Dynamics of Symmetric SSVI Smiles and Implied Volatility Bubbles

14 Pages Posted: 2 Oct 2019 Last revised: 2 Feb 2021

See all articles by Mehdi El Amrani

Mehdi El Amrani

affiliation not provided to SSRN

Antoine (Jack) Jacquier

Imperial College London; The Alan Turing Institute

Claude Martini

affiliation not provided to SSRN

Date Written: August 18, 2020

Abstract

We develop a dynamic version of the SSVI parameterisation for the total implied variance, ensuring that European vanilla option prices are martingales, hence preventing the occurrence of arbitrage, both static and dynamic. Insisting on the constraint that the total implied variance needs to be null at the maturity of the option, we show that no model -- in our setting -- allows for such behaviour. This naturally gives rise to the concept of implied volatility bubbles, whereby trading in an arbitrage-free way is only possible during part of the life of the contract, but not all the way until expiry.

Keywords: implied volatility, absence of arbitrage, SSVI, bubbles

Suggested Citation

El Amrani, Mehdi and Jacquier, Antoine and Martini, Claude, Dynamics of Symmetric SSVI Smiles and Implied Volatility Bubbles (August 18, 2020). Available at SSRN: https://ssrn.com/abstract=3458323 or http://dx.doi.org/10.2139/ssrn.3458323

Mehdi El Amrani

affiliation not provided to SSRN

Antoine Jacquier (Contact Author)

Imperial College London ( email )

South Kensington Campus
London SW7 2AZ, SW7 2AZ
United Kingdom

HOME PAGE: http://wwwf.imperial.ac.uk/~ajacquie/

The Alan Turing Institute ( email )

British Library, 96 Euston Road
London, NW12DB
United Kingdom

Claude Martini

affiliation not provided to SSRN

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