Empirical analysis of the dynamics in the limit order book. April 1, 2018

Transcription

1 Empirical analysis of the dynamics in the limit order book April 1, 218

2 Abstract In this paper I present an empirical analysis of the limit order book for the Intel Corporation share on May 5th, 214 using data from NASDAQ and analyze how the dynamics is affected by specific order book events or the time of day. The obtained results are compared to the facts stated in the lecture and show good agreement. Contents 1 Introduction 1 2 Description of the data 2 3 Intensity of limit order activity 3 4 Intensity of price changes 6 5 Intensity of market orders 8 6 Market order volume 1 7 Summary 11 1 Introduction The aim of this paper is to perform an empirical analysis of the dynamics in the limit order book and to analyze how the dynamics is affected by specific order book events or the time of day. The analysis is done for the Intel Corporation share on May 5th, 214, using data from NASDAQ that was provided with the problem sheet for this assignment. It is checked whether the facts about the dynamics stated in the lecture [1] can be confirmed from the analysis. This paper is structured as follows: we start with a brief discussion of the structure of the data that was provided and explain the meaning of the different tables and fields in sec. 2. Afterwards, we analyze the intensity of limit order activity in sec. 3. In sec. 4 we discuss how the price change intensity depends on the time of day. The seasonality of market order intensity is discussed in sec. 5. In sec. 6 we analyze the 1

3 volume of market orders. Finally, we close with a short summary of our findings and a comparison with the facts stated in the lecture [1] in sec Description of the data The data that was used for the analysis is structured into six tables: the Event table has information about all events in the limit order book and consists of the following fields: field ID field value 1 time of day in milliseconds 2 Order ID (unique order identifier) 3 Event Type: 66 - Add buy order 83 - Add sell order 69 - Execute outstanding order in part 67 - Cancel outstanding order in part 7 - Execute outstanding order in full 68 - Delete outstanding order in full 88 - Bulk volume for the cross event 84 - Execute non-displayed order 4 Volume of the order 5 Price of the order (scaled by a factor of 1) The four tables BuyVolume, BuyPrice, SellVolume and SellPrice contain snapshots of the limit order book immediately after the event with the same row number in the Event table has taken place. The first columns in these tables represent the best bid/ask prices and volumes whereas the following columns correspond to orders which are located further away from the best bid/ask. The last table MO contains information about the market orders that are executed throughout the day and consists of the following fields: field ID field value 2

4 1 time of day in milliseconds 2 best bid price immediately before MO 3 best ask price immediately before MO 4 best bid volume immediately before MO 5 best ask volume immediately before MO 6 average price per share of MO 7 volume of market order 8 indicator of buy (-1) or sell (+1) MO 9 minimum or maximum price executed by MO Trading at NASDAQ opens at 9:3 am and closes at 4: pm. Limit orders can be posted at any time of day whereas market orders can only be executed when trading is open. The Events table, however, contains several executions of orders when trading is closed. As the origin of these events is unclear, it was decided to restrict the analysis of the data to the time when trading is open, i. e. 9:3 am to 4: pm. All events taking place before 9:3 am and after 4: pm have been ignored in the analysis. 3 Intensity of limit order activity It is an interesting question whether the time of day has an influence on the intensity of limit order activity in the limit order book. In order to analyze this question we define limit order activity as placement and (full or partial) cancellation of a limit order (event types 66, 83, 67 and 68). The intensity I(t) is then defined as the number of these events that take place in the interval [t, t+ t], where the bin width is chosen to be t = 2 min. Fig. 1 shows the normalized order intensity as well as the normalized cumulative order intensity throughout the trading day. One can clearly observe that the limit order intensity varies throughout the day and is larger in the morning than in the afternoon. More than 5% of the total limit order activity takes places within the first two minutes after trading opens and almost 25% takes place within first 3 minutes. Given that these time intervals make up for only about.5% and 7.7% of the time during which the exchange is open for trading, one can conclude that a large fraction of limit order activity happens within a relatively small time interval. Towards the end of the trading day one can again observe an increase in limit order activity. This 3

5 normalized limit order intensity cumulative norm. limit order intensity time/h Figure 1: Normalized intensity of limit orders (placement and cancellation) during the trading day. Each bar represents a time interval of two minutes, the first and last 3 minutes of the trading day are shown in green. The red line indicates the cumulative normalized limit order intensity, i. e. the fraction of limit orders that have already been placed at a certain time of day. 4

