1 Introduction

Limit order is one of the most essential elements in equity trading because most markets are designed as an electronic limit order book (Foucault 1999; Hollifield et al. 2004). Time is an important piece of information in trading (Easley and O’Hara 1992) yet extant theoretical limit order book studies including Kyle (1985), Glosten (1994), Foucault et al. (2005) and Roşu (2009) focus on order placement decision and provide limited guidance for modelling limit-order execution times and time-to-next-order-event. The empirical evidence on time between order events (execution, revision and cancellation activities) is also scant.

After a limit order has been placed, the order may be fully executed, partially executed, revised, or cancelled. This study contributes to the literature by using multiple-spell duration model to study the determinants of the duration of limit order events, taking into account the full spectrum of events that occur in the life of each limit order.Footnote 1 Existing studies in the duration of limit order event such as Lo et al. (2002) assume that revision and cancellation events are censored observations. They analyze time-to-execution using a single-spell duration model hence they are unable to account for successive limit order events and their determinants.

This study is the first, to our knowledge, to employ a multiple-spell duration model to study dynamic limit order placement strategies in order to take into account the full spectrum of order events. By allowing for duration dependence and addressing the unobserved heterogeneity, a multiple-spell duration model of survival analysis is a more appropriate econometric tool to address the dynamic of limit order placement strategies. This is because order placement strategies are constructed from a series of order events rather than single, independent events.

Our empirical results from the multiple-spell duration model reveal a number of factors that determine the duration of various limit order events. For example, larger opposite-side liquidity motivates traders to intensify their revision and cancellation activities, and hence a higher occurrence probability of revision and cancellation limit order events. Importantly, the sensitivity of duration to these factors depends on whether the starting point is an order submission, partial execution or revision.

We use Australian Securities Exchange (ASX) order data from the Securities Industry Research Centre of Asia–Pacific (SIRCA) which allows us to identify various events in the life of a limit order. The ASX had two major technological upgrades during our sample period. Contrasting estimates based on data from different technological regimes (in years 2000, 2007 and 2011) illustrate that the differential impact of determinants of durations across order submissions, order revisions and partial executions persists and grows stronger in the latter lower latency periods. These results are robust across buy limit orders and sell limit orders as well as for large-capitalisation stocks and small-capitalisation stocks. An implication of our research findings is that ignoring order revision, cancellation, partial execution and considering only order submission and execution as in previous studies might lead to missing out important information in the trading process.

This study is related to the literature of limit order placement strategies, which has grown over the past two decades (see, for example, Foucault 1999; Sandas 2001; Lo et al. 2002; Cao et al. 2008; Hasbrouck and Saar 2013). The primary focus of this literature is on order submission strategies where traders choose among different order types (such as market orders vs. limit orders) and they tend to assume limit orders cannot be revised or cancelled once submitted (see Liu (2009) and the reference therein). Due to an increase in order cancellation activity observed in many markets,Footnote 2 studies began to emerge over the past decade to examine the decision to cancel and revise (Hall and Hautsch 2006; Hasbrouck and Saar 2009; Liu 2009; Fong and Liu 2010; Chan and Ma 2013; Hasbrouck and Saar 2013; Bień-Barkowska 2014; Van Ness et al. 2015). Order revision is an important element of dynamic order placement strategies where traders have an option to change the price, the size, or both, of an existing order once they are placed into the limit order book (Harris 1998; Liu 2009; Fong and Liu 2010; Menkhoff and Schmeling 2010; Tseng and Chen 2015; Viljoen et al. 2015). As the advancement of communication and computational technology in trading lowers the costs of monitoring and managing orders, the value of considering order events accurately increases.

2 ASX order data

2.1 Trading systems of the Australian securities exchange (ASX)

The Australian Securities Exchange (ASX) is a highly transparent market that relies solely on the liquidity provided by investors. There are no designated market makers or dealers on the ASX. The ASX had employed the fully computerised Stock Exchange Automated Trading System (SEATS) from 1987 to 2006. In October 2006, SEATS was replaced by the Integrated Trading System (ITS), which is a fully-electronic trading system utilised for its efficiency in dealing with fast transactions. ITS kept the same trading rules and market structure of the ASX, but provided a number of operational improvements over SEATS. From November 2010, ASX Trade, an ultra-low latency trading platform replaced ITS. Powered by NASDAQ OMX’s Genium INET platform, ASX Trade provided one of the fastest integrated equities and derivative platforms in the world at that time.

