math/SampledCurve - represents a curve which consists of n+1
arrays, one
for the independent values and n dependent values. Methods
of this
class will allow for interpolation and generating first and
second
derivative curves.
PartialDifferentialEquation - represents a
PDE
The idea behind these new classes will be to clean up the
finite
differencing code a bit. Instead of deal with raw arrays, the
code will
deal with SampledCurve's which will have facilities to
allow
interpolation, and the finite difference class will be able to pass
the
SampleCurve back up to the instrument where things can be done with
it
such as calculating delta curves and option curves.
The idea behind
a PDE class is to separate the processes from the finite
differencing
code. For example the BlackScholes process will generate a
PDE object
and the fd code will generate the finite difference operators
from the PDE
object rather than the BlackScholes process itself.
The idea behind this
is to improve code clarity as well as to allow for
PDE arithmetic.
Also, I suspect that there are some very clever things
that one can do with
Feymann-Kac once we have this in
place.
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