6 .35.3 fraction of limit orders full trading day truncated trading day time after MO [ms] Figure 2: Fraction of limit orders (placement and full or partial cancellation, event types 66, 83, 67 and 68) that arrive at the exchange within a short time interval after the execution of a market order (event types 69, 7 and 84) in dependence on the length of the time interval. The data is shown separately for the full trading day (9:3 am until 4: pm) and a truncated trading day (1: am until 3:3 pm) where the first and last 3 minutes of the trading day have been excluded. The fraction of limit orders is normalized with respect to the total number of limit orders that arrive in the respective time period under consideration. increase, however, is still small compared to the activity after trading opens in the morning. Besides the time of day one might also suspect that incoming market orders might have an influence on the limit order activity. Fig. 2 shows the fraction of limit orders (placement and full or partial cancellation, event types 66, 83, 67 and 68) that arrive at the exchange within a short time interval t after the execution of a market order (event types 69, 7 and 84) in dependence on the length of the time interval. Note that if two market orders arrive at times t 1 and t 2 t 1 and a limit order is placed or canceled at time τ which is both in [t 1, t 1 + t] and [t 2, t 2 + t], the limit order was only counted once. One can clearly observe that there exist two regimes which are separated at a time 5

7 interval length of about 1 ms after a market orders has been executed. In the first 1 ms the number of limit orders that arrive at the limit order book increases strongly as the length of the time interval is increased. As the length of the time interval is increased beyond 1 ms, the number of limit orders that arrive at the order book continues to increase but with a much smaller intensity. One can thus assume that the market needs only about 1 ms to react to an incoming market order. Although this time interval is very small we find that about 25% of all limit orders arrive within it. This implies that a huge part of the limit order book dynamics takes place within a very small fraction of the 6.5 hours that the exchange is open for trading. Considering a short time interval t of fixed length one finds that the total fraction of limit orders that arrive within this interval is slightly reduced as the first and last 3 minutes of the trading day are excluded from the analysis 1. 4 Intensity of price changes Another interesting question is how the intensity of price changes is distributed over the trading day. In order to extract this information from the available data we count how often the midprice, which is defined as midprice = changes in the interval [t, t + t]. t = 2 min. best bid + best ask, 2 As in section 3 we chose the interval width Fig. 3 shows shows the normalized intensity of price changes during the trading day. One can clearly observe that the price change intensity is larger in the morning than in the afternoon. About 5% of the total price changes take place within the first 3 minutes of the trading day. Immediately after trading opens the intensity of price changes is especially high - over 14% of the price changes happen within the first 2 minutes after the exchange opens for trading. One cannot observe an increase in the intensity of price changes during the last 3 minutes of the trading day as it is the case for the intensity of limit orders, c. f. fig Note that we normalize the fraction of limit orders with respect to the total number of limit orders that arrive within the respective time period of consideration for the analysis. 6

8 normalized price change intensity cumulative norm. price change intensity time/h Figure 3: Normalized intensity of price changes during the trading day. Each bar represents a time interval of two minutes, the first and last 3 minutes of the trading day are shown in green. The red line indicates the cumulative normalized price change intensity, i. e. the fraction of price changes that have already been placed at a certain time of day. As in section 3 we analyze the amount of price changes that take place within a short time window after a market order was executed, c. f. fig. 4. One can observe two regimes which are separated by a time interval length of about 5-1 ms after a market orders has been executed. In the first 5-1 ms the fraction of price changes that take place increase strongly as the length of the time interval is increased. As the length of the time interval is increased beyond 1 ms, the number price changes that take place within this interval continues to increase but with a much smaller intensity. About 45% of the price changes take place within the first 1 ms after a market order has been executed which implies that a huge part of the price dynamics takes place within a very small fraction of the trading day. 7

9 .6 fraction of price changes full trading day truncated trading day time after MO [ms] Figure 4: Fraction of price changes that take place within a short time interval after the execution of a market order (event types 69, 7 and 84) in dependence on the length of the time interval. The data is shown separately for the full trading day (9:3 am until 4: pm) and a truncated trading day (1: am until 3:3 pm) where the first and last 3 minutes of the trading day have been excluded. The fraction of price changes is normalized with respect to the total number of price changes that take place in the respective time period under consideration. 5 Intensity of market orders We have seen in sec. 3 that the limit order activity varies strongly throughout the day. One might suspect that a similar behavior can be found for the market order intensity. Fig. 5 shows the normalized market order intensity as well as the normalized cumulative order intensity throughout the trading day. One can clearly observe that market order intensity is generally larger in the first 3 minutes after the exchange opens and in the last 3 minutes before the exchange closes than during the rest of the day. About 2% of all market orders are executed within the first 3 minutes of the day. A very high market order intensity can be observed in last few minutes right before 8

