I'm evaluating mathematical, robust techniques for fitting a skew curve to a strip of equal maturity option implied volatilities. Ideally, the technique should be robust in the face of poorly quoted strikes (i.e. a worthless option that's being quoted wide). Anyone have any suggestion on where to get started with this?

FWIW, a little investigation revealed alglib.net (www.alglib.net) that seems to provide a fairly usable set of polynomial fit algorithms (including a native port to C#, score!). Until a different tool is conclusively shown to be better this looks like a good solution.

People use - cubic spline - never tried it, changing control points around has a bit of a oscillatory effect - unwelcome- SVI model - changing its parameters has counter intuitive results- SABR - fits OK-ish but very nasty to manipulate it seems to me- a spline of second degree polynomial and linesAre you looking on delta space or strike space? I posted a question on this in the numerical methods forum a couple of days ago.

Thanks, Bouncer, appreciate the feedback.I've been using the polynomialfit method from alglib and I'm getting fairly useful results. However, picking the right degree of polynomials turns out to be fairly important. Too few and you end up with a systematic positive bias at the trough of the skew curve, too many and you run the risk of Runge error - i.e. instability at the interval edges. I'm curious what approaches folks use to deal with Runge error. For instance, limiting the polynomial degree to the square root of the number of vol points in the skew curve seems to work fairly well. Another robust techniques out there?

Ronnotel, I am not very mathematical, but I have traded a lot and seen a lot (not all of course). All of what I have seen has shortcomings. What do you mean by robust model. One that is arbitrage free or one that is practical?

What's the application of the fit? You want to use it for trading?In that case I would not use a polynomial fit, but a spline method based on moneyness/delta or strike.You can make it robust with respect to poorly quoted strikes by adding constraints over different strike and/or different maturities

My objective in seeking a fit is not to determine a theoretical volatility (I use a kernel-based smoother for that) but rather to generate an estimate of skew (dsigma/dK), which for technical reasons my kernel-based smoother does not generate efficiently. Skew is needed to plug into the "swimming delta" formula, i.e. the adjustment to make to hedging deltas under the assumption of an ATM skew that stays constant w.r.t. underlier price move.Therefore, my definition of "robust" is a polynomial of nth degree that i) minimizes error over the interval of low strike to high strike, and ii) has a slope who's avg. error is no worse at the interval edge than anywhere else in the interval (i.e. doesn't become unstable at the interval edge).I'm not a math genius, but using a polynomial with a degree that's too high will introduce this type of instability as described at the wiki page I linked below. Piecewise polynomials are also a possibility. However, one problem we always encounter is the possibility that one or more strikes is poorly quoted, or quoted wide (i.e. a worth option which is 0 bid @ $5). If that option happens to sit on the boundary between two polynomials you can get a really rotten skew.Just curious if anyone has seen this particular problem and what they did about it.