STOCK DATA, TRADE DURATIONS, AND LIMIT ORDER BOOK INFORMATION. Ola Simonsen

Transcription

1 STOCK DATA, TRADE DURATIONS, AND LIMIT ORDER BOOK INFORMATION Ola Simonen

2 Abtract Thi thei comprie four paper concerning trae uration an limit orer book information. Paper [1], [2] an [4] tuy traer uration, e.g., the time between tock tranaction in intra-ay ata. Paper [3] focu on the information content in the limit orer book concerning future price movement in tock tranaction ata. Paper [1] conier conitional uration moel in which uration are in continuou time but meaure in groupe or icretize form. Thi feature of recore uration in combination with a frequently trae tock i expecte to negatively influence the performance of conventional etimator for intraay uration moel. A few etimator that account for the icretene are icue an compare in a Monte Carlo experiment. An EM-algorithm accounting for the icrete ata perform better than thoe which o not. Empirically, the incorporation of level variable for pat traing i rejecte in favour of change variable. Thi enable an interpretation in term of new effect. No evience of aymmetric repone to new about price an prea i foun. Paper [2] conier an extenion of the univariate autoregreive conitional uration moel to which uration from a econ tock are ae. The moel i empirically ue to tuy uration epenence in four trae tock, Norea, Föreningparbanken, Hanelbanken an SEB A on the Stockholm Stock Exchange. The tock are all active in the banking ector. It i foun that incluing uration from a econ tock may a explanatory power to the univariate moel. We alo fin that prea change have ignificant effect for all erie. Paper [3] empirically tet whether an open limit orer book contain information about future hort-run tock price movement. To account for the icrete nature of price change, the integer-value autoregreive moel of orer one i utilize. A moel tranformation ha an avantage over conventional count ata approache ince it hanle negative integer-value price change. The empirical reult reveal that meaure capturing offere quantitie of a hare at the bet bi- an ak-price reveal more information about future hort-run price movement than meaure capturing the quantitie offere at price below an above. Imbalance an change in offere quantitie at price below an above the bet bi- an akprice o, however, have a mall an ignificant effect on future price change. The reult alo inicate that the value of orer book information i hort-term. Paper [4] Thi paper tuie the impact of new announcement on trae uration in tock on the Stockholm Stock Exchange. The new are categorize into four group an the impact on the time between tranaction i tuie. Time before, uring an after the new releae are coniere. Econometrically, the impact i tuie within an autoregreive conitional uration moel uing intraaily ata for ix tock. The empirical reult reveal that new reuce the uration length before, uring an after new releae a expecte by the theoretical litterature on uration an information flow. Key wor: Finance, Maximum likelihoo, Etimation, ACD, New, Multivariate, Intraay, Market microtructure, Granger cauality, Time erie, INAR, Stock price, Open limit orer book.

3 Introuction an Summary 1 Introuction The role for market i to etermine the price of goo. The quetion i then, how i thi one? The price i etermine through an agreement between a buyer an a eller of a quantity of a goo. In aily life thi may be when a buyer an a eller contact each other irectly, for example, when buying a car or a houehol goo. Often there are a number of peron involve in buying or elling goo. The price i then the price at which the quantity for ale i equal to the quantity iniviual want to buy. In the economic literature thi i the interection of the eman an upply curve of a pecific goo. Simply, if more iniviual are interete in buying than elling a goo the price will increae an if more people are interete in elling than buying a goo the price will ecreae. When buying an elling financial aet the buyer an eller, enote traer in the finance literature, may either contact each other irectly through a pecialit or trae through a computerize ytem. A common wih among traer i to trae at a market that i liqui. Thi may be efine a the ability to quickly trae a quantity of hare with low price impact. To accomplih thi efficiently everal traing mechanim have emerge. The three main olution are orer riven market, Walraian auction an price riven market. The Stockholm Stock Exchange (SSE) i an orer riven market. At the SSE traer enter their orer irectly into a computerize ytem an orer are execute when they can be matche. Since the market i computerize mall a well a large invetor have irect acce to the market. The acce may be, e.g., through traing platform on the internet. A econ market mechanim ue at financial market i the Walraian auction. It i one of the olet market type an i ue, e.g., at the Lonon gol market. Finally, a thir alternative market mechanim i the price riving market. In that market traer trae through a market maker. The market maker ha to provie liquiity to the market, i.e. alway taning reay to buy an ell aet. A leaing example of uch a market i the New York Stock Exchange (NYSE). The common feature of the ifferent traing mechanim i that they are governe