2.2 Limit order data

This study investigates the dynamic order placement activities of 40 index stocks listed on the ASX over the three sample periods, year 2000, year 2007 and year 2011. Each sample consists of 20 large and 20 small stocks, ranked by market capitalisation. Large-cap stocks are the top 20 common stocks that are traded on the ASX200 index. For the purpose of this study, small-cap stocks are chosen as the 20 common stocks ranked from 111th to 130th on the ASX200 index. Year 2000 is chosen since it was the year that the ASX200 index was formed and started its operation. Years 2007 and 2011 are chosen as they were the years that immediately followed the inceptions of ITS and ASX Trade, respectively.

In each sample period, the month of August is chosen as the investigation period of this study as most preliminary end-of-year earnings reports are released in August. As a result, more trading activities are expected in August. The order book dataset (known as the AusEquities) is provided by SIRCA. It records the details of each order including the date, time, stock code, price, transacted volume and order type. Each order is assigned with a cross reference identifier which allows us to track the entire life of the limit orders, i.e. orders that are revised (either an order-price revision, or an order-volume revision, or both) as well as orders that are cancelled, partially or fully executed after submissions. Our sample comprises a total of 12,791,710 order events. Market orders account for about 55% and limit orders constitute about 45% of the order submissions. Apart from the number of executions, revision order events make up about 50% of limit orders, whereas cancellation events represent about 20% of all limit orders. The statistics clearly indicate that investigating the limit order placement strategies cannot be thoroughly and properly carried out without paying special attention to the revision and cancellation activities.

Table 1 provides the summary statistics for the time between order events in each of the years: 2000, 2007 and 2011, respectively. Figures 1 and 2 compare the time between order events for buy and sell limit orders, respectively, across three years: 2000, 2007 and 2011. Preliminary observations seem to suggest that technological advancement shortens the average time between order events as it enables the market to trade faster and trade more frequently.

Table 1 Summary statistics of the time between order events
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Fig. 1
figure 1

Combined charts of average time between order events for buy limit orders. This figure presents a comparison for buy limit orders between the periods before ITS, after ITS and after ASX TRADE

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Fig. 2
figure 2

Combined charts of average time between order events for sell limit orders. This figure presents a comparison for sell limit orders between the periods before ITS, after ITS and after ASX TRADE

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3 Empirical methodology

3.1 Construction of full order history

We begin the empirical analysis by constructing the complete life of each limit order placed in the limit order book during the sample periods. The full life of a limit order consists of a series of order events, including submission, execution, revision and cancellation. A limit order’s life is ended when it is fully executed or fully cancelled from the limit order book. Using the unique cross reference identifier that is assigned to each order, we are able to trace the relevant events pertaining to each limit order. Following its submission into the limit order book, a limit order can be fully executed, partially executed, revised, or cancelled. If the limit order is partially executed or revised, the possible subsequent events will be the same as in the first phase. That is, the partially executed or revised order can be followed by a full execution, a partial execution, a revision or a cancellation. Figure 3 provides a snapshot of the general transitions of limit order events. We have a total of 6,246,955 unique limit orders in our sample, and 2,226,475 (35.64%) of these orders experience more than one order event after their submission.

Fig. 3
figure 3

The general transitions of limit order events

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3.2 Survival analysis with a multiple-spell duration model

In this section, we outline the multiple-spell duration model that is used to examine the determinants of multiple order events that occur throughout the entire life of limit orders.Footnote 3

Survival analysis involves a nonnegative random variable which represents the length of a limit order spell. Let T be this random variable. It represents the time it takes for a limit-order to transit from one event to another (time-to-an-order-event). If h(t) is the hazard rate of T at time t, then h(t)dt shows the probability that an order which has survived (being placed with one event) through time t will fail (being placed with another event) in the interval [t, t + dt). Let f(t) be the probability density function of T and let F(t) be the cumulative density function of T, then the hazard function can be defined as:

$$ h\left( t \right) = \frac{f\left( t \right)}{1 - F\left( t \right)} $$
(1)

The hazard rate is the rate at which an order spell is completed (an order is completely transited from one event to another) after t, given that they last at least until time t. The survival function is defined as S(t) ≡ 1 − F(t). It shows the probability that the length of an order spell will be at least t.