10 .35 1 normalized MO intensity cumulative norm. MO intensity time/h Figure 5: Normalized intensity of market orders during the trading day. Each bar represents a time interval of two minutes, the first and last 3 minutes of the trading day are shown in green. The red line indicates the cumulative normalized market order intensity, i. e. the fraction of market orders that have already been placed at a certain time of day. the exchange closes. These orders might come from traders who want to close their positions at the end of the day. Overall we find that there is a large fluctuation in the market order intensity throughout the day. There are some quiet periods with almost no market market orders being executed and there are periods where the market order intensity is quiet large. This might indicate that a lot of market orders are triggered by other market orders. In order to analyze this further we plot the fraction of market orders that are executed within a short time interval after a market order has been executed, c. f. fig. 6. One can indeed observe a strong increase in the fraction of market orders that are executed in the first about 1-2 ms after another market order has been executed. However, only about 1% of all market orders are executed within this time interval. Therefore the influence of market orders on the the execution of additional market orders is not as big as the influence on limit order activity or prices changes, c. f. sec. 3 and sec. 4. 9

11 .12 fraction of market orders full trading day truncated trading day time after MO [ms] Figure 6: Fraction of market orders (event types 69, 7 and 84) that arrive at the exchange within a short time interval after the execution of a another market order in dependence on the length of the time interval. The data is shown separately for the full trading day (9:3 am until 4: pm) and a truncated trading day (1: am until 3:3 pm) where the first and last 3 minutes of the trading day have been excluded. The fraction of market orders is normalized with respect to the total number of market orders that arrive in the respective time period under consideration. 6 Market order volume In this section we analyze the intensity and volume of market orders. In particular we calculate the fraction of market orders that walk the book, do not fill the best queue and exactly fill the best queue. A market order walks the book if its volume exceeds the volume of the best queue such that at least a part of the second best queue has to be used to execute the order. These orders can be identified in the available data since they have an average execution price (field 6 of table MO) that differs from the maximum or minimum price at which the order was executed (field 9 of table MO). Market orders that do not fill or exactly fill the best queue can be identified straightforward as information about the volume of the order (field 4 of table Events) and the volume of the best queue (first field of tables BuyVolume and SellVolume) is available 1

12 in the data. Table 3 lists the results separately for the full trading day (9:3 am until 4: pm) and a truncated trading day (1: am until 3:3 pm) where the first and last 3 minutes of the trading day have been excluded. full trading day truncated trading day MOs that walk the book.26%.5% MOs that do not fill the best queue 74.85% 78.69% MOs that exactly fill the best queue 25.89% 21.26% Table 3: Fraction of market orders that walk the book, do not fill the best queue and exactly fill the best queue. The data is shown separately for the full trading day (9:3 am until 4: pm) and a truncated trading day (1: am until 3:3 pm) where the first and last 3 minutes of the trading day have been excluded. If one takes the whole trading day into account one finds that only about.26% of the market orders walk the book. If the day is truncated by removing the first and last 3 minutes of the trading day, this number reduces even further by a factor of 5 to about.5%. On the other hand, the fraction of market orders that do not fill the best queue is relatively large with about 74.95% for the full and 78.69% for the truncated trading day. Interestingly, even if most market orders do not walk the book, there is still a large fraction of market orders that fill the entire best queue (25.89% for the full and 21.26% for the truncated trading day). It can thus be concluded that a a very huge part of the trading happens within the best queue with about 3/4 of the executed market orders having a volume which is smaller than the best queue and about 1/4 of the orders having a volume equal to the best queue. The fraction of market orders that walk the book is almost negligible. In the first and last 3 minutes of the trading day one can observe a slight increase in the volume of the orders relative to the volume of the best queue. 7 Summary In this paper we performed an empirical analysis of the limit order book and analyzed how the dynamics is affected by specific order book events or the time of day. It was found that a huge part of the dynamics, i. e. placement and cancellation of 11

13 limit orders, takes place in a rather short time interval directly after the exchange opens and before the exchange closes. A large fraction of price changes happens in the morning within the first 3 minutes of the trading day. It has been shown that the market participants react very quickly within a very short time interval of only about 1 ms to incoming market orders. Although these intervals make up only for a tiny fraction of total time it was found that a huge part of limit order activity and price changes take place within them. The market order intensity was found to be larger in the first and last 3 minutes of the trading compared to the rest of the day. We finally analyzed the volume of market orders and found that almost all trading happens within the best queue, i. e. market orders almost never walk the book. Nevertheless, there is still a large fraction of market order that fill the entire best queue. Finally, we compare our findings to the results stated in the lecture [1] which we list below: 1. A large fraction of limit order activity happens within a few milliseconds after the execution of market orders (slide 42 of ref [1]). 2. The post market order occupation time makes up only a tiny fraction of total time (slide 41 of ref. [1]). 3. The market order intensity shows strong seasonality and is larger in the beginning and at the end of the trading day than throughout the rest of the day (slide 58 of ref. [1]). 4. Only a few market orders walk the book, but there ist still a large number of market orders that fills the full queue at best price (slides 44 and 45 of ref [1]) All these statements could be confirmed in our analysis. References [1] R. Donnelly, Limit Order Books and Market Microstructure, Lecture Notes (218). 12