Efficient Estimation Of Integrated Volatility Functionals Under General Volatility Dynamics

We provide an asymptotic theory for the estimation of a general class of smooth nonlinear integrated volatility functionals. Such functionals are broadly useful for measuring financial risk and estimating economic models using high-frequency transaction data. The theory is valid under general volatility dynamics, which accommodates both Itô semimartingales (e.g., jump-diffusions) and long-memory processes (e.g., fractional Brownian motions). We establish the semiparametric efficiency bound under a nonstandard nonergodic setting with infill asymptotics, and show that the proposed estimator attains this efficiency bound. These results on efficient estimation are further extended to a setting with irregularly sampled data.