  We derive a higher-order asymptotic expansion of the conditional
characteristic function of the increment of an It\^o semimartingale over a
shrinking time interval. The spot characteristics of the It\^o semimartingale
are allowed to have dynamics of general form. In particular, their paths can be
rough, that is, exhibit local behavior like that of a fractional Brownian
motion, while at the same time have jumps with arbitrary degree of activity.
The expansion result shows the distinct roles played by the different features
of the spot characteristics dynamics. As an application of our result, we
construct a nonparametric estimator of the Hurst parameter of the diffusive
volatility process from portfolios of short-dated options written on an
underlying asset.
