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Arbitrage-free smoothing of the implied volatility surface

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abstract The pricing accuracy and pricing performance of local volatility models depends 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 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.
   
type journal paper
   
keywords Implied volatility surface, Local volatility, Cubic spline smoothing, No-arbitrage constraints
   
language English
kind of paper journal article
date of appearance 1-1-2009
journal Quantitative Finance
publisher Routledge, Taylor & Francis Group
ISSN 1469-7688
DOI 10.1080/14697680802595585
volume of journal 9
number of issue 4
page(s) 417-428
review double-blind review
   
citation Fengler, M. (2009). Arbitrage-free smoothing of the implied volatility surface. Quantitative Finance, 9(4), 417-428, DOI:10.1080/14697680802595585.