Short-time expansion of characteristic functions in a rough volatility setting with applications

Understand

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.