DECOMPOSING THE BID-ASK SPREAD OF STOCK OPTIONS: A TRADE AND RISK INDICATOR MODEL

Transcription

1 DECOMPOSING THE BID-ASK SPREAD OF STOCK OPTIONS: A TRADE AND RISK INDICATOR MODEL David Michayluk Schl f Finance and Ecnmics Universiy f Technlgy, Sydney Ausralia Phne: Fax: [email protected] Laurie Praher Schl f Business, Technlgy and Susainable Develpmen Bnd Universiy Gld Cas 9 Ausralia Phne: Fax: [email protected] Li-Anne E. W Schl f Business, Technlgy and Susainable Develpmen Bnd Universiy Gld Cas 9 Ausralia Phne: Fax: [email protected] Henry Y.K. Yip * Schl f Banking and Finance Universiy f New Suh Wales Sydney 05 Ausralia Phne: Fax: [email protected] 4 Sep 006 * Crrespnding auhr We acknwledge he prvisin f daa by he Securiies Indusry Research Cener f Asia- Pacific (SIRCA).

2 Decmpsing he bid-ask spread f sck pins: A rade and risk indicar mdel Absrac In his paper, we develp an indicar mdel fr pin spread decmpsiin wih explici references he sck marke measure he expeced change in he value f an pin, he rade flws f muliple pin series fr he mdeling f a rade indicar reflec privae infrmain signals, and he facrs affecing he value an pin prfli fr he mdeling f hree risk indicars reflec he respecive invenry risk expsure faced by he pin marke makers. The rade and risk indicar mdel is empirically esed using panel daa bained frm he Ausralian Sck Exchange elecrnic limi rder bk. Empirical ess reveal ha he adverse infrmain cmpnen depends n he iming f rades, liquidiy, pin leverage, rade imbalance, and he pin ype. The resuls suppr muliple surces f invenry hlding css ha relae he aemp by marke makers mainain a dela neural psiin and minimize heir prfli expsure he change in he value and vlailiy f he underlying sck. The invenry hlding css als differ acrss pin series and are a funcin f he direcinal change in invenry risk expsure.

3 Decmpsing he bid-ask spread f sck pins: A rade and risk indicar mdel The hisrical develpmen f equiy bid-ask spread mdels sems frm simple cnsrucs. The hereical framewrk firs prpsed by Demsez (1968) explains why he bidask spread shuld be psiive and als idenifies hree cmpnens - adverse infrmain, invenry hlding, and rder prcessing. 1 These hree cmpnens have als feaured in subsequen empirical lieraure where several frms f saisical mdels have been cnsruced esimae he cmpnens. Opin bid-ask spread decmpsiin mdels als recgnize ha he same hree cmpnens are impran pin marke makers. The presence f infrmain rading in he pins marke is well suppred by he infrmain asymmery lieraure. Black (1975) dcumens ha infrmed raders are araced he pins marke due higher leverage. Easley e al. (1998) find ha infrmain-based pin rading vlume explains fuure sck price direcin, and faser infrmain flws frm he pins he equiy marke. The presence f invenry hlding css in he pins marke is dcumened by H and Macris (1984). They repr ha pin dealers adjus heir ques in respnse invenry psiins. 1 Fr a cmprehensive review f he hereical lieraure in bid-ask spread cmpnens, see O Hara (1995). Huang and Sll (1997) grup he varius saisical mdels in hree caegries - he cvariance mdels represened by Rll (1984), Chi e al. (1988), Sll (1989), and Gerge e al. (1991), ha use ransacin prices esimae he effecive bid-ask spread; he vecr auregressive mdels represened by Hasbruck (1988, 1991) ha examine he impac f invenry hlding and adverse infrmain css n he relain beween rade and que revisins; and he rade-indicar mdels represened by Glsen and Harris (1988), and Madhavan e al. (1997), ha use he direcin f rade flws esimae he bid-ask spread cmpnens. Subsequen Huang and Sll (1997), Bllen e al. (004) presen anher class f saisical mdel decmpse he bid-ask spread in cmpnens by reaing he invenry and adverse infrmain cmpnens as an pin wih a schasic ime expirain. 3

4 Our paper cnribues he lieraure by develping a rade and risk indicar mdel (TRIN) ha permis a 3-way decmpsiin f he pin bid-ask spread. Typical f any rade indicar mdel, we use rade flws bserved in he pins marke infer he bid-ask spread cmpnens. We explicily inegrae muliple pins series wrien n he same sck infer privae infrmain. In paricular, raher han seing a arge level f invenry which is ypical f equiy bid-ask spread decmpsiin, we ake in accun he derived naure f an pin and use a new risk-equilibraing apprach describe hw pin marke makers place heir ques in pin series sraegically influence he direcin f incming rders s as seer heir prfli wards a psiin ha is dela neural, has minimal sensiiviy sck vlailiy, and has is dela minimally affeced by a change in he value f he sck. This new apprach cnsrucs hree risk indicars infer he invenry hlding css assciaed wih managing he prfli expsure dela, vega and gamma risks. Dela and vega measure he price sensiiviy f an pin a change in he value and vlailiy f he underlying sck, respecively. Gamma measures he dela sensiiviy f an pin a change in he value f he underlying sck. During he curse f rading, i is ineviable ha he dela f he marke maker s prfli will deviae frm he arge neural psiin, causing he value f he marke maker s prfli flucuae wih subsequen sck price mvemens. We call his uncerainy dela risk and he cs cver he expsure he invenry hlding cs assciaed wih dela risk managemen. Similarly, he value f he marke maker s prfli acquired frm he curse f rading will be affeced by he schasic naure f sck vlailiy. We label his uncerainy vega risk and he cs cver he expsure he invenry hlding cs assciaed wih vega risk managemen. Finally, gamma risk and he assciaed invenry hlding cs are relaed he variains in prfli dela during he curse f rading, i.e., he exen f dela risk expsure. Thus he invenry cmpnen f he pin bid-ask spread is aribued hree separae surces accun fr he muliple risks faced by he marke makers. 4

5 The TRIN mdel develped exhibis all he advanages f he Huang & Sll (1997) indicar mdel designed fr equiy bid-ask spread decmpsiin, namely, a ne-sep regressin prcedure ha generaes separae esimaes fr he hree well defined adverse infrmain, invenry and rder prcessing cmpnens; a flexible framewrk ha can be used es a variey f micrsrucure issues; and a simple mdel wih simple inpu requiremens. 3, 4 In addiin, we apply he TRIN mdel sck pins lised n he Ausralian Sck Exchange (ASX) cmplemen he limied sudies dae n pin bid-ask spread cmpnens ha are based principally n he Chicag Bard f Exchange (CBOE). 5 The daabase frm he ASX includes he direcin f rades. There is n lnger a requiremen apply he Lee and Ready (1991) algrihm infer if a rade is buyer r seller iniiaed. In he Unied Saes, hwever, he use f such an algrihm creaes a penial bias where rade direcin and adverse infrmain css are psiively crrelaed. This paper is rganized as fllws. Secin I reviews he lieraure. Secin II develps he TRIN mdel fr sck pins decmpse he hree bid-ask spread cmpnens. Secin 3 The TRIN mdel is applied a number f sub-samples examine he inra-day disribuin f spread cmpnens, he impac f pin ype, leverage, liquidiy, and rade imbalance n he adverse infrmain cmpnen, he relainship beween he invenry cmpnen and he direcinal change in an pin prfli s dela, vega and gamma, and if he invenry cmpnen varies acrss differen pin series. 4 The TRIN mdel relaes unexpeced pin price mvemens bh rade and risk indicar variables. T deermine he inpu values assigned he indicar variables, all we require are he pin rade flws and psiin dela, vega and gamma f he pin prfli held by he pin marke maker. 5 The lieraure n equiy bid-ask spread decmpsiin is quie exensive and includes, amng hers, Glsen and Harris (1988), Gerge e al. (1991), Hasbruck (1991), Huang and Sll (1997). On he cnrary and ur knwledge, he lieraure n pin bid-ask spread decmpsiin is limied Vijh (1990), Jamesn and Wilhelm (199), and Kaul (001), wh use CBOE pins, and H and Macris (1984), wh sudy pins lised n he American Sck Exchange. 5

6 III describes he Ausralian marke micrsrucure and sample daa and Secin IV reprs he empirical resuls f he TRIN mdel. Finally, Secin V summarizes he resuls and cnclusins. I. Lieraure Review Jamesn and Wilhelm (199) pin u ha marke makers in he CBOE face unique invenry risks ha relae he schasic vlailiy f he underlying sck and failure cninuusly mainain dela neuraliy. They adp he invenry mdel specificain f H and Sll (1983) and find ha vega and gamma risks are n fully diversifiable bu accun fr 4.5% and 8% f he pin bid-ask spread, respecively. Kaul e al. (001) emply a crss-secinal mdel explain he bid-ask spread f CBOE pins using cnsruced variables ha prxy he css f adverse infrmain, invenry hlding, rder prcessing, and mdel misspecificain. Their resuls imply a large prprin f he bid-ask spread is aribuable invenry wih 50% aribuable seing up a dela neural psiin and 6.93% assciaed wih discree rebalancing; and he adverse infrmain cmpnen accuns fr 8.95% f he pin spread. While Kaul e al. (001) use he rade flws bserved in he sck marke cmpue hree alernaive adverse infrmain prxies prpsed by Gerge e al. (1991), Neal and Whealey (1998), and Lin e al (1995), Vijh (1990), and Lee and Cheng (001), n he her hand, use he rade flws bserved in he pins marke esimae he adverse infrmain cmpnen in he bid-ask spread f pins lised n he CBOE. Using a mre cmprehensive daa se, Lee and Cheng (001) repr a much larger and ecnmically significan adverse infrmain cmpnen f 19.8% f he pin spread, cmpared a mere 1% in Vijh (1990). In he nex secin, we develp he indicar mdel. When cmpared he regressin apprach in Jamesn and Wilhelm (199), Lee and Cheng (001), and Kaul e al. (001) where he bid-ask spread is regressed n facrs ha prxy he bid-ask spread cmpnens, he indicar mdel has he advanage f shwing explicily he price seing prcess, i.e., hw he 6