4 2 Introuction an Summary by rule. For example, the orer riven market at the SSE i a continuou market. Traer may enter their orer at any time uring the opening hour an, hence, orer are matche an execute continuouly over time. The implication of thi i that trae occur irregularly an may be clutere over time. In the finance literature the irregularly pace time between tranaction ha receive attention a it i thought to reflect the information flow to the market. In orer riven market traer enter their orer to an orer book. The orer book i monitore by a computer an the content i viible to traer. Accoringly, traer orer placement are oberve an may influence other market participant. Another common feature of the SSE i the exitence of automate traing or algorithm traing among intitutional an private traer. Automate traing i performe by a computer, i.e. the traing eciion i tranferre from a human traer to a computer. Strategie bae on variable uch a liquiity, time an price may trigger buy an ell orer. The purpoe of the automate traing may be, for example, to lower tranaction cot or to make profit out of traing trategie. Intitutional invetor may have reearch iviion evote to automate traing or ue oftware from companie proviing ophiticate traing olution. Alo, private invetor may have acce to automate traing through online brokerage firm. The ue of automate traing may have implication for the market characteritic at the SSE. One poible complication may be that reaction after event are fater an more powerful than without automate traing. The reaon for thi may be that the automate traing trigger a chain reaction. For example, an event reulting in a price movement may initiate a number of trae performe by computer. In thi thei high frequency ata are utilize. High frequency ata or intraaily ata i financial ata where every tranaction or event i recore. The recoring frequency i often on a econ cale in contrary to, e.g., aily or weekly. Such high frequency ata i characterize by a lack of ynchronization, i.e. event occur irregularly over time. Recore event in high frequency ata may be, e.g., how market participant place their orer or every tranaction with aociate price, prea an volume. Conequently, even hort time erie of intraaily ata contain huge amount of ata. They give much finer information of event at the market an how market

5 Introuction an Summary 3 participant are acting. The availability of high frequency ata ha ha an important impact on reearch of how the market mechanim are working an may be moelle. For example, economic quetion like the role of information to tock market participant may be tuie an moelle. The availability of high frequency ata ha alo le to the evelopment of new econometric tool. For example, the feature of irregularly pace time between event ha le to new econometric tool, e.g., for the moelling of the time between tranaction. For an overview of high frequency ata, market microtructure an econometric, ee, e.g., Bauwen an Giot (2001) an Tay (2002, ch. 5). Paper [1], [2] an [4] in thi thei tuy trae uration. Trae uration are the time between two conecutive tranaction an a tranaction i the agreement between a buyer an eller of a volume of tock at a given price. Paper [3] tuie the information content in the orer book on future price change uing ata from the Stockholm Stock Exchange. Trae uration Trae uration correpon to the time between two conecutive tranaction an a tranaction refer to a trae between a buyer an a eller of a volume of tock at a given price. Trae uration have playe a central roll in market microtructure reearch in recent ecae. The time elape between tranaction i thought to carry information about the information flow to market participant. Relevant information may be, e.g., relate to the valuation of the tock. Conequently, trae uration may be important for unertaning the price proce. The iea to tuy uration originate from the information bae moel of Gloten an Milgrom (1985). In thi moel traer are either informe or uninforme, with information varying with regar to the value of the aet they trae. Uninforme traer mainly trae for liquiity reaon, while informe traer act on their uperior information on the value of the aet. Diamon an Verrecchia (1987) how that hort uration correpon to the preence of ba new. Ealey an O Hara (1992) exten the moel of Gloten an Milgrom (1985) by highlighting the importance of time to itinguih between informe

