Efficient Estimation of Stochastic Volatility Using Noisy
Observations: A Multi-Scale Approach
With the availability of high frequency financial data,
nonparametric estimation of volatility of an asset return process becomes
feasible. A major problem is how to estimate the volatility consistently
, when the observed asset returns
contain error or noise, for example, in the form of microstructure noise.
The former (consistency) has been addressed heavily in the recent
literature, however, the resulting estimator is not quite efficient. In
Zhang, Mykland, Ait-Sahalia (2003), the best estimator converges to the
true volatility only at the rate of
. In this paper, we propose
an efficient estimator which converges to the true at the rate of
, which is the best attainable. The estimator remains valid when
the observation noise is dependent.