me that if you use a tree method the approach you have non-combining and just as expensive as any other non-combining. With Monte Carlo you have just as expensive as Monte Carlo.Is that correct? The reason I ask is for calls the HHL approximation approach is much faster than a non-recombining tree and just as (if not more) accurate. This improvement is one of the key points - so I was wondering if I've missed a key point with the American puts Cheers,qUosh.-------------The back story:I quote: "For American-style put options, as is also well-known, it can be optimal to exercise at any time prior to expiration, even in the absence of dividends. So, in this case, you are generally forced to a numerical solution, evolving the stock price according to your model. This isthe well-known backward iteration. What may differ from what you are used to is that you must allow for an instantaneous drop of D(S) on the ex-date."I think there are only two choices in evolving the stock:1) Tree - would be non-combining as a result of discreet dividend, and only difference from a 'standard' tree is to set any negative node to zero (liquidator) or don't take the dividend out (survivor).2) Monte Carlo - For each realization evolve stock price according to GBM and drop on ex-div date. If this causes negative price, set to zero or don't drop.Seems there is no computation benifit of this approach. (I'm not denying there is huge improvement of the logic of this approach).

You've got it right; for an amer.-style put/call there's a conceptual benefit.In addition, there's a computational benefit for the call, but not the put. The benefit for the call is that you get to make "one big jump" to the ex-div dates.For the put [under the GBM model], an explicit lattice method on a regular grid with some (dx = d logS, dt) seems to me the straightforward approach. The computational burden is the same (for the put) with or without the dividends,since the decision to exercise or not must be made at each dt.regards,