7 css f marke making, being embedded in and recvered frm he bid-ask spread, affec he revisin in ques prvided by he marke makers. When cmpared he regressin apprach in Vijh (1990) where he unexpeced change in pin prices is regressed n facrs ha prxy he adverse infrmain cmpnen, he indicar mdel has he advanage f decmpsing he bidask spread in hree hereical cmpnens. II. Develping he rade and risk indicar mdel The rade and risk indicar mdel fr sck pins presened in Equain 1 belw is based n he infrmain-based mdel f Huang and Sll (1997). The unexpeced change in he fundamenal value f an pin, is defined as: where s s S ( V V ) δ ( V V ) = α Q + ε, (1) V is he prevailing fundamenal value f he pin when a rade in he pin is recrded a ime, δ is he pin dela a ime -1, when he previus rade in he same pin is bserved, s V is he cncurren fundamenal value f he sck a ime, * Q is he aggregae pin rade indicar used reflec he infrmain cnen f n jus he previus pin rade bserved a -1, bu als he rades in her pins wrien n he same underlying sck bserved a and afer -1, bu befre. If he pin under sudy is a call, * Q is assigned a value f +1, 0, r -1 if during he perid he al vlume f psiive pin rades is larger han, equal, r less han ha f negaive 7

8 pin rades, respecively 6. Alernaively, if he pin under sudy is a pu, * Q is assigned a value f -1, 0, r +1 if he al vlume f psiive pin rades is larger han, equal, r less han ha f negaive pin rades. 7 S is he cnsan raded bid-ask spread f he pin be esimaed by he mdel, α is he prprin f he pin half-spread due adverse infrmain inferred frm * Q, and ε is he public infrmain shck. Equain (1) cnains w mdificains he Huang & Sll (1997) mdel ha reflec he hereical pricing relainship beween he value f an pin and is underlying sck, and anher, accuning fr rading vlume in muliple pin series wrien n he same sck. The lef hand side f equain (1) represens he unexpeced change in he pin value where s s ( V ) V δ he expeced change in pin value is remved frm he al change in pin value ( V ) V. The aggregaed rade indicar variable, vlumes f muliple pin series raher han a single pin. If Q *, is nw based n he rading * Q has infrmain cnen hen here is infrmain asymmery and α will be nn- zer. Hence, a psiive α is cnsisen wih he presence f infrmain rading in he pins 6 Fllwing Easley e al. (1998), buyer-iniiaed (seller-iniiaed) rades in calls and seller-iniiaed (buyer-iniiaed) rades in pus are classified as psiive (negaive) pin rades ha are assciaed wih gd (bad) news abu he underlying sck. 7 Vijh (1990) als uses infrmain inferred frm he rade flws f muliple pin series explain unexpeced pin price mvemens. Whereas Vijh (1990) cnsrucs w uncnsrained variables, he difference in he number and vlume beween psiive and negaive pin rades, prxy privae infrmain n he underlying sck, we cnsruc he aggregaed rade indicar variable which can nly ake n a value f -1, 0, r +1. 8

9 marke and pin marke makers will include an addiinal adverse infrmain cmpnen in he bid-ask spread recver lsses frm rades iniiaed by infrmed raders. Nex we prpse a risk-equilibraing apprach he managemen f muliple invenry risks f an pin prfli via he placemen f ques in individual pin series enice marke rders ha help resre he preferred psiin dela, vega and gamma f he prfli. 8 Opin marke makers face a variey f invenry risks when accmmdaing rades in call and pu pins. I is herefre impran fr pin marke makers ake in accun all f he risks ha affec he value f he marke maker s prfli, and n fcus enirely n invenry levels. Figlewski (1989) cnjecures ha pin marke makers hedge invenry risk expsure by using her pins in he series wrien n he same sck. Cx and Rubinsein (1985) refer he imprance f he marke maker s dela-neural psiin. These marke makers fen ake large psiins relaive heir capial and prefer small gamma psiins (lw dela expsure). Similarly, we believe ha pin marke makers prefer small vega psiins reduce he impac f unexpeced changes in he sck vlailiy n pin prfli values. Thus rainal pin marke makers will manage a prfli f pins wrien n he same sck and prefer sar each day wih a dela neural prfli wih minimal gamma and vega levels. 9 Our riskequilibraing invenry managemen apprach suggess ha as sn as he curse f rading causes he prfli s risk characerisics deviae frm desired levels, he pin marke maker will adjus he que midpin f an pin relaive he fundamenal value as fllws: 8 The risk-equilibraing apprach ha arges he invenry risk characerisics f an pin prfli is an innvain he empirical lieraure in pin bid-ask spread decmpsiin. In bh Jamesn and Wilhelm (199) and Kaul e al. (001), hey infer he invenry cmpnen by regressing he bid-ask spread f an pin n a number f variables ha measure he invenry risks f he same pin. 9 We are n cnsidering he risk expsure a change in ineres rae (rh) nr ime (hea) since he risk-free rae is relaively sable a inra-day inervals, and as Hull (000) indicaes invesrs dn hedge agains he effec f ime. 9

10 M S S S β () = V + ' + β ' + β ' where M is he midpin f he prevailing pin bid and ask ques when a rade in he pin is recrded a ime, β, β, and β are he prprins f he pin half-spread aribuable invenry ', where ', hlding css required cmpensae he pin marke maker fr acceping rades ha cause he dela, vega, and gamma f he pin prfli deviae frm he preferred values, respecively, and, ' are he dela, vega, and gamma f he pin prfli held by he pin marke maker a, he ime when a previus rade in any relaed pin clses, bu befre, is recrded. If he previus rade is in he same pin as he ne under sudy, hen = - 1, else -1 < <. The Greek values are defined as: [ nij ( 1 Qij ] m * ' = j, ' ) j = 1 m δ (3) [ n ij ( 1) Qij ] * ' = υ, ' (4) j = 1 m j [ n ij ( 1) Qij ] * ' = ϕ, ' (5) j = 1 j j n ij is ne f he m pins wrien n he same underlying sck as he pin under sudy, is he vlume f he i h rade in pin j ransaced during he perid frm marke pen up, Q ij is he rade indicar variable fr he i h rade in pin j. Q ij = +1 if he rade is buyer iniiaed, and 1 if seller iniiaed, and, 10

11 δ j,', j,' υ, and ϕ j,' are he dela, vega, and gamma f pin j as a, respecively. While n ij ( 1) Qij measures he pin marke maker invenry psiin in pin j a δ j, ' ij ij shws he psiin dela f pin j a. 10 Fr he enire prfli f ime, [ n ( 1) Q ] pins wrien n sck i, he psiin dela a, ', is bained by adding up all f he psiin delas f he m relaed pins as shwn by equain (3). A negaive (psiive) ' suggess ha he dela f he pin prfli a has fallen belw (risen abve) he preferred level. Since he delas are psiive fr calls and negaive fr pus, rever back a neural psiin, he pin marke maker is expeced raise (lwer) he nex que midpins f all he calls a abve heir fundamenal values and lwer (raise) he nex que midpins f all he pus a belw heir fundamenal values encurage seller (buyer) iniiaed rades in calls and buyer (seller) iniiaed rades in pus. Alernaively, he pin marke maker may buy (sell) scks achieve he desired dela neural psiin. Similarly, if ' and ' are less (greaer) han zer, he psiin vega and gamma f he pin prfli held by he pin marke maker a is lwer (higher) han he desired level. Vega and gamma are psiive fr bh calls and pus, hus, resre hese prfli risk characerisics, he pin marke maker is expeced raise (lwer) he nex que midpins f 10 In realiy, rades are n execued enirely by a single marke maker. There are muliple marke makers wh cmpee n jus amng hemselves, bu als wih flr brkers and he limi rder bk fr rades. I wuld be ideal if we have access he rading bk f individual marke makers. We assume ha he marke makers face similar invenry risks and he cmpsiin f rade flws faced by an individual marke maker is represenaive f ha f he marke n he premise ha inerdealer rades can limi he differences amng he bid and ask ques f individual marke makers (see H and Sll (1983)). Jamesn and Wilhelm (199) als pin u ha he cmmn pracice f rder-sharing by marke makers can disribue invenry acrss marke makers and limi he divergence amng individual bid and ask ques. 11

