On covariance estimation of non-synchronously observed diffusion processes

We consider the problem of estimating the covariance of two diffusion processes when they are observed only at discrete times in a non-synchronous manner. The modern, popular approach in the literature, the realized covariance estimator, which is based on (regularly spaced) synchronous data, is problematic because the choice of regular interval size and data interpolation scheme may lead to unreliable estimation. We propose a new estimator which is free of any `synchronization' processing of the original data, hence free of bias or other problems caused by it.