6 4 Introuction an Summary an uninforme traer. They tre that new information to market participant lea to increae trae intenity, i.e. horter uration between tranaction. Thi correpon to an increae number of informe agent trying to exploit their new information. The information may either be public or private. The public information may, e.g., be new announcement from new agencie or pre releae. The part enote private information may be not publicly releae information, e.g., analyi performe by influential invetment bank. New may not only be important for the particular tock it concern it may alo be important for relate tock. For example, private information, icovere by increae trae intenity in a tock may influence traing in relate tock, e.g., in the ame inutry. If thi i true we may fin uration epenence between tock. Thi feature ha renere attention in the finance literature. Recent tuie of epenence between tock tranaction erie are, e.g., Bauwen an Hautch (2004) an Spierijk et al. (2002) who foun epenence between tranaction erie. Paper [2] in thi thei examine the epenence between tock in the banking ector at the Stockholm Stock Exchange. The reult how that there i Granger cauality (Granger, 1969) between the tock in the banking ector at the Stockholm Stock Exchange, i.e. increae trae intenity in one of the tock from the banking ector influence traing in other tock in the ame ector. New agencie itribute price riving information from tock market companie. Companie are force to releae their price riving information publicly a the ue of not publicly releae price riving information i prohibite in mot countrie, incluing Sween. Hence, new releae from new agencie may horten uration. Several tuie have focue on the impact of new releae on price an volatility rather than uration, e.g., Berry an Howe (1994), Eerington an Lee (1993), Mitchell an Mulherin (1994), Bollerlev et al. (2000), Bauwen et al. (2005) an Kalev et al. (2004). Their reult how that new influence price an volatility. The potential link between price an trae uration ha alo been tuie by, e.g., Grammig an Wellner (2002), Dufour an Engle (2000) an Engle (2000) who tuy the interepenence between intraaily price, price volatility an trae uration. Dufour an Engle (2000) fin

7 Introuction an Summary 5 that a the time between tranaction become horter the pee of price ajutment increae uggeting that an active market with hort uration emontrate preence of informe traer. Accoringly, publicly releae new announcement that contain price riving information may not only reuce uration length but may alo affect price. Paper [4] in thi thei eal with the impact of public new releae on uration, i.e. how trae uration are affecte by new releae from new agencie. Autoregreive conitional uration moel For econometric moelling of the time between tranaction tanar econometric tool may not be appropriate a tranaction are irregularly pace over time. An influential uggetion of how to moel the irregularly pace time i ue to Engle an Ruell (1998). Their autoregreive conitional uration (ACD) moel explain the length of the next uration by conitioning on the length of pat uration an explanatory variable. Several extenion an application of the original ACD moel have been preente by, e.g., Engle an Lune (2003) an Bauwen an Giot (2001). A uration arie a the time between two conecutive tranaction at t i 1 an t i,i.e. i = t i t i 1. The conitional expectation of a uration i i pecifie a E( i i 1,..., 1 ; x) =θ i.here i, i conitione on pat uration an other explanatory variable x, anθ i i pecifie in uch a way that i = i /θ i i inepenent an ientically itribute. The θ i may be parameterize a px qx θ i = ω + α j i j + β j θ i j + π 0 x i 1. j=1 j=1 Here, θ i i a function of p lagge uration an q lag of conitional uration. Thi i calle an ACD(p,q,x), where p an q are the orer of the lag in the mean function an x i i a vector of explanatory variable uch a volume, prea an price. Engle an Ruell (1998) popularize the quai maximum likelihoo (QML) etimator builing on the exponential itribution for the etimation of the unknown parameter of the ACD moel. The etimator maximize the log-likelihoo function

8 6 Introuction an Summary ln = X ln θ i + i. θ i The etimator i wiely ue for etimating thee type of moel an, hence, an increaing amount of empirical reult buil on etimate from thi etimator. The etimator i conitent if the moel for the conitional mean i correctly pecifie an the uration i in the exponential family of itribution. A potential problem with the etimator i with the empirical uration ata often ue in the etimation. The ata are icretize with a large fraction of hort an zero uration, e.g., more than one tranaction occurring uring one econ. The icretene of the recore tranaction ata i ue to the econ cale an ata are hence integer-value. A the itribution unerlying the QML etimator i continuou the icretne may negatively affect the performance of the etimator. Kullorff (1961, ch. 2) how that inconitency of the maximum likelihoo (ML) etimator may arie from, e.g., uing mi-interval value to repreent the interval when ata are icretize or groupe. In paper [1] the problem i highlighte an etimator are propoe to account for the problem. One of the prominent feature of the reult from the ACD moel, e.g., from paper [1],[2] an [4], i the quick repone of, for example, price change an change of trae volume. The repone take place within econ after event occur an fae out quickly thereafter. The preence of automate traing at the Stockholm Stock Exchange may be one explanation for thi pattern. Traing rule programme to react to, e.g., price move of more than a preetermine number of tick, may influence the characteritic of the traing behavior. Limit orer book In orer riven market no market maker i involve in the traing proce. Traer irectly enter their orer in an orer book monitore by a computer. The orer book i viible to traer, private a well a intitutional traer. Traer may enter two type of orer, either a market orer or a limit orer. Limit orer i place in queue in the orer book an i execute when they can be matche. The priority of limit

