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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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References

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  1. Matthias R. Fengler, 2005. "Arbitrage-Free Smoothing of the Implied Volatility Surface," SFB 649 Discussion Papers SFB649DP2005-019, Sonderforschungsbereich 649, Humboldt University, Berlin, Germany.
  2. 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.
  3. Jim Gatheral & Antoine Jacquier, 2010. "Convergence of Heston to SVI," Science & Finance (CFM) working paper archive 1002.3633, Science & Finance, Capital Fund Management.
  4. 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.
  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. Stefano De Marco & Caroline Hillairet & Antoine Jacquier, 2013. "Shapes of implied volatility with positive mass at zero," Science & Finance (CFM) working paper archive 1310.1020, Science & Finance, Capital Fund Management.
  2. Gaoyue Guo & Antoine Jacquier & Claude Martini & Leo Neufcourt, 2012. "Generalised arbitrage-free SVI volatility surfaces," Science & Finance (CFM) working paper archive 1210.7111, Science & Finance, Capital Fund Management, revised Oct 2013.
  3. Samuel E. Vazquez, 2014. "Option Pricing, Historical Volatility and Tail Risks," Science & Finance (CFM) working paper archive 1402.1255, Science & Finance, Capital Fund Management.

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