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Arbitrage-free SVI volatility surfaces

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  • Jim Gatheral
  • Antoine Jacquier

Abstract

In this article, we show how to calibrate the widely-used SVI parameterization of the implied volatility surface in such a way as to guarantee the absence of static arbitrage. In particular, we exhibit a large class of arbitrage-free SVI volatility surfaces with a simple closed-form representation. We demonstrate the high quality of typical SVI fits with a numerical example using recent SPX options data.

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File URL: http://arxiv.org/pdf/1204.0646
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Bibliographic Info

Paper provided by arXiv.org in its series Papers with number 1204.0646.

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Date of creation: Apr 2012
Date of revision: Mar 2013
Handle: RePEc:arx:papers:1204.0646

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Web page: http://arxiv.org/

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  1. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
  2. Jim Gatheral & Antoine Jacquier, 2011. "Convergence of Heston to SVI," Quantitative Finance, Taylor & Francis Journals, vol. 11(8), pages 1129-1132.
  3. Cousot, Laurent, 2007. "Conditions on option prices for absence of arbitrage and exact calibration," Journal of Banking & Finance, Elsevier, vol. 31(11), pages 3377-3397, November.
  4. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, Econometric Society, vol. 41(1), pages 135-55, January.
  5. Harrison, J. Michael & Kreps, David M., 1979. "Martingales and arbitrage in multiperiod securities markets," Journal of Economic Theory, Elsevier, vol. 20(3), pages 381-408, June.
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Cited by:
  1. Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2012. "Generalised arbitrage-free SVI volatility surfaces," Papers 1210.7111, arXiv.org, revised Oct 2013.
  2. Andrey Itkin, 2014. "One more no-arbitrage parametric fit of volatility smile," Papers 1407.0256, arXiv.org, revised Jul 2014.
  3. Samuel E. Vazquez, 2014. "Option Pricing, Historical Volatility and Tail Risks," Papers 1402.1255, arXiv.org.
  4. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Papers 1310.1020, arXiv.org, revised Sep 2014.

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