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Robust calibration and arbitrage-free interpolation of SSVI slices

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Abstract

We describe a robust calibration algorithm of a set of SSVI maturity slices (i.e., a set of 3 SSVI parameters \(\theta _t, \rho _t, \varphi _t\) attached to each option maturity t available on the market), which grants that these slices are free of butterfly and of calendar spread arbitrage. Given such a set of consistent SSVI parameters, we show that the most natural interpolation/extrapolation of the parameters provides a full continuous volatility surface free of arbitrage. The numerical implementation is straightforward, robust and quick, yielding an effective and parsimonious solution to the smile problem, which has the potential to become a benchmark one. We thank Antoine Jacquier and Stefano De Marco for useful discussions and remarks. All remaining errors are ours.

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References

  • De Marco, S: On probability distributions of diffusions and financial models with non-globally smooth coefficients, Ph.D. thesis (2010)

  • De Marco, S., Martini, C.: Quasi-explicit calibration of Gatheral’s SVI model. Zeliade White Paper (2009)

  • Gatheral, J.: The Volatility Surface: A Practitioner’s Guide. Wiley (2011)

  • Gatheral, J., Jacquier, A.: Arbitrage-free SVI volatility surfaces. Quant. Finance 14, 59–71 (2014)

    Article  Google Scholar 

  • Hendriks, S., Martini, C.: The Extended SSVI Volatility Surface. SSRN, Amsterdam (2017)

    Book  Google Scholar 

  • Jäckel, P.: Let’s be rational. Wilmott 75, 40–53 (2015)

    Article  Google Scholar 

  • Le Floch, Fabien: When SVI breaks down, https://chasethedevil.github.io/post/when-svi-breaks-down/, (2017)

  • Lee R.W.: Implied volatility: Statics, Dynamics, and Probabilistic Interpretation. In: Baeza-Yates R., Glaz J., Gzyl H., Hüsler J., Palacios J.L. (eds.) Recent Advances in Applied Probability. Springer, Boston, MA (2005)

  • Tehranchi, M.R.: Asymptotics of implied volatility far from maturity. J. Appl. Prob. 46, 629–650 (2009)

    Article  Google Scholar 

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Authors and Affiliations

  1. Zeliade Systems, 56 rue Jean-Jacques Rousseau, Paris, France

    Jacopo Corbetta, Pierre Cohort, Ismail Laachir & Claude Martini

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  1. Jacopo Corbetta
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  2. Pierre Cohort
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  3. Ismail Laachir
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  4. Claude Martini
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Correspondence to Jacopo Corbetta.

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Corbetta, J., Cohort, P., Laachir, I. et al. Robust calibration and arbitrage-free interpolation of SSVI slices. Decisions Econ Finan 42, 665–677 (2019). https://doi.org/10.1007/s10203-019-00249-8

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  • DOI: https://doi.org/10.1007/s10203-019-00249-8

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