Pricing Behavior in an Off-Hours Computerized Market
Mark Coppejans
Department of Economics
Duke University
and
Ian Domowitz
Department of Finance
Smeal College of Business Administration
Pennsylvania State University
February 1999
This paper is a substantially different version of a working paper circulated under the
title, The Performance of an Automated Trading System in an Illiquid Environment. We
thank Gordon Kummel, of K2 Capital Management, Inc., for making the data available
for this paper, and the Institute for Policy Research, Northwestern University, for
financial support. We have benefited from the comments of seminar participants at
Cornell University, Georgetown University, Indiana University, the Federal Reserve
Bank of Kansas City, and the 1997 Olsen High Frequency Data Conference. Helpful
suggestions also have been received from Dick Baillie, Charles Cao, Larry Glosten, and
an anonymous referee. Correspondance may be sent to Ian Domowitz, Department of
Finance, SCBA, Penn State University, University Park, PA 16802, phone 814-8635620, email at domowitz@psu.edu.
Abstract
Automated markets are becoming increasingly widespread, and their efficiency
properties are of corresponding concern to regulators and exchange policy
makers. Many systems are implemented in settings characterized by a distinct
lack of liquidity, however, often by design. We evaluate the performance of
such a market, the GLOBEX overnight trading system, in absolute terms and
relative to a liquid benchmark, the floor market of the Chicago Mercantile
Exchange. Our results with respect to bid-ask spreads and adverse selection
suggest that the nature of the environment is an important determinant of
market performance, but that an automated market can operate well in a
relatively illiquid setting. Price clustering, indicative of a lack of pricing
efficiency, is prevalent on the automated system, but price resolution improves
as trading frequency increases.
JEL classification: G14, G15, G29
Key words:
automated trade execution, liquidity, bid-ask spreads, price
clustering, market efficiency
1. Introduction
Economic interest in automated market structure is motivated by three
interrelated factors. The form of the trading institution affects agent behavior,
the properties of transactions prices, and welfare. This list is a primary
contribution of the theoretical and experimental work on auction mechanisms,
and is a finding emphasized in the literature on financial market
microstructure.1 Second, the automated auction is transforming the landscape
of financial markets. While debates exist with respect to the plausibility of the
eventual dominance of such markets, their sheer number motivates research
interest.2 Finally, the pricing and efficiency properties of automated markets
have a strong influence on market regulation. Automated markets, their
design, and consequent impact on the price discovery process are continuing
concerns for a variety of regulatory bodies worldwide.3
Many systems are deliberately implemented in settings characterized by
a distinct lack of liquidity. Such environments include “off hours” and
overnight markets, markets characterized by listings of very new companies
and derivative instruments, emerging market venues, and trading in illiquid
classes of securities. Examples include LIFFE’s APT, the CBOT’s Project A, and
the SATO system of the Mexican Stock Exchange.
The use of automated systems for such applications is generally driven
by cost considerations, not by any logic implying that computerized market
structure is somehow uniquely suited for the purpose intended. This raises an
important question for regulators, exchange policy makers, and system
designers: can a computerized auction perform well in an illiquid setting, thus
satisfying the goals of the technology choice and the requirements of
regulators?
See Friedman (1993) for a survey of research on the auction institution. A good
example in the context of financial market structure is provided by the work of
Madhavan (1992).
2 See Domowitz (1993) for a classification of roughly 50 such markets. Debates over
viability date at least from Melamed (1977). Institutional discussion may be found, for
example, in Domowitz and Steil (1999) and Harris (1990). Glosten (1994) provides a
theoretical treatment of the dominance issue.
3 See Domowitz and Lee (1999) for general discussion and a listing of concerned
regulatory bodies on a global basis. The connection between system design and
regulation is emphasized in Corcoran and Lawton (1993), Sundel and Blake (1991), and
IOSCO (1990).
1
1
We investigate this issue by studying some aspects of pricing on the
GLOBEX automated trading system for futures contracts. GLOBEX is an “off
hours” overnight trading system. Its functional design is a paradigm adhered to
by over 70 percent of automated markets currently in operation.4 The market
environment is generally thought to be illiquid, and we present evidence on this
point. In order to do so, and to provide interpretation of the performance
results, a benchmark, the floor market of the the Chicago Mercantile Exchange
(CME) is used. The CME floor is thought to be one of the most liquid markets
in the world, especially in the instruments considered in our analysis (see, for
example, Laux and Senchack (1992)). We match trading data in the same
instruments, during the same 24-hour day, across the two market structures.
The use of the floor market as a benchmark should not be confused with
studies that attempt a comparison of floor versus automated trading during the
same trading hours.5 We make no claims of superiority in terms of market
structure, nor are we assessing relative market quality in an effort to inform
policy makers with respect to the pros and cons of automated versus open
outcry trading. Our focus is on pricing characteristics of the automated market
in an illiquid setting. Previous empirical work on automated market structure
has dealt exclusively with very liquid environments, often for reasons of data
availability. Sometimes, as in our analysis of price clustering and market
efficiency, absolute measures of performance are available. In other cases, the
benchmark is required, because there exists no absolute measure for
assessment purposes.
Prior empirical work and the characteristics of other markets also have
implications with respect to the interpretation of our results. The design of a
standard computerized continuous market does not, in and of itself, appear to
generate a poor trading environment in terms of liquidity and performance
See Domowitz (1993). This figure has undoubtedly increased somewhat since that
study was conducted, given developments in the last two to three years.
5 See Kofman and Moser (1997), Pirrong (1996), Franke and Hess (1995), and Frino,
McInish, and Toner (1998) for comparisons with respect to trading in the Bund
contract. Similar work for the Nikkei stock index futures contract, traded in Japan and
Singapore, is done by Fremault-Vila and Sandmann (1995). Related work includes that
of Grunbichler, Longstaff, and Schwartz (1994), with respect to lead-lag relationships
between the German DAX index, the underlying components of which are traded on the
floor, and the future on the index, traded by an automated system.
4
2
characteristics. The Swiss SOFFEX market and the German DTB market, for
example, are virtually identical in design to the GLOBEX system, but operate
during regular trading hours. They both are generally thought to be quite
liquid, and formal analysis supporting equal or greater liquidity in the DTB
market relative to the LIFFE floor is provided by Pirrong (1996) and Frino,
McInish, and Toner (1998).6 Taken together, these authors, and Kofman and
Moser (1997), provide evidence of roughly equal bid-ask spreads, adverse
selection components, and pricing efficiency across the automated and floor
markets. Biais, Hillion, and Spatt (1995) document excellent liquidity provision
in the CAC market of the Paris Bourse, a design based on CATS and also
virtually identical to that of GLOBEX.
There also is a revealed preference over time for the computerized
auction. The Toronto CATS system has replaced the traditional trading floor.
The French MATIF recently converted to an automated setting, a particularly
interesting experiment, since the floor was allowed to operate concurrently,
while it lasted. Domowitz and Steil (1999) document fourteen full or partial
conversions of floor markets to automated auctions over 1997-1998 alone.
Such movement suggests that computerized markets are, at least, not believed
to be inherently illiquid or to provide poor provision of trade execution services.
Our analysis of a computerized market in an illiquid environment is
organized around four topics of interest in the literature on trading market
structure. They are bid-ask spreads, adverse selection, price clustering, and
price resolution. Each topic is separately motivated in sections 3 and 4. We
examine trading in the S&P futures contract and futures contracts of the
Deutschemark, Yen, and Swiss Franc. The GLOBEX data are new, and a
description, within and across markets, is given in section 2, together with
some institutional detail.
Our results with respect to bid-ask spreads and adverse selection
suggest that the nature of the environment is an important determinant of
market performance, but that an automated market can operate well in a
relatively illiquid setting. Spreads, their adverse selection components, and the
volatility of this cost of trading are roughly the same for the S&P contract, as
6
In fact, the automated design has worked well enough that the Swiss are moving
3
for the floor benchmark. Although spreads are less sensitive to changes in
trading activity on GLOBEX relative to the floor, the relationship between
volatility and the spread appears to be the same across trading venues. In
contrast, currency futures spreads are high in the overnight market, driven by
a large adverse selection component. The environment within which the
currency futures are traded is quite different from that of the S&P contract,
however. We discuss the impact of the overnight interbank foreign exchange
market in this context.
We then examine price clustering and resolution, motivated by their
relationship to efficient pricing and to the degree with which the underlying
value of the security is actually revealed. Pronounced clustering is found on
GLOBEX, while the more liquid benchmark exhibits pricing behavior in line
with theoretical values suggesting efficient pricing. An analysis based on timevarying Markov chains reveals, however, that price resolution improves on
GLOBEX as the intensity of trading rises. This suggests better system
performance as liquidity increases.
2. Institutions and Data
2.1.
Automated Market Structure
Stoll (1992) characterizes a financial market as a communications
system consisting of three components: an information system, an orderrouting system, and a trade execution mechanism. An automated market
might be described as a computerized blueprint for Stoll’s general description.
The programming embodies specific rules concerning the form of allowable
messages that traders can send and receive, as well as the nature of
