Price discovery in a continuous-time setting

We formulate a continuous-time price discovery model and investigate how the standard price discovery measures vary with respect to the sampling interval. We find that the component share measure is invariant to the sampling interval, and hence, discrete-sampled prices suffice to identify the continuous-time component share. In contrast, information share estimates are not comparable across different sampling intervals because the contemporaneous correlation between markets increases in magnitude as the sampling interval grows. We show how to back out the continuous-time information share from discrete-sampled prices under certain assumptions on the contemporaneous correlation. We assess our continuous-time model by comparing the estimates of the (continuous-time) component and information shares at different sampling intervals for 30 stocks in the US. We find that both price discovery measures are typically stable across the different sampling intervals, suggesting that our continuous-time price discovery model fits the data very well.