Realized Laplace transforms for pure jump semimartingales with presence of microstructure noise

This paper considers the estimation of integrated Laplace transform of local volatility' by using noisy high-frequency data. We allow for the presence of microstructure noise under a pure jump semimartingale over a fixed time interval [0,t]. We propose an efficient estimator for the integrated Laplace transform of volatility via applying the pre-averaging method. Under some mild conditions on the Levy density, the asymptotic properties of the estimator including consistency and asymptotic normality are established. Simulation studies further confirm our theoretical results.