12 all he call and pu pins a ime abve (belw) heir fundamenal values encurage seller (buyer) iniiaed rades in he call and/r pu pins. In line wih he exising invenry mdels, equain () describes he sraegic placemen f he que midpin relaive he fundamenal value in an aemp manage invenry risk. Hwever, he derived naure f pins means he dimensin f risk managemen is bradened he cnrl f he sensiiviy f he pin prfli value varius Greek variables raher han a single arge invenry level. T remve he unbservable fundamenal value f he pin, equain (1) and he firs difference f equain () are cmbined yield: M δ 1 s S S * * ( V ) = α Q + β ( ) β S 1 * * S * * ( ) + β ( ) + ε. ' 1' ' 1' ' + 1' (6) Equain (6) implies ha prir an pin rade ha akes place a, he pin marke maker will revise he prevailing que midpin reflec he infrmain revealed by, and cuner he invenry risks resuling frm, he previus rade in he same pin and rades in all he her relaed pins ransaced a and afer 1, bu befre. In he spiri f a rade indicar mdel, he change in he prfli risk prfiles is cnvered in hree invenry risk indicar variables, Q, Q, and Q, n he assumpin ha invenry hlding css d n increase linearly in he deviain f he prfli dela, vega, and gamma, respecively. Furhermre, we subsiue he cnsan raded spread by he bserved qued spread and he fundamenal value f he sck by he que midpin f he sck as in Huang and Sll (1997) s ha: M s ( M ) S 1 S 1 S 1 S 1 δ 1 = α Q 1 + β Q 1 + β Q 1 + β Q 1 + ε. (7) 1

13 If pin is a call (pu), hen and -1 (+1) if ( ) Q equals +1 (-1) if ( ' 1' ) < 0, 0 if ( ' 1' ) ' ' > 0. Irrespecive f he ype f pin under sudy, * * * ( ' 1' ) < 0, 0 if ( ' 1' ) = 0, and -1 if ( ' 1' ) * * < 0, 0 if ( ' 1' ) = 0, and -1 if ( ' 1' ) > 0; and = 0, Q equals +1 if * Q equals +1 if ( ) ' > 0. The assignmen f hese values relaes he invenry risk managemen prcess explained earlier. Fr example, given a drp in prfli dela r ( ) ' ' < 0, he pin marke maker culd raise he prevailing que midpin f s each and every call abve is fundamenal value, i.e., M ( M ) 1' δ > 0 encuraging he arrival f seller iniiaed rades in calls and crrecing fr he drp in prfli dela. Thus, by assigning a value f +1 s Q, M ( M ) δ and Q are direcly relaed and β > 0 is evidence f an invenry hlding cs aribuable managing dela risk. Likewise, β > 0 and β > 0 are indicaive f he managemen f prfli gamma and vega, respecively. Esimaes f β, β, and β relae he imprance f he hree pin risk measures he pin marke makers. Furher, he relaive imprance f each measure may be imevarying. Fr example, due he high frequency naure f que adjusmens, i may be risky ignre he direcinal risk f he underlying sck such ha dela neuraliy dminaes he marke makers bjecive fr invenry cnrl. Alernaively, if here is a high degree f cmpeiin fr rder flw amng he pin marke makers, hey may fcus n gamma risk since i may be mre difficul quickly rebalance prflis. Finally, vega risk may be mre impran when rade cmmences as he marke discvers he fair value f he sck. 13

14 Equain (7) prvides he empirical represenain f he rade and risk indicar mdel fr sck pins. The adverse infrmain, invenry and rder prcessing cmpnens are measured by α, ( + β + β ) β, and [1 - α - ( β + β + β ) ], respecively. By cnfining he deerminans f he unexpeced que midpin changes he rade and risk indicar variables, ur mdel reains he simple srucure f he exising rade indicar mdels. III. Marke srucure and daa descripin ASX sck pins rade in an rder-driven marke faciliaed by a screen-based rading sysem (called he Derivaive Trading Faciliy r DTF). Marke makers are fficially designaed ensure liquidiy and each is assigned w r mre underlying scks. Nrmal rading in sck pins akes place in w sessins frm 10:00 am 1:30 pm and frm :00 4:00 pm each day. The marke makers are bligaed prvide ques and may d s eiher cninuusly, upn reques, r bh Opins raders place limi r marke rders n he DTF hrugh heir brkers, which are hen aumaically mached and raded n a price and ime pririy basis Frm February 004, he mrning nrmal rading sessin is exended by half an hur 1:00 p.m., bu ur sample is clleced prir his dae and is n affeced by his change. 1 A he cninuus level, pin marke makers are bliged prvide bid and ask ques n a cninuus basis in welve pin series per underlying sck (hree calls and hree pus in each f he firs w expiry mnhs including he a-he-mney pin, he nex-in-he-mney pin and he nex-u-f-he-mney pin fr each). A he que requess level, hey mus prvide bid and ask ques n reques fr all series wih expiries f nine mnhs r less. A eiher level hey are given a maximum elapsed ime f 30 secnds revise heir bid and ask ques r respnd a que reques and hey mus mee 60% f heir bligains a eiher level f que bligain. If hey chse prvide ques bh cninuusly and upn requess, he bligain requiremen falls 50%. 13 In each marke paricipan s ffice, he designaed rading represenaives are respnsible fr he enry f rders n behalf f he cliens f heir emplyers he DTF erminals. The rders are sen he marke via he ASX s hs cmpuer, which in urn bradcass he rders all paricipans erminals. 14

15 Opins daa during nrmal rading is exraced frm he ime-samped ASX CLICK daabase fr he en ms acive exchange-raded sck pins based n rading vlume frm January 1998 April The CLICK daabase explicily labels each rade as eiher buyer iniiaed, seller iniiaed, pen, clse, r crss. Opening and clsing rades are excluded frm he sample as hey ccur under an aucin seing and crssed rades are als eliminaed as he rade indicar is n clearly defined. 15 T avid he expirain effec r he impac f early exercise n rading aciviies, we exclude rading days ha fall n expirain daes and/r he sck s exdividend dae, respecively. Finally, since he prpsed mdel suggess ha he que revisin prcess is driven by he rade flws bserved in an acive marke, rading days wih less han a al f sixy pin rades are eliminaed. Table 1 liss he en ms acively raded sck pins by rading vlume and reprs rading aciviy infrmain regarding rading days, number f rades and rading vlume. The number f acive rading days ranges frm a lw f 359 fr Wesern Mining Crprain Ld (WMC) a high f 1,017 fr BHP Billin Ld (BHP). While pins in Telsra Crprain Ld (TLS) are he ms acively raded wih a daily average f 5,88 cnracs, he leas acively raded pins are in Wespac Banking Crprain (WBC) wih a daily average f 1,510 cnracs. In erms f he number f pin rades, WMC is he leas acive wih a daily average f 99 and News Crprain (NCP) ps he lis a 8. Inser Table 1 Here 14 The mnhly ASX Derivaives Marke Saisics shw ha he p 10 pins accun fr an average f 64% f he marke s rading vlume. 15 A rade is crssed when buy and sell marke rders arrive simulaneusly and he resul f maching f hese rders is invenry neural frm he pin marke maker s perspecive. 15

16 Only pin rades wih accepable ques are used deermine he pin que midpin change. Filer rules were adped esablish daa validiy where he bid ask spread is lwer han r equal he maximum spread prescribed by he exchange; he bid price is smaller han he ask price; r he pin ime value is less han half f he sck price. Table 1 shws he prprin f bservains ha saisfy hese cndiins. 16 Ne ha all rades are used in he analysis as he rade indicar and vlume saisics are available and heir remval culd adversely affec he pin rade flws. This has a bearing n he accuracy f he infrmain signals and invenry risk psiins held by pin marke makers. We sr pin rades by rade indicar. Fr each buyer- and seller-iniiaed grup, rading vlume is cuned by (i) pin ype, (ii) he disance frm he mney, and (iii) pin mauriy. The breakdwn f rading vlume is repred in Table, Panels A C, respecively. Panel A reveals ha call pins arac mre rading vlume (57%) han pu pins (43%). Seller-iniiaed rades accun fr 69% f he al rading vlume, which is slighly mre han wice he buyer-iniiaed rades (31%). In erms f rade direcin, psiive and negaive rading vlumes are alms idenical wih 48% frm buyer-iniiaed calls and seller-iniiaed pus cmpared 5% frm seller-iniiaed calls and buyer-iniiaed pus. Panels B and C shw ha a and near he mney pins and he w neares mauriy pins arac mre rading vlume han her pins, wih 56% f he rading vlume aking place in he hree arund-he-mney call and pu pins, and 6% f he rading vlume aking place in he w neares mauriy pins. Inser Table Here 16 Since he designaed marke maker mus mee nly 60% (50%) f heir bligains if he/she chses prvide ques a eiher he cninuus r que reques level (bh levels) we bserve sme rades wih missing r unaccepable ques. 16

