Price Discovery in High Resolution*

U.S. equity market data are currently timestamped to nanosecond precision. This permits models of price dynamics at resolutions sufficient to capture the reactions of the fastest agents. Direct estimation of multivariate time series models at sub-millisecond frequencies nevertheless poses substantial challenges. To facilitate such analyses, this paper applies long distributed lag models, computations that take advantage of the inherent sparsity of price transitions, and bridged modeling. At resolutions ranging from 1 s down to 10 μs, I estimate representative models for two stocks (IBM and NVDA) bearing on three topics of current interest. The first analysis examines the extent to which the conventional source of market data (the consolidated tape) accurately reflects the prices observed by agents who subscribe (at additional cost) to direct exchange feeds. At a 1-s resolution, the information share of the direct feeds is indistinguishable from that of the consolidated tape. At resolutions of 100 and 10 μs, however, the direct feeds are totally dominant, and the consolidated share approaches zero. The second analysis examines the quotes from the primary listing exchange vs. the non-listing exchanges. Here, too, information shares that are essentially indeterminate at 1-s resolution become much more distinct at higher resolutions. Although listing exchanges execute about one-fifth of the trading volume, their information shares are slightly above one-half. The third analysis examines quotes, lit trades, and dark trades. At a 1-s resolution, dark trades appear to have a small, but discernible, information contribution. This vanishes at higher resolutions. Quotes and lit trades essentially account for all price discovery, with information shares of roughly 65% and 35%, respectively.