Re: local volatility surface

Posted by Andrew Kolesnikov on
URL: http://quantlib.414.s1.nabble.com/local-volatility-surface-tp7862p7865.html


Kim Tang scribed:

> Using Fokker-Planck equation saves a lot of work for evaluating the cost
> function and the gradient of the cost function.
> I will integrate this in the calibration procedure. In the meantime a
> clever target function needs to be chosen to ensure stability of the
> calibration.
 
Hi, Kim.
In fact, what you want to do was already done in the article "The equity option volatility smile: an implicit finite-difference approach", B. G. Andersen and Rupert Brotherton-Ratcliffe, so try to find it.
Regarding your topic i have some questions:
- what is essential of volMatrix in your LocalVol class? I guess, that it should be local vol matrix, moreover varianceSurface_ should be replaced by localVolSurface_;
- what do you mean by 5th step, cause maybe it's a topic i'm really interested in? When you have some market data (ie option vols/variances) you should choose good extrapolation technique for the tails, cause
you need wide range (strikes) of local vols during implementation of MC or PDE, and this data have big impact on the LV calibration. I use simple bicubic interpolation, which is enough for LV calculation, but good extrapolation is still mystery for me.

PS i'm not really familiar with MC framework, but you could implement your engine via PDE in QL