information displayed to system participants. With respect to execution, a
separate rule set governs the process by which these messages are translated
into transactions prices and quantity allocations. The heart of the transactions
algorithm is a list of execution priorities assigned to each incoming order
routed to the system.
Allowable messages in the GLOBEX system are bids and offers in terms
of price-quantity pairs (limit orders), and instructions to hit an existing bid or
lift an existing offer. The system displays a variety of information, most notably
equity and fixed income trading to automated systems.
4
including separate displays of transactions, best bids and offers, and the five
best bids and offers with aggregate quantity on both sides resting on an
electronic limit order book. There are no personal identifiers attached to
messages in the display.
GLOBEX is a strict price and time priority system, with some allowance
for undisplayed order flow to be transacted at a lower secondary priority. New
orders are filled at the best available price at the time or order entry. In case of
ties at price, orders are filled on a first-in, first-out basis. A trader may elect to
simply transact at the best bid or offer in the system, without submitting a
contraside limit order. The maximum possible quantity will be traded by filling
an order on the buy or sell side, subject to liquidity available in the system.
Unfilled quantities remain on the order book until cancelled. Cancellation may
occur at any time. The design is very similar to that of the CAC system
operating on the Paris Bourse, for example.
The benchmark used in some of our analysis is the floor market of the
CME. Rules and characteristics of open outcry trading are well known. Since
we are not evaluating performance in terms of system design, we omit a
detailed comparison of institutional details. Extensive comparisons exist in
any case; see, for example, Harris (1990), Bollerslev and Domowitz (1991), and
Pirrong (1996), a list which is hardly exhaustive.
2.2.
Data
Our analysis is based on trading data for the September futures
contracts on the S&P 500 index (SP), the Deutschemark (DM), the Yen, and the
Swiss Franc (SF) over the period 7/1/94 through 9/1/94.7 Trading hours vary
for the currencies relative to the stock index. On Central Standard Time, the
trading week opens with GLOBEX trading on Sunday at 6:30 p.m., and closes
on the floor on Friday. If Monday is a holiday and Tuesday is not, trading
starts on Monday at 6:30 p.m. The floor stops trading in the S&P contract at
3:15 p.m., and GLOBEX opens at 3:45, with continuous trading up to a half
hour before the floor again opens at 8:30 a.m. Currency floor trading ends at
The data run through contract expiration, but we eliminate observations which are
close enough to the end of a cycle as to be unrepresentative, given traders’ proclivity to
roll over positions to the next expiration in advance of the expiration date. This activity
is clearly visible in our data for trading into the month of September.
7
5
2:00 p.m., with a GLOBEX opening at 2:30. It stays open until 6:45 a.m., and
floor trading again resumes at 7:20.
GLOBEX trading data include all best bids and offers, as well as
transactions prices, on a continuous basis. Continuous transactions data are
available for trading on the CME floor.8 The number of observations varies,
depending on trading system and contract type, ranging between roughly 3000
to 8000 transactions on GLOBEX and between about 72,000 to 95,000
transactions on the floor. Some of our analysis is restricted to more timeaggregated information, yielding roughly 1200 observations on floor trading as
opposed to 2700 observations on GLOBEX activity, on a 15-minute basis.
2.3.
Market Characteristics
A brief summary of the data is contained in Table I. Median prices and
percentage returns are basically the same across trading venues, with the
latter being zero to several decimal places. The volatility of logarithmic returns
is lower on the floor by a factor of two to four, depending on the contract. The
number of transactions per hour on the floor ranges from about 27 times that
observed in the overnight market for the S&P contract to an average multiple of
67 for the currencies. There is anecdotal evidence that order size also is much
lower overnight. Conversations with traders during the sample period generate
complaints that it is difficult even to transact 100 contracts at a time in
GLOBEX, while such an order is commonplace in the benchmark market.
Some theoretical models of trading behavior link volatility to volume. 9 In
these framworks, the combination of lower trading volume and higher returns
volatility suggests a low level of liquidity in the electronic market. The
impression of low liquidity relative to the benchmark is reinforced by examining
the ratio of the standard deviation of price to the number of trades. This
measure is suggested by a characterization of liquidity as the market’s ability to
absorb quantity without an appreciable effect on price. For all contracts, this
statistic is an order of magnitude smaller on the floor relative to GLOBEX. For
We thank Gordon Kummel, of K2 Capital Management, Inc., for making these data
available. The original source is the Chicago Mercantile Exchange, distributed on the
Knight-Ridder financial network.
9 Examples include Blume, Easley, and O'Hara (1994) and Domowitz, Glen, and
Madhavan (1998).
8
6
the S&P 500 contract, for example, the ratio is 0.004 for the benchmark, and
0.045 for the automated system.
There are related, but competing, explanations of the volatility
differences across trading venues. Higher volatility may be a function of system
design. The German DTB market, however, is virtually identical to the
GLOBEX system, and both Kaufman and Moser (1995) and Pirrong (1996) find
volatility on DTB to be comparable to that on the floor-based LIFFE.
Alternatively, higher volatility may be ascribed to information effects, both with
respect to the composition of the trader population and other overnight trading
activity. There is relatively little overnight trading in the equities underlying
the index, compared to the currencies, for which the overnight interbank
market operates. Interestingly, GLOBEX volatility is much higher, and
differences with the benchmark greater, for the currencies than for the S&P
contract. Finally, the characteristics of returns and associated volatility may be
largely driven by bid-ask spreads. We return to this issue in the next section.
We report some additional information for the opening hour, closing
hour, and the middle of the trading session in Table II. Statistics are given for
the S&P contract and the DM contract. Differences across time of day for the
other currencies are qualitatively the same as for the DM.
Opening and closing effects are evident in both markets, despite the
nearly continuous segue of activity from one trading venue into another. This
effect is much more pronounced for the S&P contract, however, than for the
currencies. The number of S&P trades per hour at the open on GLOBEX is
over three times that of the main trading session, while activity in the DM
contract changes little. The use of GLOBEX S&P trading facilities just prior to
the opening of the floor market is particularly notable, with a startling 103
trades in the hour just before the GLOBEX close, relative to about 12 at the
GLOBEX open. There is no formal procedure on the floor to set an opening
price, unlike many other markets. GLOBEX appears to be fulfilling the
function of a pre-opening session during its last hour.
The variance of S&P price changes per trade drops sharply before the
opening of the floor, from 0.14 at the GLOBEX open to only 0.02 at the close.
The decline is purely a function of the larger number of trades. The standard
7
deviation of price changes is almost constant across time of day. This stability
of volatility across time of day also is observed for trading on the floor, and in
both venues for the currency contracts.
We also report the first order serial correlation coefficient of price
changes. It is negative but relatively large on GLOBEX, especially at the open
and the close. Serial correlation in the benchmark market is generally smaller.
Time of day differences are reasonably large in both venues. Filtering the data
using a dynamic two-factor model (Engle and Watson (1981)) to account for
unobservable changes in inventory and shocks to order flow reduces the
magnitude of the correlations on GLOBEX, making them more comparable to
the benchmark.
3. Bid-Ask Spreads and Adverse Selection
Transactions costs and information in computerized trading venues have
been topics of debate beginning with the work of Melamed (1977). We
investigate the former using the bid-ask spread. An examination of the adverse
selection component of the spread may then shed some further light on the
behavior of the spread and information processing in the automated overnight
market. A standard model of price dynamics is used to tie the analyses
together.
3.1.
Model Specification
The approach to the examination of bid-ask spreads and adverse
selection components is driven in part by data availability on both markets. 10
We begin with the basic framework proposed by George, Kaul and Nimalendran
(1991).
Let Rt denote the difference in transactions prices from time t to time t-1
and denote the unobservable expected return for the period between
transactions at these points in time by Et. Define Qt to be an indicator taking
on a value of +1 if the transaction is at the offer and -1 if the time t transaction
is at the bid. The basic model can be expressed in terms of the following two
equations:
Models suitable for empirical implementation differ largely with respect to observable
data characteristics and certain assumptions concerning autocorrelation properties of
data and unobservable components. Huang and Stoll (1994) provide an analytical
survey.
10
8
R t  Et 
s
s
Qt  (1  )Qt 1   t ,
2
2
(1)
Et  Et 1  t
(2)
where s denotes the bid-ask spread and  is the adverse selection component
of the spread. The disturbances, t and t, are assumed to be mean zero whitenoise. The model's structure is based in part on the assumption, E(Q t|Qt-1)=0.
The emphasis of George, Kaul and Nimalendran (1991) is on the
contribution of positive serial correlation of expected returns to spread
component estimation. Huang and Stoll (1994) argue that on the level of
transactions data, changes in expectations should be unimportant. We test
this hypothesis using a moment condition derivable from the basic equations
above, namely11
E[(Rt  Rt 1 )(Rt 3  Rt 4 )]  0 .
(3)
The serial correlation coefficient is estimated by generalized method of
moments (GMM), with the usual heteroskedasticity corrections to standard
errors. We fail to reject the null hypothesis of zero serial correlation in six of
the eight cases at any reasonable level of statistical significance, and the point
estimates in the remaining two are quite small.12 We therefore follow the
suggestion of Huang and Stoll (1994), and consider estimation of the adverse
selection component setting cov (Et Et-1) equal to zero.13 Our main results are
obtained through an augmented version of equation (1),
Rt 