9 Introuction an Summary 7 orer execution i etermine by price an time of orer placement, i.e. the tock with the lowet limit ell price are ol firt an the tock with the highet limit buy price are bought firt. Market orer are, on the other han, execute immeiately to the bet bi or ak price. For example, the publicly viible limit orer book for a tock lite on the SSE how the firt five level on the bi an ak ie, repectively. Thi i illutrate in Figure 1 where Pi an Pi are the price on the bi- (eman) an ak- (upply) ie of an arbitrary orer book for the level i =1, The bi- an ak-volume containe at level i are enote Q i an Q i. Volume Bi-ie (Deman) Miprice Ak-ie (Supply) Low en High en Q 5 Q 4 Q 3 Q 2 Q 1 Q 1 Q 2 Q 3 Q 4 Q 5 Price P 5 P 4 P 3 P 2 P 1 P 1 P 2 P 3 P 4 P 5 Figure 1: Illutration of the limit orerbook. In the theoretical literature of limit orer book the aumption i that informe traer alway ue market orer intea of uing limit orer, e.g., Gloten (1994), Rock (1996) an Seppi (1997). Accoringly, there houl be limite information of oberving offere quantitie of a hare at other price than the bet bi- or ak-price, i.e. at the high an low en of the orer book. However, recent paper of Cao et al. (2004) an Bloomfiel et al. (2005) fin evience of information alo in the orer book beyon the firt level. Cao et al. (2004) introuce meaure capturing the hape of the orer book, e.g., if the orer book i aymmetric, i.e. if there i more value on the bi- (ak-) ie relative to the ak- (bi-) ie. The meaure i ue to tuy if the aymmetry of the orer book i informative regaring future price movement. The fining are that the orer book contain information regaring future price movement

10 8 Introuction an Summary uing intraaily ata with 5 minute aggregation level. Further, Foucault (1999) argue that an increae in aet volatility increae the proportion of limit orer traer an the limit orer traer have to pot higher ak price an lower bi price, i.e. market epth increae. In paper [3] of thi thei the purpoe i to empirically tuy the information containe in the open limit orer book about future hort-run tock price movement. To ae the information containe in the orer book the paper preent new meaure an extenion of exitent meaure. A new meaure capturing the market epth icue in Foucault (1999) i preente. We fin the appropriate aggregation level to be 1 minute in contrary to Cao et al. (2004), who ue 5 an 10 minute aggregation level. Summary of the paper Paper [I] Dicretize Time an Conitional Duration Moelling for Stock Tranaction Data The paper conier conitional uration moel in which uration are in continuou time but meaure in groupe or icretize form. Thi feature of recore uration in combination with a frequently trae tock i expecte to negatively influence the performance of conventional etimator for intraay uration moel. Etimator that account for the icretene are icue an compare in a Monte Carlo experiment, e.g., groupe maximum likelihoo an EM-algorithm. In the mall Monte Carlo tuy the EM-algorithm that account for the icrete nature of the ata both in the outcome an the lagge explanatory variable come out a the bet etimator of the compare one. In the empirical part of the paper the ifference between etimator are generally quite mall an the EM-algorithm an ML etimator bae on icrete ata are not too ifferent from ML bae on groupe ata an Weibull an Burr moel. When it come to the effect of explanatory variable the tuy provie upport for the ue of change rather than level to reflect new. There i throughout a ignificant an

11 Introuction an Summary 9 poitive effect of new about price an a negative effect of a change in the prea. The prea effect i, however, not ignificant. A higher volume ha an inignificant but prolonging effectinmotcae. Wecoulnotfin tatitically ignificant upport for an aymmetric repone to new about prea nor about price. A contributory caue of the quick repone after change in the explanatory variable may be the computerize traing at the tock market. The log-likelihoo function value of the Burr i larger than for other moel but the moel are not nete. In aition, the erial correlation propertie of the exponential an Weibull moel peak in favor of thee two moel. A generalize gamma wa alo employe an provie a better fit to the ata than both the exponential an Weibull moel. Paper [2] An Empirical Moel for Duration in Stock Thi paper conier an extenion of the univariate autoregreive conitional uration moel to which uration from a econ tock are ae. By incluing uration from a econ tock epenence between uration erie i capture in the moel. For example, Figure 2 illutrate the epenence from tock 2 to tock 1. Complete uration are ae from tock 2, 2 N 2 (t), to tock 1, an the complete uration from tock 2 are given weight epenent on the ize of τ 1, i.e. epening on how far away in time the complete uration are. The moel i empirically ue to tuy uration epenence in four trae tock, Norea, Föreningparbanken, Hanelbanken an SEB A on the Stockholm Stock Exchange. The tock are all in the banking ector. In the empirical part we fin Granger cauality between all the tock. Thi reult inicate that there may be uration epenence between tock active in the banking ector on the Stockholm Stock Exchange. The epenence may be caue by new information reveale by the trae intenity. In view of thi empirical reult the uggete moel extenion i able to capture epenence between uration erie an to provie an improvement of the econometric pecification of the moel.

