Observed high-frequency financial prices can be considered as having two components, a true price and a market microstructure noise perturbation. It is an empirical regularity, coherent with classical market microstructure theories of price determination, that the second moment of market...

Vast empirical evidence points to the existence of a negative correlation, named ”leverage effect”, between shocks to variance and shocks to returns. We provide a nonparametric theory of leverage estimation in the context of a continuous-time stochastic volatility model with jumps in...

A simple and robust approach is proposed for the parametric estimation of scalar homogeneous stochastic differential equations. We specify a parametric class of diffusions and estimate the parameters of interest by minimizing criteria based on the integrated squared difference between kernel...

We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other...

Using recent advances in the nonparametric estimation of continuous-time processes under mild statistical assumptions as well as recent developments on nonparametric volatility estimation by virtue of market microstructure noise-contaminated high-frequency asset price data, we provide (i) a...

We propose a functional estimation procedure for homogeneous stochastic differential equations based on a discrete sample of observations and with minimal requirements on the data generating process. We show how to identify the drift and diffusion function in situations where one or the other...