Posted by
Sinha, Amitesh-2 on
URL: http://quantlib.414.s1.nabble.com/FdAmericanOption-problem-and-Tracing-tp3483p3484.html
I am a new user on this forum. I would like to understand this problem in
order to understand & contribute.
Could somebody please mail a summary of this problem please?
-----Original Message-----
From:
[hidden email]
[mailto:
[hidden email]]On Behalf Of Joseph
Wang
Sent: Thursday, January 06, 2005 10:50 AM
To:
[hidden email]
Cc: Graham Miller; Luigi Ballabio
Subject: [Quantlib-users] FdAmericanOption problem and Tracing
I've tried some numerical experiments, and I don't think that the
problem is easily fixable,
and that the focus should be to put in some checks to make sure that the
time steps are
such that the problem doesn't develop.
I think that the problem is an interaction between large time steps,
small space steps,
and boundary conditions. If you have large time steps and small space
steps, the error
from the value of the point next to the boundary becomes large. This
results in an
artificially large second derivative which then destroys the
simulation. What I did to
convince myself this was the problem was to artifically set the problem
up so that it
is a pure diffusion problem and then run the simulation with different
differencing
methods. In all cases, you see problems start to in the penultimate
point and then
spread to the middle.
Also something that I've seen that I think is interesting syntax is
#define TRACE(x) if (turn_on_trace(x)) trace_ostream
This lets you write things like
TRACE(2) << "Trace statement";
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