Hi everybody,I've got a doubt regarding the Monte Carlo Least square approximation, suggested by Longstaff&Schwartz in order to price an american option...In short...You have to price an American OptionLet us suppose we calculate from the simulated paths an upper bound simply exercising always at the maximum (i.e I've got the trajiectories I pick for everyone the maximum value.. it is of course an ex post valuation but it should be clearly an upper bound!)How much should the L&S price be close to such upper bound ?Please any consideration is very very welcome Hope to hear from you vale

Valerie,The surprise to me was that for the American option it is not very far off if you take out the OLS and replace it by the maximum possible payoff (or dirty MC). A test on American options has been published by Chen Shen - computational complexity analysis of least squares monte carlo for pricing us derivatives. Hope this helps you forwardgreetings allu

Hi Allu and thank youuuu!!! Exactly the reference I need I'm going to read it carefully !! In my simulation basically I've found values -for the upper bound & the LS price - that are very close but still with significant dominance of the upper bounds .. And Now I've just realized that my simulated process is strongly suspected to be non-Markov ... In a few words I have a kind of regime switching model: one regime is a diffusion so, no problem regarding Markovianity , the other regime it is kind of strange bootstrapped discreate points from a huge sample of independent observations.. By the way the problem I think, is related with the length and the combination of the several regimes ... this is dictated as well by another non-parametric bootstrap!So my question is: the fact that I know during the trajectory simulation in which regime I am and when this regime will finish makes my simulated process non-Markov right?What do you suggest in order to make it Markov ? Should I include a kind of dummy variable that tells me in which regime I am? And how will change the Montecarlo Least square procedure in your opinion?Should I estimate a different Laguerre polynomial depending to the regime? Sorry guys for all this question . maybe I should open a new post on Markovianity problems...By the way any idea and comments will be so so so appreciated Many thanks in advance,vale

Valerie,The key question to me is why you know you are in a separate regime. Ofcourse looking ahead in the simulation you know what is going to happen. Is there maybe an outside variable indicating whether the probability to be in the up-regime? If that is not the case, I would not estimate a separate estimate for the two regimes. Maybe you want to try different polynomials however as you mention. There might be a different dispersion in case you are up than if you are down. Why not try both all the time?Which application are you working on?greetings allu

Paper that may be of interest:http://papers.ssrn.com/sol3/papers.cfm? ... provements to the Least Squares Monte Carlo Option Valuation MethodNelson M.P.C. Areal , Artur Rodrigues and Manuel J. Rocha Armada This paper proposes several improvements to the least squares Monte Carlo (LSMC) option valuation method. We test different regression algorithms and suggest a variation to the estimation of the option continuation value, which reduces the execution time of the algorithm by one third without any significant loss in accuracy. We test the choice of varying polynomial families with different number of basis functions. We compare various variance reduction techniques, using a large sample of vanilla American options, and find that the use of low discrepancy sequences with Brownian bridges can increase substantially the accuracy of the simulation method. The use of Halton low discrepancy sequences can improve the accuracy up to about four times when compared to the use of pseudo-random numbers. We also extend our analysis to the valuation of compound and mutually exclusive options. For the latter, we propose an improved algorithm which is faster and more accurate. Keywords: American options, real options, simulation, quasi Monte-Carlo methods

Yes but using CRR binomial parameters means your benchmark values are rubbish - and, once you correct for a typo in Jackel's book the Silva and Barbe approach is exactly equivalent to his (as I mentioned in my Wilmott column)

Schwarz as in the guy who produced the Schwarz lemma fromcomplex analysis? Nah probably not. Many Schwarzes out there.But man... I sure loved that lemma back in complex anylysiscourses. Good memories.

Oops this one is Schwartz and not Schwarz. Ignore me please.

Paper about solving the storage problem with Monte Carlo for Longstaff/Schwartz. "Just-in-Time Monte Carlo for Path Dependent American Options' Dutt and Welke, Journal of Derivatives Summer 2008. "...propagating stochastic price processess bakcward in time step...Wiener, Ornstein-Uhlenbeck, Clark, CIR"