st
s
Qt  t Qt 1 1   2 Ft 11   3 max Tt 11,o , Tt 11,c   4 Dt 1,o   5 Dt 1,c   t
2
2
(4)
We note that the moment condition in population terms produces two possible roots
in the serial correlation coefficient. In practice, various initial values are used in
estimation to isolate the parameter of interest.
12 The eight cases are composed of the stock index and three currency futures traded on
the two systems. The rejections are for the S&P 500 and SF floor-traded contracts. The
point estimates are 0.06 and 0.02, respectively. We also estimated all relationships on a
week-by-week basis, revealing that the rejections were due to trading activity in only
two of the nine weeks under study.
13 If  is not zero, we can still estimate the same parameters as before using
Rt = Rt-1 + (s/2)Qt - (s/2)(+(1-))Qt-1 +(s/2)(1-)Qt-2 + t,
in place of (1), or
E[(Rt - Rt-1)(Rt-2 - Rt-3)] = (s2/4)(1-),
together with (3).
11
9
in which Ft is a measure of market intensity, calculated as one plus the
number of transactions per five minute period; Tt ,o and Tt ,c denote one plus
the time (in minutes) to the open and close, respectively; and D t , 0 and D t ,c are
dummy variables, which take on the value of one during the hour just after the
open and prior to the close, respectively. The time series on Q t is directly
observable on GLOBEX; it is derived for the floor using the Lee and Ready
(1991) algorithm.14 The spread, s, is now allowed to vary over time, in response
to market conditions.15 This permits a calculation of the correlation of the
average estimated spread with other variables of interest below.
The additional variables index potential differences with respect to
liquidity considerations, as well as simply to account for opening and closing
activity. The variable, Ft, provides a direct correction for differences in trading
frequencies over the day. The term, max (Tt,o, Tt,c), serves much the same
function, but indexes activity by time-of-day. Finally, the open and close
dummies adjust for any differences in opening and closing activity across the
two systems. In practice, the time-of-day effects appear to capture the bulk of
any liquidity-related statistical variation in the data.
3.2
Bid-Ask Spreads
Bid-ask spread figures are contained in Table III. Point estimates and
robust GMM standard errors are reported for overall activity, the open and the
close, and for trading activity an hour after the open to an hour before the
close. The tick size for the S&P contract is 0.05, while a tick for the currencies
is 0.0001, scaled by 100 to be 0.01 in the table and discussion below. The
magnitude of the benchmark floor spreads is about two ticks for all contracts,
which represent slightly larger figures than reported by Laux and Senchack
(1992).
We also estimated the spread component using the method of Huang and Stoll (1994),
which allows separate identification of transactions costs, inventory, and adverse
selection components for the GLOBEX system. The results for the latter component are
virtually identical to those reported below.
15 We are measuring effective spreads. The variation in response to market conditions
includes an indicator for when the quoted spread based on the raw data is greater than
a single tick. Orthogonality conditions in the estimation include expected quoted
spreads by time of day.
14
10
For the S&P contract, the spread is nearly the same for the floor and
GLOBEX, regardless of time period within the trading session. Overall, the
floor spread is only 2 percent higher than that on GLOBEX. The largest
difference is a spread of 0.110 on the floor at the open, compared to 0.103
during the GLOBEX closing hour, a natural comparison given the contiguity of
trading sessions. On the other hand, GLOBEX spreads widen relative to the
floor for the traded currencies, ranging from three to five ticks, with the lowest
in the most heavily traded contract, the DM, and the highest for the least
traded contract, the SF.
The relative intensities of trading activity do not appear to account for
the difference in results across the two types of contracts. Correlations of the
spread with the frequency of trading are reported in Table IV. Existing
theoretical models deliver different predictions of the correlation between the
spread and trading activity, depending on the specification of traders'
preferences and information sets. The correlations here are large and
uniformly positive, consistent with risk averse behavior. Correlations for the
currencies are substantial, but somewhat smaller than those estimated for the
S&P contract, a finding that is also observed in floor trading.
Overnight trading environments are not necessarily the same across
instruments for a single automated trading mechanism, however. The
institutional wedge between our two classes of contracts is the existence of the
overnight interbank currency market. After-hours futures traders in
currencies have the choice of trading the contracts directly on GLOBEX or
dealing in the interbank market through the “exchange for physical”
mechanism. There are several possible factors at work here. Overnight
interbank trading activity can diminish liquidity in the automated market,
especially for the Asian currency, relative to the floor. This would account, at
least in part, for the wider spreads on GLOBEX. Another possibility is that he
overnight spot market is so large relative to GLOBEX that independent price
discovery does not occur on GLOBEX. Combined with the exchange for
physical mechanism, this would suggest that spreads on GLOBEX might look
more like those observed in the spot market. Interestingly, Lyons (1996)
reports a spread of three ticks in the DM spot market, precisely the result
11
obtained here for GLOBEX.16 Finally, there simply may be more risk and
opportunities for adverse selection, given the relative market sizes. We
investigate this issue further below.
In the last section, we raised the possibility that differences in the
characteristics of price changes might be driven by bid-ask spreads. We
investigate this issue further by computing the correlation of average spreads
with price changes and volatility. Over the full trading session, the correlation
with price changes is positive, excepting the Yen contract, consistent with the
theoretical model of Amihud and Mendelson (1986) and the empirical results of
Cao, Choe, and Hatheway (1997). Regardless of sign, however, the numbers
are generally very small. This result holds both for GLOBEX and the
benchmark, suggesting that returns themselves have little relationship with the
size of the spread for the financial instruments considered here.
Volatility differences observed across trading venues do not appear to be
directly attributable to the spread. There is generally a strong positive
relationship between volatility and the spread, consistent with the results of
Frino, McInish, and Toner (1998) for the DTB. Correlations computed over the
full trading day are only slightly smaller on GLOBEX relative to the benchmark,
however.
We also report the standard deviation of the spread, as a measure of
variability in the cost of trading. Spread volatility is clearly a function of the
size of spread, and otherwise appears to have little to do with the trading
mechanism. For the S&P contract, spread volatility is roughly the same across
markets, as is the size of the spread itself. On GLOBEX, variability increases
as the spread increases across currencies, remaining roughly the same for
currencies on the floor.
3.3.
Adverse Selection
The adverse selection component of the spread may be higher for
currencies, widening the spread during periods of increased market activity.
Such a result would be consistent with the spreads reported in Table III and
the correlations in Table IV. Trading in the interbank foreign exchange market
Lyons uses interdealer quotes as opposed to indicative quotes on Reuters screens.
Spreads based on indicative quotes tend to be higher, on the order of five to ten ticks in
the DM market, for example.
16
12
takes place at high speeds, exacerbating the potential of adverse selection for
GLOBEX currency traders operating in a thin market. The same possibility
does not exist for trading in the S&P index contract after floor trading hours in
Chicago and New York.
Estimates of the adverse selection proportion of the spread appear in
Table V. The magnitudes of the estimates are in line with those in other
studies. The S&P results are not grossly different than those obtained for a
group of liquid Major Market Index stocks by Huang and Stoll (1994), for
example. They report an average adverse selection component of 0.43 for large
trades, which is an appropriate comparison given the large dollar value of
futures trades considered here. The estimates of GLOBEX adverse selection
components for currency contracts are similar to that reported for the Bund
contract on the DTB by Frino, McInish, and Toner (1998).
The adverse selection component is larger on the computerized system,
relative to the benchmark, for all currencies and almost all time periods; the
only exception is exhibited by the DM contract at the GLOBEX open, but the
difference is small and statistically insignificant. Based on activity over the
entire trading day, GLOBEX adverse selection components exceed their floor
counterparts by 23 to 32 percent. These differences are largely driven by
activity during the GLOBEX closing hour, compared with the opening of the
floor. These are two nearly contiguous trading periods during which trading
activity in both markets, as well as in the spot market, is particularly high.
In contrast, the adverse selection component for the S&P contract on
GLOBEX is less than that observed for the benchmark. The floor component is
about 17 percent higher, on average, a difference rising to 22 percent, if the
open and close are excluded from the calculations.
The evidence suggests that while spreads and spread behavior in the
automated mechanism may be similar to that observed on the floor, even in an
illiquid environment, GLOBEX performance deteriorates in a setting
characterized by high adverse selection. A similar result is produced by Frino,
McInish, and Toner (1998), in their study of Bund trading on the DTB.
4. Price Clustering and Resolution
13
Price clustering represents the use of discrete price sets that are coarser
than those determined by the market tick size. It is a market regularity studied
empirically by Harris (1991) for stocks and by Goodhart and Curcio (1991) for
trading in the interbank foreign exchange market. Interest in this phenomenon
is motivated by its inconsistency with market efficiency (Osborne (1962),
Niederhoffer (1966)) by its potential signaling of collusion (Christie and Schultz
(1994)), and by its link to the degree with which the underlying value of the
security is actually revealed (Ball, Torous, and Tschoegl (1985)).
To the extent that a trading mechanism should encourage value
discovery through its design, the first and third interpretations above are
relevant. We first investigate the clustering phenomenon, and then proceed to
the issue of underlying value and price resolution.
4.1.
A Markov Model of Price Clustering
Let jt be the frequency with which a price will be in discrete category j at
time t. The vector of these frequencies is simply  t  (1t ,...,  st )' , where s
indexes the total number of categories. Our definition of categories necessarily
varies between the S&P contract and the currency futures. Prices in the S&P
are written to two decimal places, e.g., 470.05. We create five natural price
categories for the investigation of clustering, namely xxx.05  xxx.A5, xxx.10 
xxx.B0, xxx.25  xxx.C5, xxx.50, and xxx.00, where A = { 0, 1, 3, 4, 5, 6, 8, 9 },
B = { 1,..., 4, 6,..., 9 }, and C = { 2, 7}. Round or even price points are xxx.50
and xxx.00. Currencies are traded to four decimal places, e.g., 0.7651. For
these contracts, the categories are defined to be x.xxx1  x.xxxB, x.xxx5, and
x.xxx0. Here, round price points are x.xxx5 and x.xxx0.
Simple averages of price category frequencies are reported in Table VI. In
the interpretation of the results, it is important to note that for the S&P model,
there are 8 possible values in the xxx.05 and xxx.10 categories, 2 possible
values in the xxx.25 categories, and one each for the remainder. Similarly,
there is one possible value in the currency x.xxx5 and x.xxx0 categories, and 8
values in the residual category. For example, the S&P stationary probability
value reported in panel A for the xxx.05 category is 0.037. The probability of
the price being in any one of the eight possible subcategories is 8(0.037) =
0.296.
14
Absence of price clustering implies that the stationary probability
distribution should be uniform, appropriately modified by the scaling noted
above. A standard chi-square goodness-of-fit test rejects this hypothesis for all
contracts. The large number of observations involved will result in a formal
statistical rejection for the most minor of deviations from the null.
Direct inspection of the table entries provides a more sensible
perspective. For all contracts, the estimates of the stationary benchmark floor
probabilities are virtually at their theoretical values under the null of no price
clustering. Given our scaling, the S&P frequencies each should be compared
with the value 0.05, with the comparable figure for currencies being 0.10. For
the S&P, values such as 0.048 are common, for example. Similarly, in the
currency analysis, values of 0.098-0.10, 0.103-0.104, and 0.107-0.108
dominate the results.
In contrast, GLOBEX trading exhibits clustering at the even price points.
For the S&P contract, frequencies at xxx.00 and xxx.50 are 0.079 and 0.063,
respectively. The frequency at truly odd price points is only 0.037.
There is a great deal of serial correlation in the price frequencies,
however. We therefore adopt the suggestion of Harris (1991), that an
alternative approach should be based on a Markov chain formulation that
characterizes time dependence in clustering frequencies.17
The probability of a transaction price changing from category i at time t1 to category j at time t is given by Pij, with matrix representation P.
Frequencies and population probabilities obey the summing up constraints,
s

