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Arbitrage-free smoothing of the implied volatility surface

[journal article]

Fengler, Matthias

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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.
Classification Basic Research, General Concepts and History of Economics; Economic Statistics, Econometrics, Business Informatics
Method theory application
Free Keywords Implied volatility surface; Local volatility; Cubic spline smoothing; No-arbitrage constraints
Document language English
Publication Year 2009
Page/Pages p. 417-428
Journal Quantitative Finance, 9 (2009) 4
Status Postprint; peer reviewed
Licence PEER Licence Agreement (applicable only to documents from PEER project)