SIAM Journal on Financial Mathematics, Volume 12, Issue 2, Page SC-1-SC-15, January 2021.
We develop a dynamic version of the SSVI parameterization 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 behavior. 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.

中文翻译：

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短消息：对称 SSVI 微笑和隐含波动率泡沫的动力学

SIAM Journal on Financial Mathematics，第 12 卷，第 2 期，SC-1-SC-15 页，2021 年 1 月。
我们为总隐含方差开发了 SSVI 参数化的动态版本，确保欧洲普通期权价格是鞅，从而防止静态和动态套利的发生。坚持在期权到期时总隐含方差必须为零的约束，我们表明没有模型——在我们的设置中——允许这种行为。这自然会产生隐含波动率泡沫的概念，即无套利交易只能在合约的部分生命周期内进行，但不能一直持续到到期。