jt
1
s
and
j1
P
j 1
ij
1
(5)
for all t. The first-order Markov chain model used here can then be written as
 t  P' t 1   t
(6)
This suggestion was not actually implemented by Harris, who used an alternative
method to account for serial correlation. He relied largely on cross-sectional variation to
model clustering effects. We have no such cross-section, and necessarily must adopt a
time-series oriented approach to the problem.
17
15
where the vector error is distributed with mean zero and a variance-covariance
matrix of known form.18
Maximum likelihood estimates of the elements of P are obtained through
sample averages of numbers of transitions between categories (e.g.,
Bartholomew(1975)). Space considerations preclude the reporting of all
matrices. We checked the characteristics of the estimated matrices to verify
the ergodic nature of the chain, and then computed the stationary probabilities
for all categories,  j , j=1,...,s, via the relation19
M   es1 ,
(7)
where es+1 denotes the (s+1)th column of the identity matrix of order s+1, I s+1.
Denoting 1s as a (sx1) vector of ones,
I  P'
M s
.
 1s ' 
(8)
These stationary probabilities are reported in Table VII. Once again, a
goodness-of-fit test rejects the null hypothesis of no clustering for all contracts.
On the other hand, our remarks concerning the magnitude of frequencies
relative to their theoretical values under the null could be repeated for the
stationary probabilities of the Markov chain almost verbatim. In fact, the
values of the stationary probabilities are identical to those of the average
frequencies for the S&P contract. They also are extremely close for the
currencies.20 In that case, the degree of clustering in the GLOBEX and
benchmark markets appears to be reduced somewhat based on the dynamic
model. The small changes cannot reverse our basic conclusions. Price
clustering appears to be virtually absent in the benchmark market, while
clustering at “round” fractions is clearly evident on GLOBEX. To the extent that
There are numerous references to to the formulation and estimation of Markov chain
models. See Hamilton (1994), MacRae (1977), and Conlisk (1976).
19 For example, in the Yen market, s=3 and   = Pr( Price of Yen = x.xxx0). In the S&P,
3
18
s=5 and  3 = Pr( Price of S&P = xxx.25).
20 If the first-order Markov model is a correct description of the data, average
frequencies and stationary probabilities from the model should be the same
asymptotically. The closeness of the estimates therefore provides some support for the
model.
16
clustering is an inverse measure of efficiency, the automated overnight system
performance is relatively poor.
4.2. Price Resolution
We now consider the price resolution hypothesis of Ball, Torous, and
Tschoegl (1985), in which greater trading activity implies a reduction in price
clustering. Harris (1991) also motivates consideration of market intensity by
noting that value discovery should be enhanced as the number of transactions
per unit time increases. In particular, it is possible that clustering activity in
GLOBEX ameliorates, and price discovery is enhanced, as the market
environment becomes more liquid.
We begin with a static analysis. In the same spirit as the production of
simple averages of frequencies in the last section, a set of linear probability
models is estimated. Price category frequencies are computed based on 15minute periods of trading. The frequencies are regressed on a constant, timeof-day indicators, and a measure of market intensity, F-1. F is computed as
1/1+T, where T is the frequency of transactions in a fifteen minute period. The
coefficients on market intensity are different from zero at any reasonable level
of statistical significance for all GLOBEX regressions.
Table VIII contains estimates of the derivatives of the price category
probabilities with respect to T. The results are generally consistent with the
price resolution hypothesis. The derivatives are negative for the round price
points in the S&P contract models, and for the .xxx0 category in the currencies.
Thus, increases in trading activity move prices away from .xxx0, but clustering
on the other round point appears to be exacerbated for the Yen and Swiss
Franc, in particular.
Diagnostic tests reveal that the regression residuals are highly serially
correlated, suggesting the need for a dynamic framework. We generalize the
Markov model of equation (6) to allow time variation in the transition
probabilities, written as
 t  P' (t ) t 1   t .
(9)
The idea behind this formulation is to examine how the transitions from price
point to price point vary with market conditions. The price resolution
hypothesis would suggest that as trading intensity increases, less clustering
17
should be observed. This effect would be implied by a negative derivative of the
diagonal elements of the transition matrix with respect to intensity that
correspond to round price points.
In order to parameterize the model, we exploit a generalization of the
interactive Markov chain concept of Conlisk (1976). Equation (9) is
supplemented by


