We extend Gatheral and Jacquier SSVI volatility surface parameterisation by making the correlation maturity-dependent, obtaining necessary and su cient conditions for no calendar-spread arbitrage. Parametric families for the correlation are provided for which those conditions are explicit. This...

The rough Bergomi model introduced by Bayer, Friz and Gatheral has been outperforming conventional Markovian stochastic volatility models by reproducing implied volatility smiles in a very realistic manner, in particular for short maturities. We investigate here the dynamics of the VIX and the...

We study the term structure of the implied volatility in a situation where the smile is symmetric. Starting from the result by Tehranchi that a symmetric smile generated by a continuous martingale necessarily comes from a mixture of normal distributions, we derive representation formulae for the...