Dear all,
I hope someone can help me with the boundary conditions. I am
exploring the FDE engine (simply vanilla at the moment -- Equity.cpp
example) and I don't get around understanding the boundary conditions
-- especially Neumann. In addition, this construct with the
applyBeforeApplying, applyAfterApplying, applyBeforeSolving and such
is convoluting it even more.
1. Is the intention of the Neumann boundary conditions in QuantLib (in
this example) to keep C(i, 0) - C(i+1, 0) = C(i, T) - C(i+1, T)? C is
the call price, T is the terminal boundary (maturity) and 0 is when we
evaluate the option. This is indeed some sort of Neumann boundary
condition, since the dC/dS at the boundary is kept constant.
2. If I interpreted it correctly, what is the financial rationale
behind that sort of boundary condition? Even if I undersand it
intuitively, I've never seen it before. Maybe I misinterpreted it
alltogether, in which case I would thank if someone points me in the
right direction
3. Did you follow a particular book / notation for the implementation
that I can use as a reference (if you have anything written even
better -- even if it's unders construction). I looked at the book by
Tavella and also Wilmott (on Quantitative Finance) and I didn't see
anything similar.
4. If you know of any references I can use about boundary conditions
for BS, that would be very helpful.
Thanks a lot in advance and best regards to everyone
Eduardo
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