Are there any market practices to extrapolate the volatility smile for equities? I already have an arbitrage free interpolated call prices data and I'm looking for a method to extrapolate beyond the last available data. I tried the method described here : S. Benaim, M. Dodgson, and D. Kainth. An arbitrage-free method for smile extrapolation. Technical report, Royal Bank of Scotland, 2008. 1, 2, but I have arbitrageable prices (Plus there is no indication that beyond the vicinity of the last point, we obtain arbitrage free prices.
I'm a fan of fitting a distribution, and then implying vols from that in the wings.
You'll get an arbitrage free surface, that makes sense.
A very simple example is to use gaussians to build a pdf, and then numerically price the options from it. Here's an example fitting FTSE options using just 2 gaussians to create the implied pdf and resulting smile:
You're of course free to use other distributions as your basis functions to create your pdf, as well as mixtures of different functions - what i liike about doing this is that you get a very nice smooth distribution. No spline nodes causing weird behaviour in the derivatives, and it integrates to 1.
You just price the options by numerically integrating your pdf.
I welcome anyone to point me at a particularly nasty smile from the past and i will happily fit it and put the results here.