17 Given he higher rading vlume and mre impranly, he presence f a leas ne designaed marke maker prvide cninuus ques, we cnfine he applicain f he rade and risk indicar mdel represened by equain (7) he sudy f welve pin series (hree arund-he-mney call and pu pins in he neares w expiry mnhs). s T arrive a he expeced change in pin fundamenal value, δ ( ) M, required by he TRIN mdel, pin delas are cmpued based n implied vlailiy esimaes frm Black- Schles (1973) pin pricing mdel using he las que midpin f he a-he-mney pin and he cncurren que midpin f he underlying sck frm he previus day. The implied sck vlailiy, geher wih he signed vlume f each relaed pin recrded beween w cnsecuive rades in he pin under sudy, are used deermine he psiin dela, vega, and gamma f he pin prfli suggesed by equains (3) (5) befre a value is assigned each f he hree invenry risk indicars, Q, Q, and Q. Finally, he signed vlume f each relaed pin recrded beween w cnsecuive rades in he pin under sudy is used deermine he aggregae rade indicar, * Q. IV. Resuls This secin presens he verall and inra-day resuls fr he bid-ask spread decmpsiin fr sck pins. We als include a deailed analysis f he spread decmpsiin cmpnens based n sck pin characerisics and examine he marke makers abiliy manage each ype f invenry risk specified in he TRIN mdel. The Generalized Mehd f Mmens (GMM) prcedure is used esimae he TRIN mdel represened by equain 7. Huang and Sll (1997) emphasize he usefulness f GMM and is advanage ver rdinary leas squares when he errr erm includes runding errrs and he frm f cndiinal heerscedasiciy is unknwn. 17

18 A.1 General resuls - Bid-ask spread decmpsiin and parameer esimaes Table 3 cnains he verall resuls f he equain 7 parameer esimaes fr he pin spread cmpnens measuring adverse infrmain ( αˆ ) and invenry hlding css ( βˆ, and βˆ ). While Panel A reprs bh he cefficien esimaes fr he individual sck pins and he averages fr he enire sample, Panel B cnains parameer esimaes fr fur disinc inra-day perids and prvides Kruskal-Wallis Chi-square saisics fr inra-day cmparisns. The average αˆ repred in Panel A f Table 3 reveals ha adverse selecin accuns fr apprximaely 4.66% f he pin half spread. Cnsisen wih he assumpins f he mdel, he individual frm 0 (ANZ, NAB, NCP and WMC). αˆ esimaes are psiive wih fur sck pins significanly differen Y βˆ αˆ range beween.67% fr CBA and 7.97% fr WMC and are higher han hse figures esimaed in Vijh (1990), bu lwer han he 8.95% repred in Kaul e al. (001). These resuls suppr evidence f infrmain rading in he pins marke and sugges ha changes in he underlying sck values d n fully explain pin price mvemens. Inser Table 3 Here An analysis f he beas indicae ha pin marke makers are mre cncerned wih invenry risk managemen han adverse infrmain. On average, he invenry cmpnen accuns fr 18.03% (he sum f he average bea esimaes) f he pin half spread, which is apprximaely 4 imes he adverse infrmain cmpnen. Amng he hree surces f invenry hlding css measured by he mdel, he larges is βˆ a 9.07%. All individual esimaes are psiive and all bu WBC are significanly differen frm zer. While he average βˆ is greaer han he average βˆ r βˆ, n an individual basis each βˆ is greaer han he 18

19 crrespnding βˆ r βˆ esimaes in all cases excep BHP, TLS and WBC. These resuls shw ha pin marke makers are paricularly averse gamma risk. Since marke makers cmpee fr rder flw and managing gamma risk relies n he abiliy rade pins, i may be he mre difficul risk remve. The average βˆ indicaes ha 5.07% f he pin half spread is aribuable he managemen f dela risk. Cnsisen wih ur mdel, nine f he en individual esimaes are psiive, bu nly five f he esimaes are significanly differen frm 0. The smaller βˆ cefficiens reflec he added flexibiliy f pin marke makers minimize dela risk by rading he underlying asse as well as he pin. The invenry hlding cs assciaed wih vega risk managemen is he leas impran where n average 3.89% f he half spread is aribued βˆ. On an individual basis, eigh f he en esimaes are psiive, bu nly hree are differen frm zer a he 0.05 significance level. Since lnger erm pins are mre expsed vega risk han shrer erm pins, he use f he w neares mauriy series in his analysis may have an impac n he magniude and significance f he βˆ esimaes relaive he esimaes fr βˆ and βˆ. A. General resuls - Inra-day bid-ask spread decmpsiin T examine he inra-day disribuin f he pin bid-ask spread cmpnens, we apply he TRIN mdel fur perids: 10-11:15 am, 11:15-1:30 pm, -3 pm and 3-4 pm. The average esimaed cefficiens f he varius rade and risk indicar variables are repred in Panel B f Table 3. The inra-day adverse infrmain cmpnens fr he w mrning and w afernn sessins display similar paerns. Fr example, he average αˆ is 8.09 % in he firs mrning sessin (MS1) and falls.5% in he secnd (MS), hen, afer he lunch break, he average αˆ in he firs afernn sessin (AS1) is 6.46% and falls 1.93% in he secnd (AS). 19

20 Cnsisen wih Chan e al. (1995) ha infrmain asymmery is greaes during he pening price discvery sessin and Madhavan (199) ha raders gradually infer equilibrium prices and reslve infrmain asymmery based n ransacin price hisry, his paern reflecs increased uncerainy and cncern regarding infrmed rading in perids immediaely afer a disrupin in rading.. Kruskal-Wallis es saisics cmpare he αˆ esimaes acrss he fur rading sessins fr he en sck pins. The repred Chi-square saisics (3.86 fr bh MS1 versus AS, and AS1 versus AS) indicae ha αˆ in bh he firs mrning and he firs afernn sessins are differen frm he secnd afernn sessin a he 0.05 significance level. nly Fr he hree invenry risk indicars, he Kruskal-Wallis es saisics indicae ha βˆ f he pening mrning sessin is differen frm ha f he secnd afernn sessin a he 0.05 significance level (Chi-square = 5.85). This finding is cnsisen wih he hyphesis ha greaer price uncerainy in he underlying sck in he pening sessin expses he pin marke maker a greaer level f vega risk and hence he demand fr a larger cmpensain. Fr βˆ and βˆ, we d n find any saisically significan inra-day differences. B. Adverse infrmain and pin characerisics - Opin leverage Accrding Black (1975), infrmed raders prefer rade high leverage pins. Furher suppring his view, Easley e al. (1998) shw ha infrmed raders nly use highly levered pins and Lee and Cheng (001) empirically dcumen ha CBOE pins wih greaer leverage arac mre infrmain rading. We es he infrmed rading leverage hyphesis applying he TRIN mdel and cmparing he cefficien esimaes f αˆ acrss hree disinc sub-samples, a lw leverage grup (in-he-mney calls and u-f-he mney pus), a mderae leverage grup (a-he-mney calls and pus), and a high leverage grup (u-f-hemney calls and in-he-mney pus). 0

21 Table 4 presens he esimaes f he bid-ask spread cmpnens based n he hree degrees f leverage fr he 10 pins in he sample and he resuls suppr he leverage hyphesis. The average αˆ f 8.97% fr he high leverage grup is larger han eiher he lw r mderae leverage grups suggesing ha infrmain rading is ms prnunced in he high leverage grup and ha he marke makers build he cs in he spread. Based n he Kruskal- Wallis es saisic he αˆ esimaes fr he high leverage grup are differen frm he lw and mderae leverage grups a he 0.05 and 0.10 significance levels, respecively. Inser Table 4 Here C. Adverse infrmain and pin characerisics - Liquidiy In addiin he leverage effec, Easley e al. (1998) shw ha infrmain rading is dependen n marke liquidiy such ha when liquidiy in he pins marke is lw, infrmed raders use scks prfi frm heir privae infrmain. We examine his issue, by applying he TRIN mdel hree disinc sub-samples based n liquidiy as measured by he frequency f rading in he individual pins. 17 Fr each f he 10 sck pins, he sample is sred in 3 grups, a lw liquidiy grup frm he 4 h quarile wih he lnges ime beween rades, a mderae liquidiy grup frm he nd and 3 rd quariles, and a high liquidiy grup frm he 1 s quarile wih he leas ime beween rades. Inser Table 5 Here As illusraed in Table 5, he adverse infrmain cmpnen is greaer fr he high liquidiy grup han fr he lw liquidiy grup. Amng he 10 sck pins in he lw liquidiy 17 We als esimae he mdel parameers fr lw, mderae, and high liquidiy grups based n he number f daily rades and resuls are cnsisen wih hse based n frequency f rading. 1

22 grup, he average αˆ is -1.8% and nine f he en esimaes are n significanly differen frm zer. In cnras, amng he 10 sck pins in he high liquidiy grup, he average αˆ is 18.13%, wih eigh f he en psiive and significanly differen frm zer. Furhermre, he Kruskal-Wallis s Chi-squares, indicae ha he αˆ esimaes fr he hree liquidiy grups are differen a he 0.01 significance level. These resuls are cnsisen wih he implicains f he hereical mdel f Easley e al. (1998) ha when liquidiy in he pins marke is lw, infrmed raders avid i and use he sck marke, hus relegaing he pins marke as a venue fr liquidiy-based rading. Alernaively, when liquidiy is high, infrmed raders are beer able disguise heir rades and marke makers will incrprae he increased risk in he adverse infrmain cmpnen f he spread. D. Adverse infrmain and pin characerisics Signed vlume The impac f marke fricins n rading css may als influence he chice f markes used by infrmed raders. Fr example, infrmed raders wih psiive news can buy calls, sell pus r buy he underlying asse, while hse wih negaive news may be frced rade nly in he pins marke since cnsrains impsed in he cash marke preven shr selling n dwnicks. Thus, he prbabiliy ha an pin rade is iniiaed by an infrmed rader is higher fr negaive han psiive pin vlume, and a larger adverse infrmain cmpnen is expeced frm ques ha fllw an excess f negaive ver psiive pin vlume. T es he asymmeric impac f signed vlume, we apply he TRIN mdel w sub-samples, a psiive vlume grup cnaining que midpin changes ha fllw an excess f psiive negaive pin vlume in he previus perid and a negaive vlume grup cnaining que midpin changes ha fllw an excess f negaive psiive pin vlume in he previus perid. average The resuls repred in Table 6 suppr he asymmeric signed vlume effec. The αˆ f 8.07% fr he negaive vlume grup is mre han 5 imes he average αˆ f

