Estimating the spot volatility in presence of infinite variation jumps

Abstract: 

We study the kernel estimation of spot volatility of the semi-martingale using high frequency data, where the underlying model can contain a jump part with infinite variation jumps. The estimator is based on representation of characteristic function of the Levy process. The consistency of the estimator is established under some weak assumptions. By assuming that the process behaves like a stable Levy process within a neighbourhood of zero, we derive the central limit theorem, which shows that the proposed estimator is variance efficient. Simulation studies justify the theoretical results, and we also apply the estimator to some real high frequency database.