Robert Engle and Asger Lunde NYU and UCSD and University of Aarhus May 2001

1. Robert Engle and Asger LundeNYU and UCSD and University of AarhusMay 2001 Trades and Quotes: A Bivariate Point Process

2. MICROSTRUCTURE ECONOMETRICS FOCUSES MAINLY ON TRANSACTION TIMES. WE ALSO SEE QUOTE REVISION TIMES. CENTRAL QUESTION: HOW LONG DOES IT TAKE FOR INFORMATION TO BE INCORPORATED INTO PRICES? INSOFAR AS INFORMATION IS REVEALED BY TRANSACTIONS, A KEY INGREDIENT IS THE TIME IT TAKES FOR QUOTES TO BE REVISED IN RESPONSE TO A TRANSACTION.

3. PREVIOUS RESEARCH Dufour and Engle “Time and the Price Impact of a Trade” Extending Hasbrouck’s model, they showed that the impulse response of prices to a signed trade depends upon the time between trades, the volume of the trade and the bid-ask spread at the time of the trade. The effects are measured in transaction time but if examined in calendar time they reveal that not only are the price impacts greater when the market is active, but they are faster too.

4. Engle and Russell, “The Econometric Analysis of Discrete-Valued Irregularly-Spaced Financial Transactions Data Using the Autoregressive Conditional Multinomial Model" Showed that transaction price changes are more permanent when volume is higher, spreads are wider and transaction rates are higher. The same effects are quicker in calendar time for high transaction rates.

5. ECONOMIC MODELS OF QUOTE TIMING 1.   THERE AREN’T ANY – IN THEORY, QUOTES SHOULD BE REVISED IMMEDIATELY. • QUOTES WOULD NOT BE REVISED IF A TRADE CONTAINED VERY LITTLE INFORMATION – HENCE THE TIME WOULD BE LONG. • QUOTES WOULD NOT BE REVISED INSTANTLY BECAUSE IT TAKES TIME TO CALCULATE THE NEW PRICES. 4. QUOTES WOULD ONLY BE REVISED WHEN THE LIMIT ORDER BOOK CHANGES AND THEN WOULD REFLECT THE NEW PRICE AND DEPTH OF LIMIT ORDERS.

7. A BIVARIATE MODEL OF TT AND QQ DURATIONS IS NOT WELL SPECIFIED AS THEY ARE NOT IN A NATURAL ORDER. MORE SPECIFICALLY, THEY DO NOT HAVE A COMMON INFORMATION SET.

9. CENSORING OF TQ DURATIONS FROM THE ECONOMIC MODEL IT IS CLEAR THAT THE DISTRIBUTION OF POSSIBLE QUOTE ARRIVAL TIMES WILL BE ALTERED BY AN INTERVENING TRADE. HENCE SUCH DURATIONS SHOULD BE VIEWED AS CENSORED AND NOT OBSERVED. where

14. ESTIMATION • Each likelihood can be maximized separately • Because there are parameters in common, this will be inefficient but consistent • Instead we use these estimates as starting values for a joint maximization of the full likelihood

15. DESCRIPTION OF THE DATA –TAQ- Trades and Quotes from NYSE August and September, 1997 8 randomly selected large cap stocks THERE ARE MORE QUOTE CHANGES THAN TRADES. MANY ARE JUST DEPTH CHANGES.

16. DATA: TAQ – August 4,1997-September 30,1997 42 Trading Days (sixteenth ticks) 8 randomly selected stocks from the 50 most active. Between 25,000 and 50,000 trades Between 27,000 and 60,000 quotes Between 10,000 and 30,000 midquote changes Between 20 and 40 sec between trades Between 1000 and 3000 shares in avg trade Between 10 and 22 seconds from Trade to Quote on average Between 30 and 130 seconds from Trade to Midquote changes Between 50% and 85% midquote changes are censored

17. DATA TRANSFORMATIONS 1.LEE AND READY: Transaction is a buy when transaction price exceeds midquote Transaction is a sell when price is below midquote Prices at the midquote, we take as undetermined 2.LEE AND READY: Quotes are posted faster than transactions are recorded, hence add 5 seconds to quote times to get order correct

18. TRADE EQUATION • The expected trade duration equation: • x is the trade duration • Lev.QQ is the Mean of the 10 most recent QQ durations • Spr is the change in relative spread from the previous trade to this trade • Lev.Spr is the level of the spread over the 10 most recent relative spreads • Volume is the number of shares traded • netVolume is the sum of buy volume minus sell volume over last 10 trades • Back.Q is the time since the last quote was posted • D are hourly dummy variables

19. MIDQUOTE EQUATION • Expected time from a trade to next quote • y tilda is a trade-quote duration which may be censored • d is a dummy variable for censored trade-quote durations

20. TRADE EQUATION RESULTS • Red indicates uniform high significance across all 8 stocks • Magenta is often significant with typical sign across stocks

21. INTERPRETATION: 1.       TRADE DURATIONS ARE LONGER WHEN LESS INFORMATION IS BEING REVEALED: THAT IS- Past durations are long Trades are small Spreads are low AND WHEN Spreads have just increased Quote changes are far apart

22. MIDQUOTE RESULTS

23. TRADE TO MIDQUOTE DURATIONS ARE LONGER WHEN: • Past TQ durations are long • Current TT duration is long • QQ durations are long • It has been a long time since quotes were changed • Spreads are low • Spreads have fallen • Volume is small • Volume is unbalanced • These are all indicators of low information flow

24. QUOTE EQUATION INCLUDING PURE DEPTH QUOTES Notice reduced significance and changed signs on spread variables and volume

25. All Quote Durations are long when • Past TQ durations are long • Current TT duration is long • QQ durations are long • It has been a long time since quotes were changed • Spreads are low • XXX Spreads have fallen • Volume is small • XXX Volume is unbalanced • These are all indicators of low information flow

26. CONCLUSIONS PRICES ARE REVISED MORE RAPIDLY WHEN INFORMATION FLOWS INTO THE MARKET. VOLUME, SPREAD AND TIME BETWEEN TRADES ARE ALL INDICATORS OF INFORMATION FLOW.