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.

翻译：我们推导了伊藤半鞅在收缩时间区间上增量的条件特征函数的高阶渐近展开。该伊藤半鞅的局部特征允许具有一般形式的动态。特别地，其路径可以是粗糙的，即表现出类似于分数布朗运动的局部行为，同时可以具有任意活动度的跳跃。该展开结果揭示了局部特征动态的不同特性所发挥的独特作用。作为我们结果的一个应用，我们基于标的资产上短期期权组合，构建了扩散波动率过程的赫斯特参数的非参数估计量。