sarwesh

Market liquidity can be measured by the cost of e€ecting a transaction at a
given point of time, or by the time it takes to transact (Lippman and McCall,
1986; Amihud and Mendelson, 1989). In our examination of the order book
and order ¯ow, various aspects of the cost measure of market liquidity (such as
width, depth, resiliency and the availability of immediacy) were addressed. The
cost measure of liquidity is more relevant to market order traders whose objective
is to obtain immediacy at a low cost. The time measure of liquidity is
more relevant to limit order traders, who supply liquidity on the SSM. In a
setting where limit orders provide immediacy and wait for order execution,
liquidity is measured by the expected time to execute a limit order at a given
price, and more generally, by the probability of limit order execution. In this
section, we examine these issues.


1-Order duration given limit order characteristics


The duration of an order, Ti, is the length of time until the order is executed,
canceled or expired. In this subsection, we analyze order duration data using
survival analysis. This statistical technique is very suitable for modeling order
duration, since order durations are non-negative and random. This statistical
technique allows us to estimate the conditional distribution of limit order execution
times, Ti, as a function of explanatory variables, xi, such as order
characteristics and state of the book, F(Ti<t | xi). F …† is the CDF of the
Weibull distribution, 1 ÿ exp…ÿkit†p and ki ˆ exp…ÿx0ib†. 40 The parameters p
and b can be estimated by maximum likelihood. Following Lo et al. (1997), we
treat limit orders that are canceled or expired as censored observations. Ignoring
the information in non-executed orders can bias the estimator of the
conditional distribution of execution times.
We estimate the survival model for buy and sell limit orders. The set of
regressors in x includes a constant, an aggressiveness indicator, order size,
number of orders per package, the inside spread, order imbalance, shares in the
book, prior market order, and a volatility measure. Following Harris (1996),
we measure order aggressiveness by 1 ÿ 2…A ÿ P†=…A ÿ B† for buy orders and
the negative of this quantity for sell orders, where A(B) denotes the ®rst best
ask (bid), and P is the limit order price. This measure assigns a value of one to
market orders and less than one to limit orders. Limit orders placed at the


quote have a value of ±1, and the di€erence between the order price and the
best quote on the same side increases as this value gets smaller.
The order imbalance variable is de®ned as k ˆ Qb=…Qb ‡ Qs†, for buy orders
and …1 ÿ k† for sell orders, where Qs…Qb† is the number of shares o€ered at A
(demanded at B) at the time of order entry. Shares in the book is the number of
shares in the book ahead of the order which have a higher priority for execution.
Prior market order is the ratio of the market orders that are initiated by
the same side of the market to the total market orders submitted during the last
half-hour.


[COLOR="2-Black"]The probability of executing limit orders[/color]



When immediacy is available during a continuous trading session, a trader
can trade with certainty using a market order and not a limit order. The
probability of executing a limit order is always less than one. In this section, we
analyze the probability of order execution using a logistic probability model.
The dependent variable, y, is the execution indicator, which equals one if the
order is executed and zero otherwise. The probability of execution is conditioned
on a set of regressors, x, Prob‰y ˆ 1jxŠ ˆ K…x0b†, where K() is the logistic
cumulative distribution function. The marginal e€ect of x on the
probability is K…x0b†‰1 ÿ K…x0b†Šb. The set of regressors in x includes the same
set used in survival analysis. After pooling the data for all stocks, we estimate
the coe�cient, b, and the marginal e€ect (the slope). The results are reported in
Table 10. The marginal e€ect, K(), is evaluated at the mean of the variable.
Similar to the ®ndings in the previous subsection, price aggressiveness has a

positive e€ect on the probability of execution. Overall, limit orders with
``reasonable'' prices are highly liquid in terms of executability. The results also
indicate that more active traders have higher probabilities of execution. Active
traders frequently have standing ®rm orders at and away from the quote either
to make a market, or to seize the free option quickly. Since they also monitor
the market more closely, we expect them to adjust their exposed orders more
frequently than others. The negative signs on the estimated coe�cients for the
order size variable suggest that larger orders are more di�cult to execute. The
signs of the estimated coe�cients of the volatility measure variable imply that
sell (buy) orders have higher (lower) probabilities of execution when market
conditions are more active. This could be attributed to the 9.23% rise in the
market index over the sample period.