Robust calibration and arbitrage-free interpolation of SSVI slices

Jacopo Corbetta (), Pierre Cohort (), Ismail Laachir () and Claude Martini ()
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Jacopo Corbetta: Zeliade Systems
Pierre Cohort: Zeliade Systems
Ismail Laachir: Zeliade Systems
Claude Martini: Zeliade Systems

Decisions in Economics and Finance, 2019, vol. 42, issue 2, No 13, 665-677

Abstract: Abstract We describe a robust calibration algorithm of a set of SSVI maturity slices (i.e., a set of 3 SSVI parameters $$\theta _t, \rho _t, \varphi _t$$θt,ρt,φt 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.

Keywords: SVI; Volatility surface; Calibration; Arbitrage free interpolation (search for similar items in EconPapers)
Date: 2019
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Citations: View citations in EconPapers (3)

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DOI: 10.1007/s10203-019-00249-8

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