Posted by
Klaus Spanderen-2 on
URL: http://quantlib.414.s1.nabble.com/LocalvolSurface-cpp-tp12806p12809.html
Hi Micheal
> First of all I found some minor errors in your code which are:
yes, you are obviously right. I've changed the code in the SVN repository
accordingly. Thanks for the hint!
>
> It happens at different strikes and moneyness under some conditions that
> the d2wdy2 blows up and becomes something like -4231,12
>
Which interpolation scheme do you use for the volatility surface. The standard
interpolation is linear in the variance which very often leads to problems
with the second derivative. Therefore I've used BicubicSplineInterpolation
volTS->setInterpolation<Bicubic>();
Does this happen only for deep ITM or OTM paths? (Is this a extrapolation
problem for very large (very small) spots?) At least for "extrem"
extrapolations" I found simillar problems and "solved" it be setting negative
variances to zero.
Can I get access to the parameters of your test-surface?
> For some reason I don't get rid of the feeling that we would be better of
> to work completely without the second derivative since it seems to be
> impossible to get this numerically under control.
No, IMO the second derivative is needed.
> But would that probably
> make the dupire formula useless to us?
People your using e.g. splines together with an optimization technique like in
Reconstructing The Unknown Local Volatility Function, Thomas F. Coleman,
Yuying Li, ARUN VERMA,
http://citeseerx.ist.psu.edu/viewdoc/summary?doi=10.1.1.41.6202to solve the instability. But a lot of code is needed to implemented this;-(.
For the time being I think we should give Nando's approach a try and use the
first and second derivatives taken from the interpolation method
regards
Klaus
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