23 1.57% repred fr he psiive vlume grup suggesing ha here is mre infrmed rading n negaive infrmain. The Chi-square saisic f 7.41 frm he Kruskal-Wallis es cnfirms ha αˆ is differen beween he w signed vlume grups fr he 10 sck pins a he 0.01 significance level. Furhermre, amng he en αˆ esimaes in he negaive vlume grup, all are psiive and fur f hem significanly differen frm 0 cmpared seven psiive esimaes and nne saisically significan fr he psiive vlume grup. αˆ Inser Table 6 Here E. Adverse infrmain and pin characerisics - Opin ype I fllws frm he asymmeric signed vlume resuls previusly discussed ha infrmed raders faced wih margin requiremens and unlimied dwnside risk assciaed wih wriing pins, may prefer rade ne pin ype ver anher. T cnsider wheher he same level f infrmain exiss beween he markes fr calls and pus, we esimae he TRIN mdel cefficiens separaely fr a calls nly sample and a pus nly sample. The resuls repred in Table 7 dcumen an asymmeric pin ype effec. Fr pu pins an average f 8.0% f he spread is due adverse infrmain 1.49% fr call pins. All f he en αˆ esimaes in he pu pin grup have he expeced psiive sign and six are differen frm 0 a he 0.05 significance level. This cmpares eigh psiive esimaes and nly w differen frm 0 fr he call pin grup. The w grups f αˆ s fr he 10 sck pins are als differen a he 0.05 significance level accrding he Kruskal-Wallis Chi-square saisic f 6.. Hence, he pu pin marke serves n jus fr prfli insurance rading, bu als as a venue fr infrmain rading, where mre infrmed raders use pus han calls. Resuls are als cnsisen wih he asymmeric signed vlume effec fund earlier. Given ha negaive pin vlume cnains mre privae infrmain han psiive pin vlume and ha negaive pin vlume includes buyer-iniiaed pus and seller-iniiaed calls, he margin requiremen and larger 3

24 dwnside risk f wriing an pin means ha infrmed raders wih negaive news may prefer using pus han calls. Inser Table 7 Here F. Invenry hlding css and he Greeks - Dela, vega and gamma The resuls ha fllw explre he relaive imprance f he hree surces f invenry hlding css (dela, vega, gamma) idenified in he TRIN mdel. The mdel represened by equain (7) assumes ha pin marke makers demand he same level f cmpensain fr invenry risk caused by rades ha raise r lwer he psiin dela, vega and gamma f heir prflis. In pracice, marke imperfecins may creae cs asymmeries pin marke makers when hey aemp crrec fr he direcinal variains in psiin dela, vega and gamma. G. Invenry hlding css and he Greeks - Dela Of he hree ypes f invenry risk, dela risk may be he easies manage since he marke maker has he added flexibiliy rade he underlying securiy as well as he pin. Thus, resring arge delas des n rely slely n he liquidiy f he pins marke. Fr example, when an pin rade resuls in a decrease in he prfli dela he marke maker may sraegically raise (lwer) he que midpins f he relaed calls (pus), and/r buy he underlying sck. Alernaively, when an pin rade resuls in an increase in he prfli dela he marke maker may sraegically lwer (raise) he que midpins f he relaed calls (pus), and/r shrsell he underlying sck. Due cnsrains impsed n shrselling scks and he unlimied dwnside risk assciaed wih shrselling, hwever, dela adjusmens subsequen decreases in dela are easier faciliae and less risky since shrselling isn necessary. Thus, we expec a smaller esimae fr βˆ in ques ha fllw decreases in prfli delas. 4

25 T es his asymmeric impac f signed dela risk, we apply he TRIN mdel w sub-samples, a psiive dela grup cnaining que midpin changes ha fllw an increase in he prfli dela and a negaive dela grup cnaining que midpin changes ha fllw a decrease in he prfli dela. Table 8 presens he TRIN mdel cefficien esimaes fr he en pins fr hese w grups. The average βˆ fr he psiive dela grup is 7.95% cmpared 1.39% fr he negaive grup. Cnsisen wih expecains, hese figures reflec higher invenry hlding css assciaed wih riskier, mre csly adjusmens. The Kruskal-Wallis Chi-square es saisic fr cmparing he βˆ esimaes f he w grups indicaes ha heir invenry hlding css due dela risk are differen a he 0.01 significance level. While he negaive dela grup has nly w cefficien esimaes differen frm zer, he βˆ s fr he psiive dela grup are all greaer han zer and seven f he en esimaes are significanly differen frm zer. Resuls indicae ha dela risk is n cmpleely diversifiable and ha i is less csly resre dela psiins ha fall belw desired levels cmpared hse ha rise abve he arge. Inser Table 8 Here H. Invenry hlding css and he Greeks Vega and gamma Similar cs relaed argumens will als hld when cnsidering he pin marke maker s aciviy relaed managing vega and gamma risk. Fr example, i may be easier and cheaper crrec fr a rise han a fall in vega and gamma. When an pin rade resuls in a rise (fall) in prfli vega r gamma he marke maker will adjus ques encurage buyeriniiaed (seller-iniiaed) rades in he relaed calls and pus resre he vega r gamma psiin. In hese cases, marke imperfecins in he frm f margin requiremens make wriing pins mre csly han buying hem, in addiin, here is unlimied dwnside risk assciaed 5

26 wih wriing naked pins. Thus, he invenry hlding css assciaed wih vega and gamma risk managemen shuld be smaller in respnse a rise han a fall in vega and gamma. T es he asymmeric impac f signed vega risk, we apply he TRIN mdel w subsamples, a psiive and a negaive vega grup cnaining que midpin changes ha crrespnd he vega risk indicar being assigned a value f +1 and -1, respecively. Similarly, es he impac f signed gamma risk, we apply he TRIN mdel w subsamples, a psiive and a negaive gamma grup cnaining que midpin changes ha crrespnd he gamma risk indicar being assigned a value f +1 and -1, respecively. Table 9 presens he TRIN mdel cefficien esimaes fr he en pins fr he w grups based n he signed vegas. The average βˆ Y fr he psiive vega grup is 5.7% cmpared 8.6% fr he negaive vega grup. Cnsisen wih expecains, hese figures reflec higher invenry hlding css assciaed wih higher cs and greaer risk. The Kruskal- Wallis Chi-square es saisic fr cmparing he Y βˆ esimaes f he w grups indicaes ha he invenry hlding css assciaed wih vega risk managemen fr he w grups are differen a he 0.05 significance level. Fr he negaive vega grup, all f he cefficien esimaes are psiive and all bu w (RIO and WBC) are significanly differen frm zer. These resuls indicae ha vega risk is n cmpleely diversifiable and ha i is cheaper and less risky resre a rise in vega han resre a fall in vega. Inser Table 9 Here Table 10 presens he TRIN mdel cefficien esimaes fr he en pins fr he w grups based n he signed gamma. The average βˆ fr he psiive gamma grup is smaller (11.04%) han fr he negaive gamma grup (13.74%) which is in line wih expecains. Hwever, in he case f gamma risk, we cann rejec he null hyphesis ha here is n difference in he en pairs f βˆ s beween he w grups. 6

27 Inser Table 10 Here I. Invenry hlding css and he Greeks - Dela, vega and gamma as a funcin f ime mauriy and exercise price The dela, vega and gamma f an pin vary as a funcin f ime mauriy and exercise price (see Cx and Rubinsein (1985) fr a deailed analysis f he relainships). The larger he dela (vega), he mre sensiive is he value f he pin a change in he value (vlailiy) f he sck. The larger he gamma, he mre sensiive is he dela f he pin a change in he value f he sck. Thus faciliaing rades in he mre sensiive pin series expses he marke maker greaer invenry risk and his will be refleced in a larger invenry cmpnen f he spread. The analysis and resuls ha fllw address he sensiiviy issue fr each f he invenry risk indicars, dela, vega and gamma. T measure he impac f dela risk acrss differen pin series, we esimae he TRIN mdel cefficiens fr hree sub-samples: a lw, a medium, and a high dela grup cmprised f u-f-he-mney, a-he-mney, and in-he-mney calls and pus, respecively. Fr he vega risk effec, we apply he TRIN mdel w sub-samples: a lw vega grup cnsising f u-f-hemney and in-he-mney calls and pus, and a high vega grup f a-he-mney calls and pus. Finally, explre he gamma risk effec, we firs apply he TRIN mdel w shr mauriy sub-samples bh wih up 14 days mauriy: a lw gamma grup f u-f-he-mney calls and in-he-mney pus, and a high gamma grup f a-he-mney calls and pus. Nex, we apply he TRIN mdel hree medium mauriy grups, all f which have a leas 15 days bu n mre han 70 days mauriy: a lw gamma grup f in-he-mney calls and u-f-he-mney 7

