Trades and Quotes: A Bivariate Point Process

Recent empirical work has studied point processes of transactions in financial markets and observed clear time dependent patterns in these arrival times. However, these studies do not examine the timing of quoted price changes. This paper formulates a bivariate point process to jointly analyze transaction and quote arrivals. In microstructure models, transactions may reveal private information that is then incorporated into new prices. This paper examines the speed of this information flow and the circumstances that govern it. A joint likelihood function for trade and quote arrivals is specified which is a generalization of the ACD model of Engle and Russell (1998) and which recognizes that an intervening trade sometimes censors the time between a trade and the subsequent quote. Models of trades and quotes are estimated for 8 stocks using TAQ transaction data. A series of diagnostic tests and alternative estimates are presented. The essential finding for the arrival of price quotes, is that information flow variables, such as high transaction arrival rates, large volume per trade, and wide bid/ask spreads, all predict more rapid price revisions. This means prices respond more quickly to trades when information is flowing so that the price impacts of trades and ultimately the volatility of prices, are high in such circumstances. When quote arrivals that modify only depth are included as well, a somewhat different answer is found. Now the information variables such as volume and trade arrival rate and level of spread have a slowing or ambiguous effect on quote arrivals. This result is an indication that depth revisions are relatively more frequent when the market is slower. A possible explanation is that depth quotes are derived directly from the limit order book and limit orders are submitted more cautiously when the market shows informational trading.