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@article{ Fengler2009,
 title = {Arbitrage-free smoothing of the implied volatility surface},
 author = {Fengler, Matthias},
 journal = {Quantitative Finance},
 number = {4},
 pages = {417-428},
 volume = {9},
 year = {2009},
 doi = {https://doi.org/10.1080/14697680802595585},
 urn = {https://nbn-resolving.org/urn:nbn:de:0168-ssoar-221375},
 abstract = {The pricing accuracy and pricing performance of local volatility models depend on the absence of arbitrage in the implied volatility surface. An input implied volatility surface that is not arbitrage-free can result in negative transition probabilities and consequently into mispricings and false greeks. We propose an approach for smoothing the implied volatility smile in an arbitrage-free way. The method is simple to implement, computationally cheap and builds on the well-founded theory of natural smoothing splines under suitable shape constraints.},
}