Hello,Sometimes, the Implied vol surface on Bloomberg or extracted from trades options are not quite smooth, before using it for local vol model, is it a good idea of doing a process of smoothing (for example with Sabr)? Thanks in advance for your help,Amang

When using your IVF in a LV model you would normally require an arbitrage free IVF. Otherwise negative local variances will appear...You can use and calibrate models to rough market data and then deduce the shape of the IVF or you can parameterize the IVF with the desired properties and fit to market data or calibrate LV's directly...

Thanks for your reply Quantosaurus.You can use and calibrate models to rough market data and then deduce the shape of the IVF or you can parameterize the IVF with the desired properties and fit to market data or calibrate LV's directly... TextIt is not quite clear to me, do you mean it is not necessary to smooth the implied vol surface before using local vol model? What I should do if the surface is not regular, not smooth? Thanks,Amang

Do you want to use the Dupire Formula?If yes you need a IVF that has certain properties: must existand the resulting local variances should be positive - which means the IVF should be arbitragefree.Does your IVF have the desired properties?

Yes, I want to use Dupire.The IVF I have is not so regular to have these properities.So I need to smooth it to obtain a arbitragefree IVF, right? And what is the common method to do this please?Thanks a lot for your help,Amang

Maybe this paper of Fengler could help you.Arbitrage free smotthing of the implied volatility surface

Thanks FrenchX! I will read it in detail.I have another question about local vol model (Dupire): If I want to price a call spread with strikes K1 and K2, may I just choose 2 points (strike = K1 and K2, maturity = maturity of call spread) on the implied vol surface to construct the local vol? and why?

No thats not the way you have to do it. Have you read the original paper by Dupire yet? It might give you an good intuition about how the model works...The calculation of LV's via option prices leads to other difficulties. The second derivative with respect to K in the denominator can be really small. And thats nasty!

Thanks to all for your help! I will read more in detail the papers and do some tests;Best Amang

I was using the Fengler method before and found it a little disappointing (complex to implement, and some instabilities on the resulting vol surface).Rather than that, I switched to the method described in this paper: http://www.zeliade.com/whitepapers/zwp-0005.pdfIt's quite easy to use and the results are impressive. It does not describe interpolation but a simple linear interpolation of vol or of var seems to work quite well.

Has anyone implemented the Carr/Wu 'A New Simple Approach for Constructing Implied Volatility Surfaces' ?Several people wanted to but gave up---too many areas to understand and too complex for them.

Have to pimp my own stuff regarding this.Basically, we can perform the interpolation in a space (other than IV or call option space) in which the monotonicity and convexity constraints are all linear. Then, quadratic programming can be used to find the model parameters. However, the method is relatively hard to implement. So if you are looking for something straightforward, go with Gatheral's SVI. Also note that it is not necessary to use regression-splines. Polynomials perform OK too, but in that case one has to make assumptions about the model.Nonparametric version of the model is described here: http://papers.ssrn.com/sol3/papers.cfm? ... 38Abstract of the parametric version is here (published already so the paper is not available):http://papers.ssrn.com/sol3/papers.cfm? ... id=1911104[/