 
Pij (t )  exp  ijo  1i  it 1   2i Ft11   3ii D i  j  it 1   4ii D i  j Ft11 exp g ijt 1 ,
(10)
where F is the measure of market intensity (one plus the number of
transactions per fifteen minute period) and Di=j is a dummy variable equal to 1
if i=j and 0 otherwise. The function g is a linear parameterization of time-ofday effects, including dummy variables for the hour after the open and before
the close, as well as the minimum of the time until the open and close,
modeled in the same fashion as in the last section.
The inclusion of lagged state probabilities in the transition structure is
the defining feature of the interactive Markov chain model. This specification
allows interaction between traders, as evidenced through their transactions,
whereas the standard chain model assumes such interactions away (see
Conlisk (1976)). In our case, the lagged state probabilities also constitute a
statistic for market behavior up to and including that at time t-1. The
dependence of Pij on state i is motivated largely by the fact that Pij can be
considered to be a measure of the attractive power of the ith state. The crucial
element of  to Pij() might intuitively be i. A more pragmatic reason concerns
the degree of parameterization of the model, which can grow to over a hundred
parameters without such restrictions. Given our constraints across rows of P,
the dummy variables allow for different effects on transactions that remain at
the same set of price points, as opposed to shifts to other price points available
in the market.
Even with such restrictions, the parameterization is still extremely rich,
and we adopt an additional modeling strategy to make estimation and inference
tractable. The constant terms,  ij0 , are fixed at values such that conditional on
all other parameters being zero, a uniform distribution is obtained over rows of
the transition matrix. This permits an intuitively reasonable interpretation of
the estimates of the time-varying components. Parameter estimates now
18
measure movements away from uniformity; uniformity should obtain were
clustering not an influence on price transitions.
Estimation of the model is based on the natural orthogonality conditions
implied by equations (9) and (10). We implement the adding-up constraint
through an additional set of moment restrictions,
s

