Journal of Computational Finance

The extended SSVI volatility surface

Sebas Hendriks and Claude Martini

  • We extend the Gatheral and Jacquier SSVI volatility surface parameterization by making the correlation variable maturity-dependent.
  • We present necessary and sufficient conditions for this extended SSVI surface for no calendar-spread arbitrage.
  • We show the increased calibration accuracy of this extended SSVI parameterization compared to the regular SSVI parameterization for DJX vanilla option data.

We extend Gatheral and Jacquier’s  surface stochastic  volatility-inspired (SSVI) parameterization by making the correlation maturity  dependent and obtaining the necessary and sufficient conditions for no calendar-spread arbitrage. The parametric families for the correlation for which those conditions are explicit are also provided. This extension of the SSVI formula typically increases the calibration accuracy for short maturities and may also be more robust in stressed market conditions.

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