28 pus, and medium gamma grup f u-f-he-mney calls and in-he-mney pus, and a high gamma grup f a-he-mney calls and pus. 18 The resuls presened in Tables prvide evidence suppring he nin ha he hree ypes f invenry risk increase wih he sensiiviy f he pin series. Inser Table 11 Here Referring Table 11 fr he relainship beween invenry cmpnen and he dela f an pin series, he average βˆ is fund increase wih he dela f he pin series, frm a lw f.% fr he lw dela grup a high f 8.97% fr he high dela grup. The Kruskal- Wallis es indicaes ha he en pairs f βˆ frm he lw and high dela grups are significanly differen suggesing ha invenry hlding css are greaer fr pin series wih higher dela. The relainship beween he invenry cmpnen and vega is presened in Table 1. While he average βˆ esimaes increase wih vega frm 4.% fr he lw vega grup 5.37% fr he high vega grup, based n he Kruskal-Wallis es, he en pairs f βˆ s are n significanly differen. Thus, he invenry hlding cs due vega appears be less respnsive he magniude f vegas. Inser Table 1 Here The resuls in Table 13 shw ha beween he w shr mauriy grups f pin series wih differen levels f gamma, he average βˆ increases frm 9.45% fr he lw gamma grup 18.34% fr he high gamma grup. The Kruskal-Wallis es cmparing he en pairs f βˆ indicaes ha he invenry hlding css due gamma fr he w grups are significanly 18 In ur enire sample f welve, arund he mney pin series in he nex w mauriy mnhs, nne f he pins exceed 70 days mauriy, hus we d n explre he gamma risk effec fr lng mauriy pins. 8

29 differen. Finally, he resuls presened in Table 14 shw ha amng he hree medium mauriy grups f pin series wih differen levels f gamma, he expecain ha he grup wih he larger gamma wuld display he larger average βˆ hlds beween he lw and medium gamma grups nly, bu n beween he medium and he high, nr beween he lw and high gamma grups. Specifically, he average βˆ fr he medium gamma grup is 10.13% cmpared 1.85% fr he lw gamma grup, and he en pairs f βˆ frm he lw and medium gamma grups are differen a he 0.05 significance level. Hwever, we d n find any saisical difference beween he en pairs f βˆ frm he lw and high gamma grups, r he medium and high gamma grups. Inser Tables 13 and 14 Here V. Summary and Cnclusins We develp a rade and risk indicar mdel esimae he cmpnens f pin bid-ask spreads. Our empirical ess reveal ha pin marke makers are unable cmpleely diversify expsure dela, vega, and gamma risks. Our esimaes f hese hree surces f invenry hlding css are 5.07%, 3.89%, and 9.07%, respecively. The remainder f he spread is explained largely by 77.31% rder prcessing css and 4.66% adverse selecin css. Cnsisen wih prir hery, he adverse infrmain cmpnen is absen in pins wih lw leverage bu is higher in perids immediaely fllwing a disrupin rading. The laer finding suggess ha he exchange can help lwer he ransacin css in he pins marke by remving he emprary clsure during he lunch break. The adverse infrmain cmpnen als increases wih sck pin liquidiy and is higher fr pu pins han call pins. Adverse selecin als increases when he ne pin vlumes mve frm psiive negaive. 9

30 Taking in accun he pssibiliy f using bh he pin and he sck markes manage invenry risk, ur resuls als reveal ha pin marke makers bear invenry risk ha is cmmensurae wih he level f risk expsure and ps ques accrdingly. We als discver ha he pin marke makers face asymmeric css when resring he arge levels f dela, vega and gamma and hese hree ypes f invenry risk vary acrss pin series. Specifically, he invenry hlding cs ha arises frm expsure dela risk is smaller in ques ha fllw a drp han a rise in prfli dela and he invenry hlding css ha arise frm expsure vega and gamma risks are bh smaller in ques ha fllw a rise han a fall in prfli vega and gamma. In summary, an pin prfli expses he pin marke maker a muliude f invenry risks, differen pin series d n expse he pin marke maker he same amun f invenry risk and ha he addiinal css and cnsrains assciaed wih wriing pins and shr-selling sck resul in differenial css f managing he psiin dela, vega, and gamma levels f pin prflis. Overall, here is meri in mdeling hese css mre vigrusly and in a manner which is cnsisen wih real-wrld pin marke maker risk prfiling. References Black, F., 1975, Fac and Fanasy in he Use f Opins, Financial Analyss Jurnal, 31, 36-41, Black, F. and M. Schles, 1973, "The Pricing f Opins and Crprae Liabiliies," Jurnal f Pliical Ecnmy, 81(3), Bllen, N. P. B., T. Smih, and R. E. Whaley, 004, Mdeling he Bid/Ask Spread: Measuring he Invenry-Hlding Premium, Jurnal f Financial Ecnmics, 7, Chan, K. C., W. G. Chrisie, and P. H. Schulz, 1995, Marke Srucure and he Inraday Paern f Bid-Ask Spreads fr NASDAQ Securiies, Jurnal f Business, 68, Chi, J. Y., D. Salandr, and K. Shasri, 1988, On he Esimain f Bid-Ask Spreads: Thery and Evidence, Jurnal f Financial and Quaniaive Analysis, 3, Cx, J. C., and M. Rubinsein, 1985, Opins Marke, Prenice Hall. 30

31 Demsez, H., 1968, The Cs f Transacing, Quarerly Jurnal f Ecnmics, 8, Easley, D., M. O Hara, and P.S. Srinivas, 1998, Opin Vlume and Sck Prices: Evidence n Where Infrmed Traders Trade, Jurnal f Finance, 53, Figlewski, S., 1989, Opins Arbirage in Imperfec Marke, Jurnal f Finance, 44, Gerge, T. J., G. Kaul, and M. Nimalendran, 1991, Esimain f he Bid-Ask Spreads and is Cmpnens: A New Apprach, Review f Financial Sudies, 4, Glsen, L. R., and L. E. Harris, 1988, Esimaing he Cmpnens f he Bid-Ask Spreads, Jurnal f Financial Ecnmics, 1, Hasbruck, J., 1988, Trades, Ques, Invenries, and Infrmain, Jurnal f Financial Ecnmics,, 9-5. Hasbruck, J., 1991, Measuring he Infrmain Cnen f Sck Trades, Jurnal f Finance, 46, H, T. S. Y., and R. G. Macris, 1984, Dealer Bid-Ask Ques and Transacin Prices: An Empirical Sudy f Sme Amex Opins, Jurnal f Finance, 39, H, T. S. Y., and H. Sll, 1981, Opimal Dealer Pricing Under Transacins and Reurn Uncerainy, Jurnal f Financial Ecnmics, 9, H, T. S. Y., and H. Sll, 1983, The Dynamics f Dealer Markes Under Cmpeiin, Jurnal f Finance, 38, Huang, R. D., and H. R. Sll, 1997, The Cmpnens f he Bid-Ask Spread: A General Apprach, Review f Financial Sudies, 10, Hull, J. C., 000, Opins, Fuures, and Oher Derivaives, 4 h ediin, Prenice Hall. Jamesn, M., and W. Wilhelm, 199, Marke Making in he Opins Markes and he Css f Discree Hedge Rebalancing, Jurnal f Finance, 47, Kaul, G., M. Nimalendran, and D. Zhang, 001, Infrmed Trading and Opin Spreads, wrking paper, Universiy f Flrida. Lee, C., and M. Ready, 1991, Inferring Trade Direcin frm Inraday Daa, Jurnal f Finance, 46, Lee, J., and H. Y. Cheng, 001, Trade Size and Infrmain-Mivaed Trading in he Opins and Sck Markes, Jurnal f Financial and Quaniaive Analysis, 36, Lin, J., G. C. Sanger, and G. G. Bh, 1995, Trade Size and Cmpnens f he Bid-Ask Spread, Review f Financial Sudies, 8,

32 Madhavan, A., 199, Trading Mechanisms in Securiy Markes, Jurnal f Finance, 47, Madhavan, A., M. Richardsn, and M. Rmans, 1997, Why D Securiy Prices Change? A Transacin-Level Analysis f NYSE Scks, Review f Financial Sudies, 10, Neal, R., and S. M. Whealey, 1998, Adverse Selecin and Bid-Ask spreads: Evidence frm Clsed-End Funds, Jurnal f Financial Markes, 1, O Hara, M., 1995, Marke Micrsrucure Thery, Blackwell Publishers. Rll, R., 1984, A Simple Implici Measure f he Effecive Bid-Ask Spread in an Efficien Marke, Jurnal f Finance, 39, Sll, H., 1989, Inferring he Cmpnens f he Bid-Ask Spread: Thery and Empirical Tess, Jurnal f Finance, 44, Vijh, A. M., 1990, Liquidiy f he CBOE Equiy Opins, Jurnal f Finance, 45,

33 Table 1 Exchange-Traded Opins and Trade Infrmain The sample cnsiss f he en ms acive exchange-raded sck pins based n rading vlume frm January 1998 April 003. The fllwing infrmain is prvided, he cde f he underlying sck f each sck pin, he number f acive days wih a leas 60 pin rades, he al number f pin rades and vlume during he sample perid, he average daily number f pin rades and vlume, he number and percenage f pin rades wih accepable bid and ask ques, are repred. Underlying sck N. f acive rading days Tal n. f rades Tal vlume Average rades per day Average vlume per day Accepable rades Percenage f accepable rades TLS % NCP % BHP % NAB % WMC % ANZ % CBA % AMP % RIO % WBC % Average % 33

