Title: Short-time expansion of characteristic functions in a rough volatility setting with applications
Authors: Carsten Chong - Columbia University (United States)
Viktor Todorov - Northwestern University (United States)
Viktor Todorov - Northwestern University (United States) [presenting]
Abstract: The aim is to derive a higher-order asymptotic expansion of the conditional characteristic function of the increment of an Ito semimartingale over a shrinking time interval. The spot characteristics of the Ito semimartingale are allowed to have dynamics of general form. In particular, their paths can be rough; that is, they exhibit local behavior like that of a fractional Brownian motion, while at the same time have jumps with an 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.