In order to estimate hazard function and survival function, a non-parametric or a parametric survival analysis can be utilised. The non-parametric approach does not rely on any parametric assumption when estimating the survival function. On the other hand, the parametric approach assumes a particular parametric distribution of failure times and the survival function can be estimated using maximum likelihood based on the distributional assumption. This research employs a parametric survival analysis in the estimation of both the hazard function and the survival function due to its dominance over the non-parametric counterpart (see, for example, Lo and Farmer 1999; Lo et al. 2002; Lancaster 1979; Van den Berg 2001). The model assumes the (non-negative) arrival rate to be constant per unit time.Footnote 4 Preliminary analysis (unreported) shows that our duration data exhibits exponential distribution. We estimate both the hazard function and the survival function parametrically using the exponential distribution as it is one of the most widely used distributions for duration analyses (Kalbfleisch and Prentice 2011).

Our econometric specification of the multiple-spell duration model is similar to Gagliarducci (2005) who used the model to study the path to a permanent job from a sequence of temporary contracts and periods of unemployment. Gagliarducci’s labour market setting possesses some similarities with placement activities of order events. Similarly to labour market transitions, following the initial submission, a limit order can pass through a sequence of multiple events before it can be fully filled or completely cancelled from the system.

In our case, we consider twelve event transitions.Footnote 5 They include (1) submission-to-full-execution, (2) submission-to-partial-execution, (3) submission-to-revision, (4) submission-to-cancellation, (5) partial-execution-to-full-execution, (6) partial-execution-to-partial-execution, (7) partial-execution-to-revision, (8) partial-execution-to-cancellation, (9) revision-to-full-execution, (10) revision-to-partial-execution, (11) revision-to-revision, and (12) revision-to-cancellation.

Let ti be a sequence of adjacent periods of time (spells) spent in different states. For each series of limit order events, a sequence ti={t ci } is observed. The duration spent is denoted by t, the particular series of limit order events occur for an individual stock is denoted by the subscript i. cth spell in a specific state is denoted by the superscript c. This multiple-spell duration model specification captures the dynamic aspect of transition between different states.

The hazard rate, θkj, is defined as the intensity of the transition to the destination state (denoted by j) after a visit in the origin state (denoted by k). The function of the hazard rate, θkj, for the series i at its cth spell is expressed as the following:

$$ \theta_{kj} \left( {t_{i}^{c} |X_{ikj} ;\beta } \right) = h_{kj} \left( {t_{i}^{c} } \right){ \exp }\left( {\beta_{kj}^{{\prime }} X_{ikj} } \right)v_{ikj} $$
(2)

where \( h_{kj} \left( {t_{i}^{c} } \right) \) is a baseline hazard; \( X_{ikj } \) is a set of explanatory variables which incorporate both stock market conditions and limit order characteristics that can influence the duration remaining in the origin state or the probability of transitioning from state k to state jFootnote 6; and \( v_{ikj} \) is a random individual effect to capture the unobserved heterogeneity. All the individual covariates, \( X_{ikj} \), which determine the hazard rate of transition between limit order events, are fixed to their values at the beginning of each spell. The construction of the explanatory variables is described in further details in Sect. 3.3.

3.3 Incorporating explanatory variables in the duration models

The duration models employed in this study allow for the inclusion of explanatory variables which describe the limit order characteristics and the stock market conditions in which the order events occur. Since the survival times of limit orders depend on several factors such as limit order price, order size, market depth and market liquidity, the limit order characteristics and market conditions are highly influential on the decisions and strategies of traders in placing orders in the market. In the multiple-spell duration model, explanatory variables are measured at the beginning of each limit order spell. The variables are defined and calculated separately for buy and sell limit orders.Footnote 7

Let P be the most recent transaction price, L be the limit price, B be bid price, A be the ask price, MQ be the mid-quote price, Sb be the bid size, Sa be the ask size and Sl be the limit order size. For buy limit orders, the explanatory variables are defined as follows:

