The uncertain volatility model has long ago attracted the attention of practitioners as it provides worst-case pricing …

used, in particular for long expiries and in high volatility environments. For example, we obtain positive sensitivities to …

We revisit the so-called Bergomi-Guyon expansion (Bergomi and Guyon, Stochastic volatility's orderly smiles, Risk, May … 2012). The expansion provides the smile of implied volatility at second order in the volatility of volatility for general … stochastic volatility models, including variance curve models. First, we present a new derivation of the price expansion which …