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Arbitrage-Free Smoothing of the Implied Volatility Surface

version (55.5 KB) by Philipp Rindler
Function to smooth call option prices and implied volatilities free of static arbitrage.


Updated 16 Apr 2014

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The function is an implementation of the method proposed in Fengler, M. (2009). Arbitrage-Free Smoothing of the Implied Volatility Surface. Quantitative Finance, 9:4, 417-428.
The method uses smoothing splines under shape constraints to estimate call option prices as a function of strike and time-to-maturity. Based on these prices, implied volatilities can be obtained.

Cite As

Philipp Rindler (2020). Arbitrage-Free Smoothing of the Implied Volatility Surface (, MATLAB Central File Exchange. Retrieved .

Comments and Ratings (4)


Xuchen, you would set those to minimum tick


Xuchen Zhang

I got some negative prices (although very close to 0). How can I get the implied volatility from these numbers?


Is there a problem when the output gamma \gamma is negative as did in you example?
seems to me that the paper urges to have positive second derivative..

MATLAB Release Compatibility
Created with R2013b
Compatible with any release
Platform Compatibility
Windows macOS Linux

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