Re: [Quantlib-dev] LocalvolSurface.cpp

[Dima <dim...@go...>]

Just a remark regarding interpolation. I've implemented kernelinterpolation
(its in the trunk), which can be made sufficiently smooth
by choosing a proper standard deviation of the gaussian kernel. I've heard
that this smoothness property makes it a good choice for local vol
calibrations.
I don't have any personal experience with that though.



2009/4/29 Klaus Spanderen <kl...@sp...>

> Hi
>
> > I ran my tests with both. BiLinear and BiCubic intrapolation. I
> encountered
> > the instability issues with both.
>
> BiLinear interpolation doesn't work due to the jumps in the first
> derivative.
> BiCubic should be much better.
>
> > You are right that the problems appear far ITM and OTM. But I cant really
> > figure out why, since I set up a constant extrapolation for both, Strike
> > and Maturity in my BlackVarianceSurface.
>
> Constant extrapolation could introduce arbitrage violations far ITM or far
> OTM
> and these arbitrage violations can lead to negative variances. Is this part
> of the problem in your tests?
>
> > Thank you also for the link. To me it seem like if we want to use the
> > dupire formula efficient, stable and productive, we wont get around
> > implementing some fancy optimization-splines and smoothing algorithm.
>
> yes.;-)
>
> regards
>  Klaus
>
>
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