Efficient estimation of integrated volatility functionals under general volatility dynamics

• Main Authors: LI, Jia, Liu, Yunxiao
• Format: text
• Language: English
• Published: Institutional Knowledge at Singapore Management University 2021
• Subjects: Brownian motion; Economic model; Transaction data; Nonlinear system; Estimator; Applied mathematics; Mathematics; Financial risk; Volatility (finance); Econometrics
• Online Access: https://ink.library.smu.edu.sg/soe_research/2561; https://ink.library.smu.edu.sg/context/soe_research/article/3560/viewcontent/efficient_estimation_of_integrated_volatility_functionals_under_general_volatility_dynamics_av.pdf
• Institution: Singapore Management University

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.