E Pij ( t 1 , Ft 1 , g t 1 , )  1  0 ,
 j1

(11)
for j=1,...,s, which work extremely well in practice.21 As with the linear
probability models, we estimate the model on data at 15 minute intervals.
The parameters generally are estimated precisely, in the sense of small
standard errors. Space considerations preclude the reporting of all parameter
estimates, which by themselves have little intuitive content in any case. We
report the more interpretable derivatives of P, with respect to  and F. We
further limit this reporting to the diagonal elements of the transition matrix in
Table IX, which contains estimates of   i [ Pij ] and  F[ Pij ] , for i=j, evaluated
at the means of the data for all contracts and both market venues. There is
little variation over time of day, and we do not report separate sets of estimates
for the open and close.
We have included past state probabilities largely to control for the effects
of previous trading activity. On the other hand, examination of the derivatives
of the diagonal elements with respect to  i mildly reinforces the evidence of
clustering on GLOBEX. Some negative derivatives for odd price points are
observed, suggesting avoidance of odd prices.
For the round fractions, derivatives of price transitions with respect to
intensity now are uniformly negative for GLOBEX. Increases in activity tend to
move trading away from round numbers to other price points, consistent with
the price resolution hypothesis. This finding supports the notion of improved
system performance as the environment becomes more liquid. The qualitative
conclusions are the same across time of day. The price resolution hypothesis
also is generally supported in the benchmark market, but a comparison here is
less relevant than others in the paper, and we do not elaborate further. Price
19
clustering is virtually absent on the floor in any case, accounting in part for the
small magnitudes of the reported derivatives.
5. Concluding Remarks
As the presence of automated trading systems becomes more widespread, their efficiency properties are of increasing concern to regulators,
exchange policy makers, and system builders. The use of such market
structure, at least at the present time, remains prevalent in settings
characterized by a distinct lack of liquidity, including overnight trading, the
introduction of new instruments, emerging markets, and trading in illiquid
classes of securities more generally. We provide some evidence on pricing
behavior in one such market. A balanced view of the results suggests that the
automated system performs reasonably well in a variety of dimensions.
Not all illiquid environments are created alike, however. The magnitude,
components, and behavior of the bid-ask spread for the S&P futures contract
on GLOBEX look very much like that observed on the benchmark floor market.
In contrast, GLOBEX currency futures exhibit high spreads, driven by large
adverse selection components. The main difference between environments in
the trading of the instruments is the operation of the overnight spot foreign
exchange market. The potential for adverse selection is arguably much higher
in the overnight currency futures market, relative to the trading of the index
future. Harris (1990) and Stoll (1992) note that traders on an automated
system may be reluctant to submit limit orders and supply liquidity in the face
of increased adverse selection. Liquidity suffers, and pricing deteriorates as a
consequence. Our results in this respect are consistent with those of Frino,
McInish, and Toner (1998). They find that the performance of the automated
DTB system deteriorates during periods of high adverse selection, relative to
the benchmark of floor trading on LIFFE.
The empirical results in this paper alone do not imply that market
liquidity is exogenously determined relative to the automated trading
mechanism. We do not, therefore, claim a clear "natural experiment" within
which to study system performance. It is arguably the case that the demand
This technique for discrete probability models is more fully elaborated upon in
Bollerslev, Domowitz and Wang (1997) in a different context.
21
20
for trade execution services and what resources to expend on the development
of information may depend on the mechanism. On the other hand, liquidity
provision is excellent in many markets of same or similar design to that studied
here, operating during regular trading hours. Our findings suggest that the
nature of the environment is an important determinant of market
performance, but that an automated market can operate well in a relatively
illiquid setting.
21
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25
Table I
Summary Statistics
This table contains summary statistics on prices and logarithmic price returns from trading on
the GLOBEX automated system and the Chicago Mercantile Exchange floor market, for the
September 1994 S&P 500, the Deutschemark (DM), the Yen, and the Swiss Franc (SF) contracts
over the period 7/1/94 through 9/1/94. The number of observations varies from about 3000 to
8000 on GLOBEX to roughly 72,000 to 95,000 for the floor, depending on the contract.
Panel A:
S&P 500 Futures Contract
Globex
price
return
std. dev.
lag correlation
trades/hour
Panel B:
DM Futures Contract
Globex
price
return
std. dev.
lag correlation
trades/hour
Panel C:
0.6395
0.0000
0.0005
-0.1345
4.108
Yen Futures Contract
Globex
price
return
std. dev.
lag correlation
trades/hour
Panel D:
458.44
0.0000
0.0002
-0.2402
11.67
1.0115
0.0000
0.0004
-0.0754
6.807
Swiss Franc Futures Contract
Globex
price
return
std. dev.
lag correlation
trades/hour
0.7586
0.0000
0.0007
-0.1111
2.143
Floor
459.30
0.0000
0.0001
-0.0708
312.9
Floor
0.6387
0.0000
0.0002
-0.0420
225.9
Floor
1.0117
0.0000
0.0001
-0.0189
249.2
Floor
0.7578
0.0000
0.0002
-0.0493
239.5
Table II
Intra-Session Variation in Market Characteristics
This table contains summary statistics on price changes, volatility computed as the averaged
absolute price changes, number of trades per hour, and the variance of price relative to number
of trades, from trading on the GLOBEX automated system and the Chicago Mercantile Exchange
floor market, for the September 1994 S&P 500, and the Deutschemark (DM contracts over the
period 7/1/94 through 9/1/94. Columns marked “open” contain figures for the first hour of the
trading session, while columns marked “close” contain analogous numbers for the last hour of
the trading session. The indicator “middle” covers the hours of 18:30 through 2:45 on Globex,
and 11:30 through 13:00 on the floor, for the DM. For the S&P 500 contract, “middle”
encompasses 19:45 through 4:00 on Globex and 11:00 through 12:45 on the floor.
Panel A:
S&P 500 Futures Contract
p
volatility
trades/hour
2(p)/trades
lag correlation
a
b
c
c
close
-2.79a
0.05
11.8
0.14
-0.46
0.35a
0.05
3.54
0.05
-0.34
0.33a
0.06
103
0.02
-0.29
open
7.12b
0.06
447
3.67a
0.10
Floor
middle
0.55a
0.05
258
3.84a
-0.09
close
0.36a
0.06
293
5.63a
-0.01
DM Futures Contract
p
volatility
trades/hour
2(p)/trades
lag correlation
b
Globex
middle
x 10-3
x 10-5
x 10-7
Panel B:
a
open
x 10-3
x 10-5
x 10-7
open
Globex
middle
close
open
Floor
middle
close
-2.35b
0.20a
3.29
0.07b
-0.25
0.20b
0.21a
3.69
0.01b
-0.08
-1.23b
0.19a
5.36
0.03b
-0.21
0.11b
0.10a
300
0.05c
-0.04
0.08b
0.10a
240