PRICEGAP

= MQ − L

INITRADE

= 1

if the previous transaction price is greater than MQ

= − 1

if the previous transaction price is less than MQ

= 0

if the previous transaction price is equal to MQ

SSLIQUIDITY

= (1 + B − L) × logSb

if L ≤ B

= 0

if L > B

MKDPR

= (P − L) × SSLIQUIDITY

if P ≥ L

= 0

if P < L

OSLIQUIDITY

= logSa/(1 + A − L)

if A ≥ L

= logSa

if A < L

ORDSIZE

= logSl (1 + A − L)

if A > L

= log(Sl − Sa)

if A = L and Sl> Sa

= 0

if otherwise

The above explanatory variables capture the characteristics of the limit orders as well as the conditions of the stock market where the orders are placed. The variable PRICEGAP measures the distance of the limit buy price from the mid-point of the prevailing quotes. The variable INITRADE indicates if the previous transaction is a buyer-initiated trade or a seller-initiated trade. SSLIQUIDITY is the same side (buying side) liquidity and is constructed as a measure of the market depth scaled by the distance between the bid price and the limit buy price. The variable MKDPR is an interactive term added to the model to capture nonlinearities between market depth and market price relative to the limit price. OSLIQUIDITY shows the liquidity that is available in the market on the opposite side (selling side). OSLIQUIDITY decreases as the limit buy price drops further below the ask price. The variable ORDSIZE is a measure that captures the number of shares demanded by the limit order and the measure is scaled by the difference between the limit buy price and the ask price.

The explanatory variables for sell limit orders are defined in a similar way as buy limit orders, but some of the effects are in the opposite direction. As a result, four of the above explanatory variables are redefined as follows:

PRICEGAP

= L − MQ

SSLIQUIDITY

= (1 + L − A) × logSa

if L ≥ A

= 0

if L < A

MKDPR

= (P − L) × SSLIQUIDITY

if P ≤ L

= 0

if P > L

OSLIQUIDITY

= logSb/(1 + L − B)

if B ≤ L

= logSb

if B > L

ORDSIZE

= logSl (1 + L − B)

if L > B

= log(Sl− Sb)

if L = B and Sl> Sb

= 0

if otherwise

The summary statistics of the time between order events are presented in Table 1. With enhanced trading and monitoring technology, the time between successive order events has reduced remarkably. For example, the average time between limit buy order submission and the first revision fell by more than tenfold from 19 min in 2000 to 1.6 min in 2011, while the corresponding time to cancellation fell by 19 times from 38 to 2 min. Table 2 presents the summary statistics of the explanatory variables.

Table 2 Summary statistics of explanatory variables
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In addition, the survival analysis with multiple-spell duration in this study also includes PREVDUR as an additional explanatory variable to ensure that the duration dependence between successive spells is taken into account in the analysis. This variable PREVDUR is defined as the time spent previously in the preceding states prior to the current limit order spell.

4 Empirical results

4.1 Survival analysis with a multiple-spell duration model

Table 3 presents the results for the multiple-spell duration analysis of buy limit orders (in Panel A) and sell limit orders (in Panel B) in the pooled sample of the initial period (August 2000). Limit order dynamics are specified as sequences of multiple limit order events. The estimation model used in this analysis, as abovementioned, is the proportional hazard model under the exponential distribution for limit order times.

Table 3 Multiple-spell duration analysis of limit orders of the pooled sample in the initial period (August 2000)
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The first explanatory variable of interest is PRICEGAP. The coefficient estimates of this variable are mostly negative and significant for all order spells in both samples of buy limit orders and sell limit orders. The result implies a negative relationship between the hazard rate of order events and the distance from the limit price to the mid-quote price. In other words, the closer the limit price is placed from the mid-quote (i.e. the smaller PRICEGAP), the higher the transition-specific hazard rate, implying a higher probability of transition from one event to another. This is consistent with the argument put forth by Liu (2009) and Fong and Liu (2010), who assert that traders monitor their limit orders closely, particular when a limit order is submitted with a more aggressive price due to high non-execution (NE) and free-option (FO) risks.

