Re: [Quantlib-dev] LocalvolSurface.cpp

[Michael H. <Mic...@gm...>]

Hallo Klaus,


> BiLinear interpolation doesn't work due to the jumps in the first
derivative. 
> BiCubic should be much better.

I totally agree that BiLinear interpolation is not the smoothest
interpolation out there. And you are right that in theorie you would get
points of discontinuity exactly everywhere where the linear slope changes.
Moreover the first derivative would look like a step function. That would in
theory lead to a sum of dirac delta functions in the second derivative. But
this is only in theory. Since we do discrete approximations in quantlib, I
doubt that we have this effect ...

Anyways, I do also have problems with BiCubic Interpolation. My hope is now
that the newly implemented kernel interpolation (thanks to Dima) gives
better test results.



> 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?


I would love to not use the constant extrapolation but instead the
InterpolatorDefaultExtrapolation. But this doesn't work since I run into
another problem by doing this. That is very far ITM/OTM the monoton variance
criteria is violated at some point and the program crashes due to this
issue. I have now Idea how to encounter this problem?? So I cant really say
if that would make it better ...


Anyways, can you send me a link or a paper with more information about the
arbitrage violations due to constant extrapolation? I still cant see why
constant extrapolation is violating the arbitrage criteria. At least it
doesn't violate any of the arbitrage criterias that I know (see Roger Lee or
Gatheral or Musiela/Rutkowski) ...


Greetings from Munich
Michael