This paper proposes a consistent and efficient estimator of the high frequency covariance (quadratic covariation) of two arbitrary assets, observed asynchronously with market microstructure noise. This estimator is built upon the marriage of the quasi-maximum likelihood estimator of the...

We propose a model of market making where a strategic high frequency trader exploits his speed and informational advantages to place quotes that interact with the orders of low frequency traders. We characterize the optimal market making policy of the high frequency trader analytically. Our...