Re: FdDividendAmericanOption

Posted by Joseph Wang on Dec 29, 2004; 1:36pm
URL: http://quantlib.414.s1.nabble.com/FdDividendAmericanOption-tp3453p3461.html

Still looking but I think I know what the basic trouble is.  Basically there
is a numerical instability if you make the time steps too large.  I
think that the
stepper is missing the Courant condition.

One way of thinking about this is to imagine the simulation as sound waves.
If the time step is longer than the time it takes for a wave to "move"
across
the grid, then the grid elements start getting disconnected from each other.
The consequence is that if you make the grid steps small, you have to also
make the time steps small, so that the grid steps don't get disconnected
from each other.

There are a number of ways to fix the problem.  The first is to just refuse
to do the simulation when the Courant condition fails.  The second is
involves changing the way that the time steps get calculated.

What confuses me is that the Courant condition normally doesn't affect
financial equations since financial equations usually involve "smoothing"
rather than "waves."  But I suspect that the interest rate which involves
"drifting" rather than "smoothing" is causing the finite differencer to
break.