Robust calibration and arbitrage-free interpolation of SSVI slices

We describe a robust calibration algorithm of a set of SSVI maturity slices (i.e., a set of 3 SSVI parameters θ _t, ρ _t, φ _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.