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

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Robert Engle and Asger LundeNYU and UCSD and
University of AarhusMay 2001
Trades and Quotes A Bivariate Point Process
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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.
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PREVIOUS RESEARCH   Dufour and Engle Time and
the Price Impact of a Trade   Extending
Hasbroucks 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.
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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.
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ECONOMIC MODELS OF QUOTE TIMING

• 1.   THERE ARENT 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.

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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.
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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
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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

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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.
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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
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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
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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

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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

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TRADE EQUATION RESULTS

• Red indicates uniform high significance across
  all 8 stocks
• Magenta is often significant with typical sign
  across stocks

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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
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MIDQUOTE RESULTS
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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

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QUOTE EQUATION INCLUDING PURE DEPTH QUOTES

• Notice reduced significance and changed signs on
  spread variables and volume

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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

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