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My problem is that I have a surface of implied black volatilites that is supposed to represent market data. However, the surface contains some slight arbitrage. More precisely, the graph contains butterfly arbitrage for some strikes due to non-convexity of the discrete graph of call-option values. This arbitrage, obviously, causes problems in later mathematical procedures that requires no arbitrage.

So my question here is: Is it possible, in a not too time consuming and complicated way, "wash" the data from arbitrage? To find the closest arbitrage free surface in some way. Any references to articles about the subject would be appreciated.

(Not interested in references to Matlab/Mathematica or other premade functions/libraries/programs. I am interested in the mathematics behind the problem and implementing it myself if possible)

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It sounds like you haven't filtered away static arbitrage strategies (such as butterfly spreads, call spreads and calendar spreads) from your data. To keep my answer short and concise, there's a paper by Carr & Madan (2005) that establish the structure of a finite set of tests (a filtering procedure) on your option quotes. When you are left with options satisfying these 'static' no-arbitrage bounds, then the quotes are free of static arbitrage, which will help you further on. I recommend you to take a look at that paper, if you haven't already. Hopefully this provide some guidance.

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  • $\begingroup$ Thanks, I will have a look at that paper. It is not my own data I try to use, but rather external crappy data that I try to make the best of. $\endgroup$ – Jesper Tidblom Feb 8 at 11:39

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