Efficient high-frequency variance estimators

Alexander Saichev, Didier Sornette and Vladimir Filimonov

Abstract

ABSTRACT

We present a theory of efficient high-frequency integrated variance estimators and illustrate it in the case where the underlying asset price follows stochastic processes with statistically independent increments. Our main result is the derivation of homogeneous (nonquadratic) integrated variance estimators, resting on the high and low values of log-price bridges within given sample time intervals. We demonstrate that the proposed estimators are significantly more efficient than the Garman and Klass estimator, obtaining a 27% improvement in their variance. Another advantage of our estimators is that they are almost unbiased for any drift of log-price process.