This paper develops a real-time structural model of price formation, and uses it to investigate the dynamics of effective quotes and bid-ask spreads between consecutive trades. There is some evidence that the effective bid-ask spreads increase over time when no orders arrive. The effective quotes are found to change over time when no orders arrive. The dynamics of bid and ask are different and are related to the direction of previous transaction. Market makers act as though they believe that clustering trades with middle-range duration (coming one or two minutes after the last trades) are more likely to contain private information, while reversing trades with same duration are less likely to contain private information. Some stylized facts are also established regarding the average duration and frequency for clustering trades, reversing trades,upticks, and downticks.Price formation, Bid-ask spread, Trade duration, Quote dynamics
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