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I'm looking for an implementation of Arbitrage-Free Smoothing of the Implied Volatility Surface - Matthias R. Fengler.

Does anyone know of any existing libraries that have implemented this paper? Any method is ok (Excel, C++, Matlab, Mathematica, C#, etc).

In fact, any method that implements arbitrage free smoothing of the implied volatility surface is ok (can QuantLib do this?).

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3 Answers 3

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Arbitrage free smoothing of a local volatility surface is actually quite a difficult feat to accomplish. Its unlikely that this sort of library will be available outside of the big institutions, for some time to come.

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it is difficult.... and noisy. but totally doable actually. you just need to project onto a parametric set which by construction is arbitrage free (thats one way to do it). but hey his question is answered, no ? –  nicolas Jul 16 '11 at 19:45

I know that this question is quite old, but I uploaded a matlab implementation of the method to fileexchange: http://www.mathworks.com/matlabcentral/fileexchange/46253-arbitrage-free-smoothing-of-the-implied-volatility-surface

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A little off-topic, but arbitrage conditions are locals. and no one cares about local arbitrage (to the extent that it can not be put in practice with reasonable chance).

It's like saying look, you gamma is infinite 1 seconds before expiry : but if your dirac is 1 eur, you'll never make more than that. or, in math speak, time to look if higher order derivatives are not high as well in the region.

All this to say, I'd like to see a non parametric vol surface that actually takes the tradable grid as input. Otherwise it's like talking about angel's sex.

If you know one such lib, I'd like to hear about it.

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The whole point of specifying "arbitrage free" is to ensure that the vol surface is somewhat stable (i.e. its not offering obvious arb opportunities). You may not be able to profit from an obvious arb, but the CBOE certainly can, and it does. You want a non parametric vol surface that takes a tradable grid as input? Browse to intermarkit.com, and pay them $7500 for their local volatility surface library. These libraries exist, they are just extremely difficult to get hold of. –  Contango May 23 '11 at 10:10
I have no idea what you mean by "you can't but the CBOE can" –  nicolas May 28 '11 at 16:24
I think my remark conveys a point, which is that this notion of non arbitrability exists within some boundaries. And it just does not make sense to extend it beyond. –  nicolas May 28 '11 at 16:28
I dont mean to convey the idea that local vol arb does not exist. only that each theory has its limit. for the less gifted among you, as a mechanical engineer, I wont use formula for equilibrium when there is a air density which is less than a certain level. then it becomes particle physics. neither would one apply classical mechanics to explain laser. I wont use equilibrium formula for out of equilibrium phenomena. each theory has a domain of definition, and local vol arbitrage too. if your tools cant deal with that you should change your tools, and not the vol surface. –  nicolas Jul 16 '11 at 19:41

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