Arbitrage-Free Smoothing of Implied Volatility Surfaces
Summary
The document discusses implementation options for smoothing an implied volatility surface while enforcing arbitrage-free conditions. One response characterizes this as a difficult task and suggests that ready-made implementations may be uncommon outside large institutions. Another points to a MATLAB implementation of the cited method, indicating that an academic approach had been made available as a practical tool.
A dissenting response questions how useful local arbitrage constraints are when they cannot be exploited on a reasonable trading scale. It argues that surface construction should account for the tradable grid, since extreme local behavior may not translate into realizable profit once trade size and higher-order sensitivities are considered. The discussion does not compare implementations, establish that a particular library is suitable, or provide performance evidence; it highlights both implementation scarcity and the gap between mathematical arbitrage conditions and tradable opportunities.
Key ideas
- Arbitrage-free smoothing of an implied volatility surface is described as technically difficult.
- A MATLAB implementation of the referenced smoothing method is cited as an available resource.
- Local arbitrage violations may have little practical relevance if they cannot be traded at useful scale.
- A useful surface method should consider the market’s tradable strikes and expiries.
- The discussion offers opinions and pointers rather than comparative implementation results.
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Full text
# Lib for Arbitrage-Free Smoothing of Implied Volatility Surface? # Lib for Arbitrage-Free Smoothing of Implied Volatility Surface? 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?). ## Answer by Contango (score 4, accepted) https://quant.stackexchange.com/a/1268 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. ## Answer by pbr142 (score 3) https://quant.stackexchange.com/a/10958 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 ## Answer by nicolas (score -3) https://quant.stackexchange.com/a/1201 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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