Econometric Analysis of Continuous-Time Asset Return Models Using High Frequency Data

This paper proposes a new approach to the statistical inference of continuous-time asset return models with latent or unobserved state variables using high frequency return observations. We construct unbiased minimum-variance estimators of the latent variables that are also consistent with the model specification. We illustrate using examples the construction of unbiased minimum-variance estimators of latent variables and demonstrate via simulation their properties in comparison with other commonly used proxies. The unbiased estimators of latent variables enable us to develop a parsimonious and yet flexible GMM estimation procedure for the continuous-time asset return models, which involves neither path simulation nor discretization of the continuous-time process. Using the high frequency return observations of S&P 500 index and FTSE 100 index, we implement our estimation approach to various continuous-time stochastic volatility asset return models.