0.03c
0.02
0.07b
0.11a
154
0.09c
-0.29
Table III
Bid/Ask Spreads
This table contains estimates of bid/ask spreads. The minimum price variation for the S&P 500
futures contract is 0.05, and that for the currency futures is 0.0001, scaled by a factor of 100 to
be 0.01 for reference in the table. The notations G and F denote GLOBEX trading and CME floor
trading, respectively. The row heading “Total” refers to estimated spreads over the entire trading
day. “Open” and “Close” denote estimates taken over the hour after trading begins and the hour
before trading ends, respectively. “Middle” denotes estimates over trading activity between the
hour after the open and the hour before the close. Generalized-method-of-moments robust
standard errors are reported in parentheses.
S&P
DM
YEN
SF
Total-G
0.104
(0.002)
0.030
(0.001)
0.042
(0.001)
0.053
(0.003)
Total-F
0.106
(0.000)
0.020
(0.000)
0.024
(0.000)
0.024
(0.000)
Open-G
0.104
(0.002)
0.030
(0.001)
0.043
(0.001)
0.053
(0.003)
Open-F
0.110
(0.000)
0.019
(0.000)
0.023
(0.000)
0.023
(0.000)
Close-G
0.103
(0.002)
0.031
(0.001)
0.041
(0.001)
0.053
(0.003)
Close-F
0.104
(0.000)
0.019
(0.000)
0.023
(0.000)
0.024
(0.000)
Middle-G
0.107
(0.002)
0.030
(0.001)
0.042
(0.001)
0.053
(0.003)
Middle-F
0.106
(0.002)
0.021
(0.000)
0.024
(0.000)
0.024
(0.000)
Table IV
Bid-Ask Spread Correlations
This table contains the correlations of the estimated average spread with price changes, volatility
computed as the averaged absolute price changes, and number of trades. The last row is the
standard deviation of the spread. The data are from trading on the GLOBEX automated system
and the Chicago Mercantile Exchange floor market, for the September 1994 S&P 500, and the
Deutschemark (DM contracts over the period 7/1/94 through 9/1/94. Columns marked “open”
contain figures for the first hour of the trading session, while columns marked “close” contain
analogous numbers for the last hour of the trading session. The indicator “total” contains figures
for the full day's trading session in each market.
Panel A:
p
volatility
trades
(s)
a
open
Globex
total
close
open
Floor
total
close
0.009
0.187
0.135
0.025
0.146
0.256
0.426
0.018
0.111
0.325
0.412
0.019
-0.117
0.309
0.849
0.018
0.057
0.289
0.840
0.017
0.016
0.341
0.772
0.017
x 10-3
Panel B:
p
volatility
trades/hour
 (s)
a
S&P 500 Futures Contract
x 10-3
DM Futures Contract
open
Globex
total
close
open
Floor
total
close
-0.101
0.202
0.103
0.063a
0.007
0.257
0.386
0.047a
-0.002
0.299
0.251
0.064a
0.060
0.398
0.779
0.034a
0.043
0.299
0.759
0.033a
0.049
0.381
0.621
0.033a
(table IV, continued)
Panel C:
p
volatility
trades/hour
(s)
a
open
Globex
total
close
open
Floor
total
0.017
0.103
0.122
0.075a
-0.02
0.183
0.305
0.063a
-0.054
0.045
-0.011
0.074a
0.243
0.447
0.764
0.038a
-0.013
0.323
0.660
0.040a
-0.055
0.374
0.595
0.038a
close
x 10-3
Panel D:
p
volatility
trades/hour
(s)
a
Yen Futures Contract
x 10-3
SF Futures Contract
open
Globex
total
close
open
Floor
total
close
0.024
0.289
0.148
0.124a
0.002
0.265
0.281
0.081a
-0.027
0.175
0.207
0.130a
0.011
0.325
0.754
0.039a
0.014
0.279
0.701
0.037a
0.016
0.259
0.607
0.040a
Table V
Adverse Selection Components of the Spread
This table contains statistics relating to the adverse selection component of bid-ask spreads,
expressed as a proportion of the spread. The notations G and F denote GLOBEX trading and
CME floor trading, respectively. The row heading “Total” refers to estimated adverse selection
components over the entire trading day. “Open” and “Close” denote estimates taken over the
hour after trading begins and the hour before trading ends, respectively. “Other” denotes
estimates over trading activity between the hour after the open and the hour before the close.
Generalized-method-of-moments robust standard errors are reported in parentheses.
S&P
DM
YEN
SF
Total-G
0.472
(0.014)
0.563
(0.032)
0.690
(0.025)
0.672
(0.043)
Total-F
0.552
(0.003)
0.424
(0.011)
0.559
(0.003)
0.540
(0.004)
Open-G
0.632
(0.061)
0.348
(0.135)
0.536
(0.185)
0.808
(0.170)
Open-F
0.573
(0.003)
0.381
(0.013)
0.520
(0.004)
0.496
(0.006)
Close-G
0.467
(0.021)
0.657
(0.083)
0.728
(0.094)
0.665
(0.140)
Close-F
0.547
(0.004)
0.340
(0.013)
0.539
(0.006)
0.536
(0.006)
Other-G
0.449
(0.024)
0.570
(0.036)
0.697
(0.026)
0.661
(0.047)
Other-F
0.548
(0.003)
0.440
(0.011)
0.575
(0.003)
0.553
(0.004)
Table VI
Price Clustering: Average Tick Frequencies
This table contains average price category frequencies. Prices in the S&P 500 are written to two
decimal places, e.g., 470.05. The five price clustering categories are denoted by xxx.05 (8
possible prices), xxx.10 (8 possible prices), xxx.25 (2 possible prices), xxx.50, and xxx.00. For
example, the stationary probability reported in panel A for the xxx.05 category is 0.037,
representing the probability of price being in any one of the eight possible subcategories divided
by 8. Prices in the currency futures are written to four decimal places, e.g., 0.7651. The price
categories are denoted by x.xxx1, x.xxx5, and x.xxx0, where the first category has 8 elements.
Standard errors are not reported in the tables, but are zero rounded to three decimal places.
Panel A:
S&P 500 Futures Contract
price
Globex
xxx.05
xxx.10
xxx.25
xxx.50
xxx.00
Panel B:
Floor
0.037
0.058
0.049
0.063
0.079
0.048
0.053
0.048
0.049
0.053
Currency Futures Contracts
DM
Yen
SF
price
Globx
Floor
Globx
Floor
Globx
Floor
.xxx1
.xxx5
.xxx0
0.091
0.129
0.140
0.100
0.098
0.104
0.083
0.141
0.200
0.098
0.107
0.112
0.079
0.156
0.214
0.099
0.103
0.108
Table VII
Price Clustering: Stationary State Probabilities
This table contains estimates of stationary price category probabilities obtained from maximum
likelihood estimation of the transition matrix of a first-order Markov chain. Prices in the S&P 500
are written to two decimal places, e.g., 470.05. The five price clustering categories are denoted by
xxx.05 (8 possible prices), xxx.10 (8 possible prices), xxx.25 (2 possible prices), xxx.50, and
xxx.00. For example, the stationary probability reported in panel A for the xxx.05 category is
0.037, representing the probability of price being in any one of the eight possible subcategories
divided by 8. Prices in the currency futures are written to four decimal places, e.g., 0.7651. The
price categories are denoted by x.xxx1, x.xxx5, and x.xxx0, where the first category has 8
elements. Standard errors are not reported in the tables, but are zero rounded to three decimal
places.
Panel A:
S&P 500 Futures Contract
price
Globex
Floor
xxx.05
xxx.10
xxx.25
xxx.50
xxx.00
0.037
0.058
0.049
0.063
0.079
0.048
0.053
0.048
0.049
0.053
Panel B:
Currency Futures Contracts
DM
Yen
SF
price
Globx
Floor
Globx
Floor
Globx
Floor
.xxx1
.xxx5
.xxx0
0.091
0.129
0.140
0.099
0.098
0.106
0.087
0.146
0.157
0.099
0.106
0.100
0.087
0.138
0.166
0.099
0.101
0.108
Table VIII
Price Resolution: Intensity Effects in a Static Framework
This table contains estimates of the derivatives of the price category, or state, probabilities,  ,
with respect to the frequency of transactions per 15-minute period of trading, T at time t-1. The
derivatives are evaluated at sample means of the data, and are based on parameter estimates of a
static linear probability model, augmented by time of day effects.
Panel A:
S&P 500 Futures Contract,
price
Globex
xxx.05
xxx.10
xxx.25
xxx.50
xxx.00
a
b

