Explicit No Arbitrage Domain for Sub-SVIs via Reparametrization

41 Pages Posted: 8 Jun 2021

See all articles by Arianna Mingone

Arianna Mingone

Ecole Polytechnique de Paris (CMAP); Zeliade Systems

Claude Martini

Zeliade Systems

Date Written: June 4, 2021

Abstract

The no Butterfly arbitrage domain of Gatheral SVI 5-parameters formula for the volatility smile has been recently described. It requires in general a numerical minimization of 2 functions altogether with a few root finding procedures. We study here the case of some sub-SVIs (all with 3 parameters): the Symmetric SVI, the Vanishing Upward/Downward SVI, and SSVI, for which we provide an explicit domain, with no numerical procedure required.

Keywords: Implied volatility, volatility smile, calibration, SVI, sub-SVIs, arbitrage-free parameterization

JEL Classification: G12, G13, C60, C63

Suggested Citation

Mingone, Arianna and Martini, Claude, Explicit No Arbitrage Domain for Sub-SVIs via Reparametrization (June 4, 2021). Available at SSRN: https://ssrn.com/abstract=3860011 or http://dx.doi.org/10.2139/ssrn.3860011

Arianna Mingone (Contact Author)

Ecole Polytechnique de Paris (CMAP) ( email )

Paris
France

Zeliade Systems ( email )

Paris
France

Claude Martini

Zeliade Systems ( email )

Paris
France

HOME PAGE: http://www.zeliade.com

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