We consider an extension of the Roll model where the trade direction, i.e. whether the trade is buyer or seller initiated, is multiplied by the dynamic quoted half-spread. Employing tick-by-tick maximum likelihood estimation on S&P 500 constituents, we find that the efficient price is quite...

The asymptotic distribution of the score test of the null hypothesis that marks do not impact the intensity of a Hawkes marked self-exciting point process is shown to be chi-squared. For local asymptotic power, the distribution against local alternatives is also established as non-central...