34 Table Signed Opin Vlume sred by Type, Mauriy, Disance frm he Mney Panel A: Percenage f buyer- and seller-iniiaed rading vlume in each f he ypes f pins. Opin Type Calls Pus Buyer-iniiaed Seller-iniiaed Buyer-iniiaed Seller-iniiaed AMP 17% 34% 15% 34% ANZ 18% 39% 14% 9% BHP 17% 40% 13% 9% CBA 18% 34% 15% 3% NAB 17% 37% 14% 3% NCP 17% 4% 1% 9% RIO 15% 38% 13% 34% TLS 17% 40% 11% 3% WBC 1% 39% 15% 5% WMC 19% 43% 11% 7% Average 18% 39% 13% 30% Panel B: Percenage f buyer- and seller-iniiaed rading vlume in each f he 5 disance-frm-he-mney grups. Opin disance frm he mney Buyer iniiaed seller iniiaed Furheruuin -in u u in in Nex- Nex- Furher Furher- Nex- Nex- Furher- A A AMP 10% 8% 8% 4% 3% % 14% 14% 7% 1% ANZ 8% 9% 9% 4% % 18% 16% 18% 9% 7% BHP 9% 8% 9% 4% % 0% 15% 17% 9% 9% CBA 13% 7% 7% 4% 3% 5% 11% 1% 7% 11% NAB 1% 6% 6% 3% 3% 7% 11% 1% 7% 1% NCP 11% 7% 6% 3% % 8% 13% 11% 8% 1% RIO 14% 4% 4% 3% 3% 34% 9% 10% 6% 13% TLS 5% 8% 9% 3% % 15% 19% 19% 10% 10% WBC 5% 11% 15% 5% 1% 10% 16% 4% 9% 5% WMC 11% 6% 6% 3% 3% 7% 1% 13% 8% 11% Average 10% 7% 8% 4% % % 14% 15% 8% 10% Panel C: Percenage f buyer- and seller-iniiaed rading vlume in each f he 3 mauriy grups. mauriy buyer iniiaed seller iniiaed near nex far near nex far AMP 14% 10% 8% 19% 18% 3% ANZ 15% 10% 7% 1% 17% 30% BHP 15% 10% 6% % 18% 9% CBA 17% 10% 7% 1% 16% 9% NAB 17% 8% 6% 3% 16% 9% NCP 17% 8% 4% 4% 18% 9% RIO 15% 9% 5% 1% 18% 3% TLS 10% 9% 9% 17% 15% 40% WBC 17% 1% 8% 0% 17% 7% WMC 1% 9% 9% 19% 19% 33% Average 15% 9% 7% 1% 17% 31% 34

35 Table 3 Resuls f he Trade and Risk Indicar Mdel This able presens resuls f he rade and risk indicar mdel applied welve arund he mney call and pu pin series which an pin marke maker is designaed prvide bid and ask ques a he cninuus level. The mdel represened by equain (7) is defined as: s S ( ) 1 S S S M δ 1 M = α Q 1 + β Q 1 + β Q 1 + β Q 1 + ε. (7) The en sck pins are lised in alphabeical rder and Panel A cnains he esimaed cefficiens fr he rade and risk indicar variables wih heir respecive -values in parenheses. Panel B reprs he breakdwn f he average esimaed cefficiens ver fur separae inra-day perids, w in he mrning and w in he afernn. Als included are Kruskal-Wallis Chi-square saisics fr he inra-day cmparisns. Chi-square values indicaing significan inraday differences a he 5% (1%) level are highlighed wih ne (w) aserisk(s). Panel A Opin Nbs αˆ βˆ βˆ βˆ R AMP ** (1.3) (1.71) (0.45) (4.97) ANZ ** ** (.79) (1.76) (0.79) (4.99) BHP ** 0.056** ** (1.75) (4.00) (3.00) (4.64) CBA ** ** (1.63) (3.98) (1.7) (6.13) NAB ** ** ** (.88) (4.63) (-0.5) (6.66) NCP * ** * ** (.13) (4.06) (.49) (5.30) RIO ** (1.60) (1.17) (0.83) (3.64) TLS ** ** (1.61) (4.81) (1.1) (4.1) WBC ** (0.53) (-0.67) (.75) (0.61) WMC * ** (.48) (1.81) (-1.46) (3.70) Average Panel B: Average esimaed cefficiens f he rade and risk indicar variables in each f he fur inra-day perids. Inra-day perid Sessin αˆ βˆ βˆ βˆ R 10:00 11:15 am MS :15 1:30 pm MS :00 3:00 pm AS :00 4:00 pm AS Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm any w inra-day perids are differen. Sub-samples f esimaes under cmparisn MS1 vs MS MS1 vs AS MS1 vs AS 3.86* *.06 MS vs AS MS vs AS AS1 vs AS 3.86* αˆ βˆ βˆ βˆ 35

36 Table 4 Cmparing he Bid-Ask Spread Cmpnens f Opins wih Differen Degrees f Leverage This able presens resuls f he rade and risk indicar mdel applied hree sub-samples f daa: a lw leverage grup cnaining he in-he-mney calls and u-f-he mney pus, a mderae leverage grup f a-he-mney calls and pus, and a high leverage grup f u-f-he-mney calls and in-he-mney pus. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables are differen in any w leverage grups. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). pin nbs αˆ Lw leverage grup (L) Mderae leverage grup (M) High leverage grup (H) βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R AMP * * ** (-0.4) (1.84) (-0.5) (.54) (1.51) (0.3) (1.73) (.91) (0.65) (1.01) (-0.37) (3.08) ANZ ** * ** ** * (0.17) (3.15) (-0.18) (.7) (1.9) (1.10) (0.3) (4.51) (3.53) (-1.08) (1.66) (.14) BHP * ** ** ** * (1.90) (0.75) (.04) (1.94) (-0.5) (3.65) (1.40) (5.8) (0.66) (.89) (.50) (0.96) CBA * ** * ** * (1.01) (1.50) (1.38) (.4) (0.0) (3.60) (.35) (4.) (1.68) (.14) (-0.9) (3.87) NAB ** ** ** ** ** ** (0.16) (3.08) (0.54) (3.61) (1.88) (4.03) (0.74) (4.67) (.86) (1.14) (-1.37) (3.7) NCP ** ** ** * ** * * (-0.93) (3.6) (0.11) (3.79) (3.3) (1.47) (.36) (3.33) (1.46) (.0) (.08) (1.89) RIO ** (1.31) (0.5) (0.13) (1.41) (0.79) (1.68) (1.54) (1.78) (1.09) (-0.05) (-0.13) (3.36) TLS ** ** * ** (0.48) (3.6) (0.49) (1.19) (0.39) (3.99) (.00) (4.1) (1.76) (0.85) (-0.44) (1.7) WBC ** (0.79) (-1.08) (3.) (-1.95) (-0.78) (-0.18) (1.87) (1.00) (1.44) (0.5) (0.18) (1.3) WMC * * * ** (0.95) (1.86) (0.01) (0.98) (.78) (0.5) (-0.) (.46) (0.48) (1.14) (-.16) (.98) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm any w leverage grups are differen. Sub-samples αˆ βˆ βˆ βˆ αˆ βˆ βˆ βˆ αˆ βˆ βˆ βˆ L vs M L vs H 4.17* M vs H

37 Table 5 Cmparing he Bid-Ask Spread Cmpnens f Opins wih Differen Liquidiy Levels sred by Time beween rades in he same series This able presens resuls f he rade and risk indicar mdel applied hree sub-samples f daa: a lw liquidiy grup frm he 4 h quarile wih he lnges ime beween rades, a mderae liquidiy grup frm he nd and 3 rd quariles, and a high liquidiy grup frm he 1 s quarile wih he leas ime beween rades. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables are differen in any w liquidiy grups. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). pin nbs αˆ Lw liquidiy grup (L) Mderae liquidiy grup (M) High liquidiy grup (H) βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R nbs αˆ βˆ βˆ 37 βˆ R AMP ** ** ** (-0.57) (0.13) (-1.14) (.95) (0.59) (1.67) (0.54) (.57) (3.9) (0.57) (0.77) (1.5) ANZ * * ** ** (-1.07) (1.0) (-0.87) (.18) (.54) (1.8) (0.57) (4.33) (4.38) (-1.44) (1.86) (1.13) BHP * * ** ** * * (-1.38) (.04) (0.1) (1.30) (1.6) (.6) (.7) (3.11) (.01) (.17) (1.0) (1.8) CBA * ** ** * ** * (-0.) (1.30) (-0.3) (.38) (0.8) (3.0) (0.45) (5.01) (.04) (1.75) (3.71) (1.96) NAB * * ** 0.067** ** ** ** (-0.87) (.0) (-1.13) (.35) (.65) (.96) (-0.13) (5.47) (3.7) (1.83) (0.67) (4.01) NCP * ** * ** ** * 0.197** (-1.06) (.39) (0.81) (1.19) (1.85) (.77) (1.99) (4.58) (4.46) (0.07) (.3) (3.60) RIO * (-0.09) (0.34) (-0.1) (1.53) (0.97) (1.60) (1.65) (.47) (1.86) (-0.64) (-0.83) (1.64) TLS ** ** * * ** * * * (-.58) (.79) (-.) (.05) (1.3) (3.5) (.3) (.0) (.7) (1.7) (0.81) (1.88) WBC * (1.1) (-0.7) (1.9) (1.14) (-0.34) (-0.45) (.01) (-0.10) (0.61) (0.33) (0.04) (0.16) WMC ** ** ** (-1.7) (0.51) (-1.60) (-0.93) (1.6) (1.40) (-1.37) (3.08) (4.4) (-0.9) (0.6) (.94) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm any w liquidiy grups are differen. Sub-samples αˆ βˆ βˆ βˆ αˆ βˆ βˆ βˆ αˆ βˆ βˆ βˆ L vs M 7.00** * 0.8 L vs H 10.57** *.9 M vs H 13.7**

