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arXiv · 1804.04924

Robust calibration and arbitrage-free interpolation of SSVI slices

Pierre Cohort·Jacopo Corbetta·Claude Martini·Ismail Laachir
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Abstract

We describe a robust calibration algorithm of a set of SSVI slices (i.e. a set of 3 SSVI parameters $\theta, \rho, \varphi$ attached to each option maturity available on the market), which grants that these slices are free of Butterfly and 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, parsimonious solution to the smile problem, which has the potential to become a benchmark one.

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Pierre Cohort, Jacopo Corbetta, Claude Martini, Ismail Laachir. 2018-04-13. Robust calibration and arbitrage-free interpolation of SSVI slices. https://arxiv.org/abs/1804.04924

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