I'm working on a project to test different vol surface models based on ordinary B&S implied vols. The idea is similar to that taken when creating zero coupon curves, either an economic model with a "no arb constraint" or functional smooth models with weighted best fit approaches. There should be loads of different surface models, fitting and smoothing techniques for this but I can't seem to find anything written on this for ordinary index and equity impl surfaces?!Anyone?Rgds,Rutger

hi, are you asking about the actual forward equation or the interpolation scheme?

Sorry about being unclear. I'll exemplify from building zero curves from interest rate data. Then I see two options;1) use the actual zero yields (read impl. volatilities) and connect the points on the surface with some algorithm (usually bootstrap, but could be linear interpolation or some sort of spline). This will obviously demand the surface to be "complete" with regards to pricing.2) propose a functional form, making financial sense or not, and fit the points with some sort of least squares (i.e. for interest rates, Nelson-Siegel,etc.)So back to the questions:1) if one has got a fairly complete set of impl. vols, what would be appropriate liquidity adjustment and interpolation schemes?2) if one (also) need a functional form, any good examples, using which fitting schemes?If I don't remember incorrectly, ORC Software, trading platform for equity options, use two second degree equations joined together to form the surface. There must be much better examples ...Thank's in advance!Rutger - newbie in equities -

maybe Nadaraya-Watson kernel will help?it belongs to Applied Nonparametric Regression and Smoothing.http://www.xplore-stat.de/ebooks/ebooks.htmlnik

Nicol,That's certainly one way to do it ...Will try the smoothing model for some other data (for a bit more illiquid examples),and see how it looks.Thanks for the link!Rgds,Rutger

i tried this kernelworks pretty fast. after some sorting of past historical data and clever addition of current points it can help in on-line surface monitorbecareful to apply it. general advice: generate some random points over some surface (kind of simulate actual trades activity), add noisereconstruct surface and compare with input.change noise level, change trading frequency, tabulate optimal smoothing parameters h_i's for different regimes and your surface_reconstructor is ready.good luck.nik