>> Good notation makes a field much easier to learn and mistakes harder to make. Using lots of different letters with no relationships is a bad habit from the days of fixed-character processing.agree, part of the problem is that Quantitative Finance is (as we said again and again) a young disciplineI think (hope) that in twenty years assumptions and notations will be much more uniform

Hi Paul, Could you tell me what should be considered for the value-matching and the smooth pasting when the process is not a Brownian motion? e.g fat-tailed processes.Thankyou.

Hi,Apologies if this has been answered before but I couldn't find it with a search. I am interested in pricing american options on futures. I would welcome a reference if it's easier.I think that this can be done by finding the european value and using whaley (or alternative) algorithm. Is one of these algorithms considered optimal?Also, how would the calculation for the greeks be affected by the options being american and on futures?Finally. Hypothetically how would one go about pricing excotics on futures. Would you have to work from first principles with Black's (?) pde, use appropriate boundary conditions and then try and estimate it?

At the moment, I am comparing several methods to price American options.From what I know, the speed of computation and the accuracy are the most important criteria. Furthermore, one can check whether the method is easy to implement and whether it can be used to value more complicated structures.Are there any other meaningful criteria that have to be considered when comparing the methods?Svunt

Perhaps some sort of stability/reliability criterion. But perhaps that's covered by "accuracy"?

Thanks Johnny,I guess the stability/reliability criterion is only relevant to the explicit finite difference scheme. Correct me if I am wrong.However, I just remembered a paper by Broadie and Detemple*. They mention additional factors such as theeconomic insight offered by the method and the availability of derivative information.These are pretty broad definitions and I don't understand what exactly the authors mean by those factors. For example, when I read the word "economic", I tend to think of macro- and microeconomics. I cannot think of what the economic implications of methods suggested by CRR, Leisen and Reimer, Barone-Adesi and Whaley, etc., are.Forgive me if I am too shortsighted on this subject. Any enlightenment is therefore welcome.Svunt*American Option Valuation: New Bounds, Approximations, and a Comparison of Existing MethodsMark Broadie, Jerome DetempleThe Review of Financial Studies, Vol. 9, No. 4. (Winter, 1996), pp. 1211-1250.

it seems to me that the valuation of standard american options is very well developed . There are pretty accurate and fast methods around.so I wonder what is done in terms of future research in american options pricing. is still a lot of research done on how to price standard american options or is there a switch towards more complicated payoffs? if quite a lot of research effort is put in the valuation of standard American options, what is the main focus at the moment? svunt

It seems like everyone and their brother comes up with yet another semi-analytic approximation for American pricing under Black-Scholes.However, I've yet to see anyone do anything about American pricing under a more complex model (like Heston or Merton). I think a semi-analytic approximation there would be cool.

QuoteOriginally posted by: mghigginsIt seems like everyone and their brother comes up with yet another semi-analytic approximation for American pricing under Black-Scholes.However, I've yet to see anyone do anything about American pricing under a more complex model (like Heston or Merton). I think a semi-analytic approximation there would be cool.This is not an accident. Black-Scholes is not only analytic, it can be evaluated with only a few arithmetic operations. Models that require numerical evaluation or simulation can generally incorporate the American feature directly.