No arbitrage global parametrization for the eSSVI volatility surface

Abstract

This article describes a global and arbitrage-free parametrization of the eSSVI implied volatility surfaces introduced by Hendriks and Martini [The extended SSVI volatility surface. J. Comput. Finance, 2019, 22, 25–39]. A calibration of such surfaces has already been proposed by the quantitative research team at Zeliade Systems [Cohort et al., Robust calibration and arbitrage-free interpolation of SSVI slices. Decisions Econ. Finance, 2019, 42, 665–677], but the calibration algorithm is sequential in expiries (one maturity is calibrated after the other), lacking a global view on the surface. The alternative calibration suggested in this article targets all maturities at once and always guarantees an arbitrage-free fit of market data.

Keywords:

• Implied volatility
• Volatility surface
• Calibration
• SVI
• eSSVI
• Arbitrage-free parametrization

JEL Classification:

• G12
• G13
• C60
• C63

Acknowledgments

The findings in this paper and their implementation would not have been possible without the key support of Zeliade Systems team and especially Claude Martini, who supported the project and laid the foundations for the results, Pierre Cohort, who implemented the Python code, and Ismail Laachir, who took care of the whole data manipulation.

I thank Stefano De Marco for the detailed and patient reading of the article and for the improvements suggested.

I also thank TASE for providing the data displayed in the present article and in particular or Amir and his team for technical suggestions on the parameters setup.

Disclosure statement

No potential conflict of interest was reported by the author.