Dynamics of Symmetric SSVI Smiles and Implied Volatility Bubbles
14 Pages Posted: 2 Oct 2019 Last revised: 2 Feb 2021
Date Written: August 18, 2020
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
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