  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.
