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Arbitrage-free SVI volatility surfaces

  • Jim Gatheral
  • Antoine Jacquier

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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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
Contact details of provider: Web page: http://arxiv.org/

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  1. 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.
  2. Matthias Fengler, 2009. "Arbitrage-free smoothing of the implied volatility surface," Quantitative Finance, Taylor & Francis Journals, vol. 9(4), pages 417-428.
  3. Clark, Peter K, 1973. "A Subordinated Stochastic Process Model with Finite Variance for Speculative Prices," Econometrica, Econometric Society, vol. 41(1), pages 135-55, January.
  4. Jim Gatheral & Antoine Jacquier, 2010. "Convergence of Heston to SVI," Papers 1002.3633, arXiv.org.
  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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