The coefficient estimates of INITRADE for buy limit orders are all significantly negative, whereas those for sell limit orders are all significantly positive. This result suggests that if the previous transaction is a seller-initiated trade, a buy limit order tends to experience a higher probability of execution (both full and partial execution), as well as revision and cancellation. On the other hand, a sell limit order is likely to experience a higher chance of execution, revision or cancellation if the prior transaction is a buyer initiated trade.

Two different types of liquidity are captured by the two explanatory variables SSLIQUIDITY and OSLIQUIDITY. The variable SSLIQUIDITY shows the relation between the same-side depth of the limit order book and the hazard rate of order events. The results are mostly negative and significant for both buy limit orders and sell limit orders. This negative relation suggests that the deeper the limit order book on the same-side, the lower the probability of transition to subsequent order events. As the limit order book is congested with same-side orders, any arriving limit orders will find it harder to be executed (Parlour 1998). Moreover, the significantly negative coefficient estimates of the variable SSLIQUIDITY also suggest that when the depth of the limit order book on the same-side increases, unless the limit order is revised more aggressively, revision or cancellation (and resubmission) would cause these orders to lose their time priority. As a result, these existing limit orders will tend to have a lower probability of being revised or cancelled.

The coefficient estimates of OSLIQUIDITY show some differences in the results among the categories of submission, revision and execution, for both buy and sell limit orders. The coefficient estimates are generally positive and significant for spells that transit to an order revision. The effect, however, is stronger for buy limit orders than sell limit orders. This result is in line with the view that as the opposite-side liquidity increases, traders tend to revise their limit orders so that the orders can avoid being adversely executed in an unfavourable market. Traders can try to gain a better execution outcome by revising the limit order to a better price. Consequently, it results in a higher probability of transition into limit order revisions. Moreover, the significantly positive relationship between the opposite-side liquidity and the intensity of limit order cancellation is also worth noticed, especially for orders originating from submission or partial execution. This result is consistent with Ranaldo (2004) who finds evidence to indicate that there is a higher level of defensive trading activities when the opposite side book is thicker. When experiencing an adverse situation in the market, traders might choose to cancel their existing limit orders as a way to avoid unwanted executions.

Regarding the order characteristic measures, the ORDSIZE coefficient estimates are mostly positive and significant for both buy and sell limit orders, except in the category of orders originating from partial execution. This result indicates that the limit order with a larger size has a higher probability of being executed, revised or cancelled following its previous submission or revision. The limit order, however, has a lower chance to be transited to these three order events if it has been remained in the limit order book as a result from a partial execution. The coefficient estimate results observed for ORDSIZE confirm the intuition regarding opportunity costs of large orders. Larger size limit orders tend to be monitored more closely since the cost of non-execution is higher than that of smaller orders (see, for example, Fong and Liu 2010), and they are revised in response to changing market conditions in order to improve the chance of execution.

The coefficient estimates of the duration dependence variable, PREVDUR, are significantly negative across limit order events that are originated from both limit order revision and partial execution. This result suggests that the longer the limit order’s previous duration, the lower the probability that the order will be transited to another state. In other words, limit orders which spend more time in the previous spells tend to have a smaller chance of being executed, revised or cancelled. This result could be explained by the fact that if the revised or partially executed order stays in the limit order book for an extended period, traders are demotivated in taking further action on the order, which is somewhat in line with the job search literature.Footnote 8

For completeness and robustness check, we also conduct separate multiple-spell duration analyses for two groups of large and small stocks. Panels A in Tables 4 and 5 present the estimation results for buy limit orders of large-cap and small-cap stocks, respectively. The majority of the results are consistent with the pooled sample and thus the coefficient estimates can also be interpreted in a similar way. Some exceptions, however, are found in the sample of large-cap stocks, in which the coefficient estimates of OSLIQUIDITY are insignificant (rather than negatively significant) for explaining the probability of transition from submission to partial execution and that from revision to partial execution. It is significantly positive (rather than insignificant) for probability of transition from submission to cancellation and that from revision to revision. In small-cap stocks, the coefficient estimates of OSLIQUIDITY are insignificant for all limit buy order events that followed a limit order submission and for most of the limit buy order events that followed a limit order revision. The difference is also observed for the coefficient estimates of ORDSIZE for most of the limit buy order events.

