questions about pricing American Option in MC method

[kangyin ye]

Hi guys,

I found that the QuantLib MCAmericanEngine implement has a little different from the reference paper 

"Valuing American Options by Simulation: A Simple Least-Squares Approach". 

In AmericanPathPricer constructor, except the parabolic function a+bX+cX*X, the payoff function is also 

incorperated into basis function. I guess the author assume the additional one improves the accuracy of 

fitting the conditional expectation. 

Can anyone give more info about the consideration of adding payoff function. Thanks in advance!

ky

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[Kakhkhor Abdijalilov]

The payoff function always included into the basis system, even into
monomial system. Yes, including the payoff might improve the accuracy.
Even if the effect negligible, it doesn't hurt anything. Any
collinearity in the basis is taken care off by SVD.

Note to the developers:
I was looking into the file  longstaffschwartzpathpricer.hpp and
noticed that moving vectors x and out of the for loop will avoid
re-allocation.

//--------------Original Code -----
for (Size i=len-2; i>0; --i) {
    std::vector<Real>      y;
    std::vector<StateType> x;

//------------Replace with this ----
std::vector<Real>      y;
std::vector<StateType> x;
for (Size i=len-2; i>0; --i) {
    y.clear();
    x.clear();
//---------------------------------------

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[Luigi Ballabio]

On Tue, 2010-09-07 at 14:09 -0500, Kakhkhor Abdijalilov wrote:
> Note to the developers:
> I was looking into the file  longstaffschwartzpathpricer.hpp and
> noticed that moving vectors x and out of the for loop will avoid
> re-allocation.

Right, I'll do that.

Luigi


--

Hanlon's Razor:
Never attribute to malice that which is adequately explained
by stupidity.



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