Arbitrage-Free Smoothing of the Implied Volatility Surface
AbstractThe pricing accuracy and pricing performance of local volatility models crucially depends on absence of arbitrage in the implied volatility surface: an input implied volatility surface that is not arbitrage-free invariably results in negative transition probabilities and/ or negative local volatilities, and ultimately, into mispricings. The common smoothing algorithms of the implied volatility surface cannot guarantee the absence arbitrage. Here, we propose an approach for smoothing the implied volatility smile in an arbitrage-free way. Our methodology is simple to implement, computationally cheap and builds on the well-founded theory of natural smoothing splines under suitable shape constraints. Unlike other methods, our approach also works when input data are scarce and not arbitrage-free. Thus, it can easily be integrated into standard local volatility pricers.
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Bibliographic InfoPaper provided by Sonderforschungsbereich 649, Humboldt University, Berlin, Germany in its series SFB 649 Discussion Papers with number SFB649DP2005-019.
Length: 37 pages
Date of creation: Mar 2005
Date of revision:
Arbitrage-Free Smoothing; Volatility; Implied Volatility Surface;
Other versions of this item:
- Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
- C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
- C81 - Mathematical and Quantitative Methods - - Data Collection and Data Estimation Methodology; Computer Programs - - - Methodology for Collecting, Estimating, and Organizing Microeconomic Data; Data Access
- G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates
This paper has been announced in the following NEP Reports:
- NEP-ALL-2005-11-19 (All new papers)
- NEP-ETS-2005-11-19 (Econometric Time Series)
- NEP-FIN-2005-11-19 (Finance)
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