Table 4 Multiple-spell duration analysis of limit orders of large-cap stocks in the initial period (August 2000)
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Table 5 Multiple-spell duration analysis of limit orders of small-cap stocks in the initial period (August 2000)
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Panels B in Tables 4 and 5 report the estimation results for sell limit orders for large-cap and small-cap stocks, respectively. The results obtained in the sample of large-cap stocks are mostly consistent with the pooled sample and thus the coefficient estimates can be interpreted in a similar way. However, there are some differences in the sample of small-cap stocks, which are captured in the coefficient estimates of OSLIQUIDITY and ORDSIZE. Specifically, the coefficient estimates of ORDSIZE are insignificant for all limit sell order events that followed a limit order partial execution.

4.2 Multiple-spell survival analysis of dynamic limit order placement strategies following the two major structural changes of the ASX

In October 2006, ASX replaced SEATS by the ITS and in November 2010, the ITS was replaced by the ASX Trade. The structural changes have reduced the market latency significantly, providing an environment for high-frequency trading in the marketplace. The results of multiple-spell duration model for the sample of the ITS period (August 2007) are reported in Table 6: Panels A and B for buy and sell limit orders, respectively. The results for the sample of the ASX Trade period (August 2011) are presented in Table 9: Panels A and B for buy and sell limit orders, respectively.

Table 6 Multiple-spell duration analysis of limit orders of the pooled sample in the ITS period (August 2007)
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The sign of the PRICEGAP coefficient estimates is perhaps one of the most noticeable differences in the results of the two periods following the major structural changes as compared to the initial period of year 2000. Specifically, most of the PRICEGAP estimates are positive and significant in both samples of the ITS and ASX Trade periods. This positive effect is especially more evident in the sample of buy limit orders. The PRICEGAP estimates are, however, mostly negative in the year 2000 period. This observation could be explained by a higher trading intensity which is a result of improvements in latency. The decision by the ASX to upgrade its trading platform to ITS in October 2006 significantly reduced the latency from 85 to 30 ms and created a low-latency environment with a higher level of intensive trading activities. Meanwhile, the ASX Trade, ASX’s new platform for equities and derivatives trading which was launched in November 2010, has improved the exchange’s latency from 30 to 300 ms. Furthermore, capacity has been upgraded to 100,000 orders per second from 20,000 orders per second before. ASX Trade is claimed to be among the fastest in the world (The Trade nd).

A higher value of PRICEGAP indicates the initial position of a limit order as being more defensive (a lower limit price for a buy order and a higher limit price for a sell order). A positive relationship with the hazard rates, especially for spells that transit to revision and cancellation events, seems to indicate active trading and monitoring activities in these periods. Whenever the order placement starts from a defensive position, there is a higher probability that the limit order will be revised or cancelled.

The market environment with improved technology is characterised by a significant amount of trading that has been carried out by machines (also known as algorithmic trading) to reduce the labour effort devoted to monitoring activities. With virtually unlimited information processing capacity, machines have the advantage of responding more quickly to the arrival of information, working out an optimal solution quicker based on a number of input parameters. With better access to markets and information via electronic connections, algorithmic trading has led to a significant reduction in monitoring cost. This also helps reduce the submission risks for limit orders. However, high-frequency trading (HFT) could cause the stock market to become significantly volatile at times where new opportunities for defensive traders are presented, or their opportunity costs are reduced, or their positions are adversely affected. Consequently, traders respond to these market conditions by intensifying their revision and cancellation activities.

Due to the fundamental volatility of many types of financial securities and their rapidly changing prices in the market, it is important for traders to improve their speed of trading. The ability to trade faster than other traders can create potential profit opportunities by enabling a prompt response to the arriving news of the market. This observation creates an arms race in which traders utilise technology innovations and position their trading computers closer to the exchange location with an effort to gain a quicker access to the market. As a result, it can be observed in the financial markets today that there are intensive trading activities in the low-latency market environment.

The coefficient estimates of PREVDUR, the duration dependence variable, show consistent results with the earlier period. Specifically, they are significantly negative across limit order events that are originated from both revisions and partial executions. Negative duration dependence is a common finding in many studies on survival analysis with multiple-spell duration (see, for example, Booth et al. 2002; De Graaf-Zijl et al. 2011; Esteve-Perez et al. 2013). Even after the structural changes, the limit order spells experience a similar pattern where the probability of completing a spell is lower if the limit order’s previous duration is longer.

