DIFFUSION COEFFICIENT ESTIMATION AND ASSET PRICING WHEN RISK PREMIA AND SENSITIVITIES ARE TIME VARYING: A COMMENT

The purpose of this note is to analyze the diffusion coefficient estimator suggested by Chesney, Elliott, Madan, and Yang (1993). I start by correcting their formula (4.1), and by showing that their procedure is a member of a class of estimators sharing the same Milstein approximation. I then show how to select the minimum variance estimator (for constant μσ) within a two-parameter subclass of procedures which do not depend on the current realization of the process. I also show that if μ is small the best procedure only allows moderate reduction in variance with respect to the classical quadratic variation estimator (which is a member of the same class). the note concludes by highlighting the fact that the empirical use of the filtered volatilities poses an error in variables problem which can be addressed using instrumental variables methods.