Dynamics of symmetric SSVI smiles and implied volatility bubbles

TL;DR

This paper introduces a dynamic SSVI model for implied volatility that prevents static and dynamic arbitrage, revealing the existence of implied volatility bubbles where arbitrage-free trading is only feasible part of the option's lifespan.

Contribution

It develops a dynamic SSVI framework with no arbitrage, and demonstrates the impossibility of null implied variance at maturity within this setting, leading to the concept of volatility bubbles.

Findings

No arbitrage-free model allows null implied variance at maturity.

Implied volatility bubbles restrict arbitrage-free trading to part of the option's life.

Dynamic SSVI can prevent static and dynamic arbitrage in implied volatility modeling.

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.