Our results support the view in Fong and Liu (2010) that non-execution cost is a major source of risk in limit order placements. Whenever it is uneasy to buy or sell in the market place (for instance, in an illiquid market), traders are likely to adjust their orders faster to make sure that their orders can be filled. Alternatively, traders can cancel the orders to reduce opportunity costs. This result is also in harmony with Biais et al. (1995), Ahn et al. (2001) and Fong and Liu (2010) that traders’ order placement strategies tend to vary with market conditions. Specifically, when the spreads are wide, there would be more limit orders. Meanwhile, when the spreads are narrow, there would be more market orders.

For completeness and robustness check, survival analyses with multiple-spell duration model are also conducted for the two samples of large-cap and small-cap stocks in both periods following ASX’s structural changes. For the ITS period (the August 2007 sample), Panels A in Tables 7 and 8 present the estimation results for buy limit orders. The results obtained in the samples of both large-cap and small-cap stocks are generally consistent with the pooled sample. There are only a few exceptional cases in the sample of small-cap stocks, which are captured in the coefficient estimates of INITRADE, OSLIQUIDITY and ORDSIZE. Panels B in Tables 7 and 8 report the estimation results for sell limit orders for large-cap and small-cap stocks, respectively. Overall, the results obtained in both samples of large-cap and small-cap stocks are mostly consistent with the pooled sample (Table 9).

Table 7 Multiple-spell duration analysis of limit orders of large-cap stocks in the ITS period (August 2007)
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Table 8 Multiple-spell duration analysis of limit orders of small-cap stocks in the ITS period (August 2007)
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Table 9 Multiple-spell duration analysis of limit orders of the pooled sample in the ASX trade period (August 2011)
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Similarly, for the ASX Trade period (the August 2011 sample), Panels A in Tables 10 and 11 present the estimation results for buy limit orders for large-cap and small-cap stocks, respectively. The results obtained in the sample of large-cap stocks are mostly consistent with the pooled sample and the coefficient estimates can thus be interpreted in a similar way. On the other hand, there are some minor differences observed in the sample of small-cap stocks, which are captured in the coefficient estimates of INITRADE and OSLIQUIDITY. Panels B in Tables 10 and 11 report the estimation results for sell limit orders for large-cap and small-cap stocks, respectively. The majority of the results in the sample of large-cap stocks are, again, similar with those obtained from the pooled sample. The only exception is in the coefficient estimates of INITRADE for most of the limit buy order events that follow a limit order revision. On the contrary, there are some further differences in the sample of small-cap stocks as compared with the pooled sample, which are captured in the coefficient estimates of INITRADE, and OSLIQUIDITY.

Table 10 Multiple-spell duration analysis of limit orders of large-cap stocks in the ASX trade period (August 2011)
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Table 11 Multiple-spell duration analysis of limit orders of small-cap stocks in the ASX trade period (August 2011)
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5 Conclusion

Limit order revision and cancellation activities play a critical role in forming dynamic order placement strategies. However, the existing literature only employs single duration models which mainly concern with the time-to-execution and thus could not take into account all limit order events and the factors that determine the occurrence of these events. This is because order placement strategies are constructed from a series of multiple order events rather than from single, independent events. This study is probably the first of its type to examine the full spectrum of order events that occur in a life of an order by using a multiple-spell duration model to investigate dynamic limit order placement strategies.

Our empirical results indicate that a number of factors determine the hazard rates of limit order event transitions. These factors include limit order size, limit price, market liquidity, previous duration of the limit order spell, as well as other unobserved factors. For example, the probability of a limit order being revised or cancelled is higher when there is a higher level of opposite-side liquidity. Importantly, the impact of these factors depends on whether the initial limit order event is a limit order submission, partial execution or revision.

The study also examines the dynamic limit order placement strategies following the two major structural changes in the ASX (namely, the adoption of the ITS in 2016 and the ASX Trade in 2010). The results indicate that the improvement in latency has shown to definitely increase the responsiveness of dynamic order placement strategies across most types of limit order transitions. Hence the value of modelling limit order events as they are would produce more accurate results in the lower latency environment.