No Arbitrage SVI

38 Pages Posted: 4 Jun 2020 Last revised: 25 May 2021

See all articles by Claude Martini

Claude Martini

Zeliade Systems

Arianna Mingone

Ecole Polytechnique de Paris (CMAP); Zeliade Systems

Date Written: May 25, 2021

Abstract

We fully characterize the absence of Butterfly arbitrage in the SVI formula for implied total variance proposed by Gatheral in 2004. The main ingredient is an intermediary characterization of the necessary condition for no arbitrage obtained for any model by Fukasawa in 2012 that the inverse functions of the -d1 and -d2 of the Black-Scholes formula, viewed as functions of the log-forward moneyness, should be increasing. A natural rescaling of the SVI parameters and a meticulous analysis of the Durrleman condition allow then to obtain simple range conditions on the parameters. This leads to a straightforward implementation of a least-squares calibration algorithm on the no arbitrage domain, which yields an excellent fit on the market data we used for our tests, with the guarantee to yield smiles with no Butterfly arbitrage.

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

JEL Classification: G12, G13, C60, C63

Suggested Citation

Martini, Claude and Mingone, Arianna, No Arbitrage SVI (May 25, 2021). Available at SSRN: https://ssrn.com/abstract=3594528 or http://dx.doi.org/10.2139/ssrn.3594528

Claude Martini (Contact Author)

Zeliade Systems ( email )

Paris
France

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

Arianna Mingone

Ecole Polytechnique de Paris (CMAP) ( email )

Paris
France

Zeliade Systems ( email )

Paris
France

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