 i 
T
Floor
1.03a
-0.24a
-0.49a
-0.84a
-0.51
0.11a
-6.31b
-3.52b
-2.59b
-0.24a
x 10-3
x 10-5
Panel B:
Currency Futures Contracts,
DM

 i 
T
Yen
SF
price
Globx
Floor
Globx
Floor
Globx
Floor
.xxx1
.xxx5
.xxx0
2.27a
-1.52a
-0.58
0.97b
-2.48b
-7.19b
-1.29a
0.41a
-0.51
-3.93b
9.89b
-0.97a
-4.49a
3.01a
-0.74
2.79b
0.77b
-0.81a
a
b
x 10-3
x 10-5
Table IX
Market State and Intensity Effects in a Dynamic Model of
Price Clustering
This table contains estimates of the derivatives of the diagonal elements of a Markov chain
transition matrix at time t, with respect to price category, or state, probabilities,  , and the
frequency of transactions per 15-minute period of trading, T, both at time t-1. The derivatives are
evaluated at sample means of the data, and are based on parameter estimates of a time-varying
interactive Markov chain model.
Panel A:
S&P 500 Futures Contract
Market State

Pij
 i
 
i j
Market Intensity

Pij
T
 
i j
price
Globex
Floor
Globex
Floora
xxx.05
xxx.10
xxx.25
xxx.50
xxx.00
-0.521
0.406
0.505
2.247
0.135
0.479
0.644
1.649
1.771
1.737
-0.012
-0.018
-0.025
-0.008
-0.021
0.021
-0.016
-0.112
-0.295
-0.456
a
x 10-2
Panel B:
DM Futures Contracts
Market State

Pij
 i
 
i j
Market Intensity

Pij
T
 
i j
price
Globex
Floor
Globex
Floora
.xxx1
.xxx5
.xxx0
0.622
0.539
-1.854
0.000
1.765
3.060
0.369
-0.007
-0.118
0.000
-0.261
-0.495
a
x 10-2
(Table IX, continued)
Panel C:
Yen Futures Contracts
Market State

Pij
 i
 
i j
Market Intensity

Pij
T
 
i j
price
Globex
Floor
Globex
Floora
.xxx1
.xxx5
.xxx0
-0.144
-0.252
0.065
0.446
0.780
0.839
-0.050
-0.090
-0.081
0.774
-0.310
-0.344
a
x 10-2
Panel D:
SF Futures Contracts
Market State

Pij
 i
 
i j
Market Intensity

Pij
T
 
i j
price
Globex
Floor
Globex
Floora
.xxx1
.xxx5
.xxx0
0.096
0.732
0.534
-0.013
0.292
0.274
0.096
-0.372
-0.552
-0.051
-0.128
-0.139
a
x 10-2