Re: Odd/Even errors in FdDividendAmericanOption

[Joseph Wang]

I think I know what is causing this, but it is not clear to me how to
fix it.

If you choose an odd number of grid points, then the code creates a grid
with the
underlying as one of the grid points.  If you choose an even number of
grid points
then the value of the underlying falls half way between the grid points
and you
have to interpolate to get final value of the option.

What I think you are seeing with an even number of grid points is the
error due to
the interpolation which turns out to be quite high since the underlying
is near the
strike price.  With an odd number of grid points, the underlying falls
on one of
the grid points and so there isn't this error.

I tried to modify the interpolation code, but I haven't had much luck
because things
are changing a lot near the strike price.

One way of brute forcing this is to add an extra point if the number of
grid points
is even.  Another (and probably better way) is to make the grid slightly
off center
if you have an even number of grid points so that the underlying is
always on
grid point floor(j/2).

Thoughts?

[Luigi Ballabio]

On 01/01/05 06:29:35, Joseph Wang wrote:
> I think I know what is causing this, but it is not clear to me how to fix  
> it.
>
> If you choose an odd number of grid points, then the code creates a grid  
> with the underlying as one of the grid points.  If you choose an even  
> number of grid points then the value of the underlying falls half way  
> between the grid points and you have to interpolate to get final value of  
> the option.

Yes, I agree.  As in the old joke ("Doctor, it hurts when I do this."  
"Well, don't do it.") my advice is: don't use an even number of points.  
Lame, I know :)

However, I can't reproduce the divergence without your patch. Maybe it was  
a side effect of using the price grid?

Later,
        Luigi