12 10 Introuction an Summary 1 N¹(t)-2 1 N¹(t)-1 1 N¹(t) t 1 N¹(t)-3 t 1 N¹(t)-2 t 1 N¹(t)-1 t 1 N¹(t) Stock 1 2 N¹(t)-2 2 N 2 (t)-1 τ 1 t 2 N 2 (t)-3 t 2 N 2 (t)-2 t 2 N 2 (t)-1 t 2 N 2 (t) Stock 2 2 N 2 (t) Figure 2: Illutration of two tock, tock 1 an tock 2, with tranaction time t an uration. τ 1 i the oberve length of the mot recent uration in tock 2 at time t 1 N 1 (t) 1. Paper [3] Doe the Open Limit Orer Book Reveal Information About Short-run Stock Price Movement? The purpoe of thi paper i to empirically tuy the information containe in the open limit orer book about future hort-run tock price movement. Specifically, attention i pai to whether change or aymmetrie in the orer book concerning offere quantitie of a hare at price below the bet bi price (low en of the orer book) an above the bet ak price (high en of the orer book) are informative. To ae the information containe in the orer book the paper preent new meaure a well a extenion to exiting meaure ummarizing orer book movement. To account for the icrete nature of price change, the integer-value autoregreive moel (e.g., McKenzie, 1985, 1986, Al-Oh an Alzai, 1987) i utilize to moel the icrete nature of high frequency tock price ata. The empirical reult reveal that meaure capturing offere quantitie of a hare at the bet bi- an ak-price reveal more information about future hort-run price movement than meaure capturing the quantitie offere at price below an above.

13 Introuction an Summary 11 However, imbalance an change in offere quantitie at price below an above the bet bi- an ak-price o have a mall an ignificant effect on future price change. The reult alo inicate that the value of orer book information i hort-term. Thi can be compare to Cao et al. (2004) who foun informational value of the higher level of the orer book at an aggregation level of 5 an 10 minute. The effect in thi paper are mot apparent at a low aggregation level (1 minute) while etimation reult for higher aggregation level (2, 5 an 10 minute) how motly inignificantly reult. Paper [4] The Impact of New Releae on Trae Duration in Stock - Empirical Evience from Sween Thi paper examine empirically the hort-run impact of public new announcement on trae uration in tock trae on the Stockholm Stock Exchange in Sween. Econometrically, the impact i tuie within an autoregreive conitional uration moel uing intraaily ata for ix tock. The new are categorize into four group an ae a explanatory variable to the moel. The new categorie are Company/Sector, EU macro, Sweih macro an US macro new. The new categorie are ae to the moel through a ummy variable tructure that capture the impact before, uring an after the new. The empirical reult reveal that new reuce the uration length before, uring an after new releae. For example, Company/Sector relate new horten uration by 20 to 40 percent. The caue of reuce uration before the actual new releae may originate from anticipate new releae, while the ignificant reult of the impact uring an after the new releae may be ue to both anticipate an unanticipate new event. The reult upport the preiction in the theoretical literature of horter uration in connection to new.

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16 14 Introuction an Summary Rock, D. (1996). The Specialit Orer Book an Price Anomalie. Working paper Harvar Univerity. Seppi, D. (1997). Liquiity Proviion With Limit Orer an Strategic Specialit. Review of Financial Stuie, 10, Spierijk, L., Nijman, T.E. an van Soet, A.H.O. (2002). Moeling Comovement in Traing Intenitie to Ditinguih Sector an Stock Specific New. Unpublihe manucript, Tilburg Univerity. Tay, R.S. (2002). Analyi of Financial Time Serie. New York: John Wiley & Son, Inc.