Non-Commuting Price Discovery in Fragmented Equity Markets
Studies multi-venue IBM prices to separate permanent price discovery, frequency-dependent adjustment, and non-commuting venue dynamics.
This project studies price discovery in fragmented equity markets using synchronized IBM prices from five U.S. trading venues. The empirical question is whether fragmented price discovery is fully summarized by a single permanent-price contribution ranking, or whether sampling frequency and venue-specific adjustment order also matter.
The benchmark is a cointegrated vector error-correction model estimated at several sampling frequencies. The analysis separates three objects that are easy to conflate in high-frequency market data: Hasbrouck information shares, short-run lead-lag timing, and the frequency consistency of the fitted transition matrices.
The public-practice part of the project is the commutator diagnostic. It treats venue-specific adjustment channels as update operators and asks whether applying two market updates in different orders changes the implied spread adjustment. In the current IBM application, these effects are empirically visible but economically small, making the paper a useful rehearsal for turning abstract operator ideas into measurable market-microstructure diagnostics.
Current manuscript: non-peer-reviewed working paper.