38 Table 6 Cmparing he Bid-Ask Spread Cmpnens f Ques preceded by Psiive and Negaive Vlume This able presens resuls f he rade and risk indicar mdel applied w sub-samples f daa: a psiive and a negaive pin vlume grup cnaining que midpin changes ha crrespnd a ne increase in psiive pin rades and a ne increase in negaive pin rades, respecively. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he w signed vlume grups are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). Psiive vlume grup (P) pin nbs αˆ βˆ βˆ βˆ R nbs αˆ Negaive vlume grup (N) βˆ βˆ βˆ R AMP ** ** (1.7) (0.41) (-0.18) (3.93) (0.30) (1.69) (0.65) (.69) ANZ ** * (1.79) (1.68) (0.43) (5.1) (.09) (0.96) (0.90) (1.94) BHP ** ** * ** (-0.57) (3.84) (1.58) (4.38) (.54) (1.70) (3.43) (1.84) CBA ** ** ** * ** (-1.09) (3.74) (0.09) (4.37) (3.77) (1.15) (.00) (4.37) NAB ** ** ** ** (0.33) (4.67) (1.0) (4.13) (4.39) (1.1) (-0.8) (5.31) NCP * ** ** ** (0.58) (.09) (1.90) (3.63) (1.81) (3.50) (1.63) (3.77) RIO ** (0.35) (1.53) (0.9) (3.19) (1.85) (-0.10) (0.98) (1.86) TLS ** * ** ** (1.75) (3.51) (1.68) (.06) (0.35) (.94) (-0.4) (4.03) WBC ** (-0.41) (-0.47) (.79) (-0.64) (1.19) (-0.74) (1.) (1.41) WMC * ** (1.85) (.19) (-1.43) (3.76) (1.44) (0.70) (0.07) (1.35) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he w signed vlume grups are differen. Sub-samples αˆ βˆ βˆ βˆ P vs N 7.41**

39 Table 7 Cmparing he Bid-Ask Spread Cmpnens f Call and Pu Opins This able presens resuls f he rade and risk indicar mdel applied w sub-samples: a grup f call nly pins and anher grup f pu nly pins. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he w ypes f pins are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). Call pin grup (C) Pu pin grup (P) pin nbs αˆ βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R AMP ** ** ** ** (-0.58) (.77) (-1.00) (3.75) (.75) (-0.68) (1.70) (3.13) ANZ ** ** ** ** * (0.70) (3.19) (-0.97) (4.76) (.55) (-0.11) (.59) (.14) BHP ** ** ** * 0.060* ** (0.61) (3.16) (.90) (3.08) (.6) (.10) (1.16) (3.58) CBA ** ** ** * ** (-0.1) (3.05) (1.48) (4.59) (.57) (.3) (0.34) (4.40) NAB * ** ** ** ** (.3) (.60) (-0.49) (5.49) (1.74) (4.0) (0.61) (3.89) NCP * 0.067** ** ** ** (0.98) (.34) (3.00) (3.66) (1.95) (3.0) (0.8) (3.54) RIO ** ** ** (1.40) (-0.) (-0.88) (3.98) (0.39) (.65) (.88) (0.87) TLS ** ** * * * (0.6) (4.6) (0.36) (3.57) (.4) (.16) (1.33) (.51) WBC * (-0.64) (-0.3) (.48) (0.4) (1.55) (-0.89) (1.36) (0.74) WMC * * ** (.14) (1.50) (-0.77) (.17) (1.) (1.16) (-1.9) (3.09) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he call pin grup are differen frm hse f he pu pin grup. Sub-samples αˆ βˆ βˆ βˆ C vs P 6.*

40 Table 8 Cmparing he Bid-Ask Spread Cmpnens f Ques preceded by a Rise and a Fall in Dela This able presens resuls f he rade and risk indicar mdel applied w sub-samples: a psiive and a negaive dela grup cnaining que midpin changes ha are preceded by a rise and a fall in dela, respecively. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he w signed dela grups are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). pin nbs αˆ Psiive dela grup (P) βˆ βˆ βˆ R nbs αˆ Negaive dela grup (N) βˆ βˆ βˆ R AMP * ** (1.69) (0.45) (1.39) (.7) (0.) (1.69) (-0.4) (4.7) ANZ * * ** ** (.0) (.17) (0.76) (.88) (1.73) (0.79) (0.55) (4.64) BHP ** ** ** * ** (0.5) (4.80) (.57) (3.4) (1.78) (1.11) (.05) (3.6) CBA ** 0.047* ** ** ** (-0.01) (5.19) (.36) (4.60) (.65) (0.07) (0.0) (4.8) NAB ** ** ** ** (0.85) (5.70) (-1.16) (5.7) (3.57) (0.75) (1.1) (4.10) NCP * ** ** * 0.046* ** (.15) (3.39) (1.77) (3.70) (0.64) (.19) (.05) (3.6) RIO * ** (1.3) (.39) (1.55) (1.71) (1.06) (-0.17) (0.05) (3.13) TLS ** ** ** 0.067* (0.67) (3.01) (-0.4) (4.88) (1.1) (4.1) (.35) (1.45) WBC (0.0) (0.48) (1.43) (0.96) (0.61) (-1.55) (.59) (-0.18) WMC ** * ** (1.16) (1.80) (-1.9) (.73) (1.96) (1.15) (-0.37) (.61) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he w signed dela grups are differen. Sub-samples αˆ βˆ βˆ βˆ P vs N **

41 Table 9 Cmparing he Bid-Ask Spread Cmpnens f Ques preceded by a Rise and a Fall in Vega This able presens resuls f he rade and risk indicar mdel applied w sub-samples: a psiive and a negaive vega grup cnaining que midpin changes ha crrespnd he vega risk indicar being assigned a value f +1 and -1, respecively. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he - values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he w signed vega grups are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). pin nbs αˆ Psiive vega grup (P) βˆ βˆ βˆ R nbs αˆ Negaive vega grup (N) βˆ βˆ βˆ R AMP ** ** ** (0.11) (1.35) (0.51) (3.78) (0.90) (0.68) (.85) (3.68) ANZ ** ** ** ** (0.98) (1.18) (1.7) (3.98) (3.30) (0.87) (3.50) (4.5) BHP ** ** 0.091** ** * * (-0.85) (4.57) (3.08) (4.01) (3.07) (1.48) (.14) (.30) CBA ** ** ** * ** * (0.04) (3.33) (0.00) (5.89) (.81) (.50) (4.1) (.38) NAB * * ** ** * ** (.19) (.31) (1.53) (3.91) (1.15) (3.7) (.8) (7.41) NCP * ** ** ** ** ** (1.07) (.4) (3.65) (3.38) (1.75) (3.7) (3.54) (4.33) RIO ** * (0.38) (1.48) (1.44) (.60) (1.66) (0.54) (0.96) (.13) TLS ** ** * * * ** ** (-0.57) (5.14) (3.13) (.37) (1.97) (.3) (3.1) (4.34) WBC * (1.05) (-0.95) (.40) (1.0) (0.0) (-0.11) (1.90) (-0.56) WMC ** * * * 0.135** (.64) (0.07) (-1.79) (.54) (0.74) (.40) (1.98) (3.47) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he w signed vega grups are differen. Sub-samples αˆ βˆ βˆ βˆ P vs N *

42 Table 10 Cmparing he Bid-Ask Spread Cmpnens f Ques preceded by a Rise and a Fall in Gamma This able presens resuls f he rade and risk indicar mdel applied w sub-samples: a psiive and a negaive gamma grup cnaining que midpin changes ha crrespnd he gamma risk indicar being assigned a value f +1 and -1, respecively. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he - values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he w signed gamma grups are differen. Esimaed cefficiens and Chisquare saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). Psiive gamma grup (P) pin nbs αˆ βˆ βˆ βˆ R nbs αˆ Negaive gamma grup (N) βˆ βˆ βˆ R AMP ** ** (1.46) (0.8) (0.3) (4.4) (-0.3) (1.68) (0.94) (6.33) ANZ ** * ** (1.39) (0.99) (0.68) (5.0) (.4) (1.4) (1.35) (7.05) BHP ** * ** ** * 0.075** (-0.5) (4.06) (.6) (3.30) (.75) (1.90) (.5) (3.) CBA ** ** ** * ** (0.04) (3.0) (1.84) (3.87) (.73) (.0) (0.0) (8.84) NAB * 0.05** ** ** ** (.33) (.55) (-1.16) (6.86) (0.88) (3.47) (1.78) (7.91) NCP ** ** ** ** ** (1.1) (.61) (1.1) (4.67) (1.4) (.8) (3.80) (6.65) RIO ** ** (1.18) (0.5) (-0.16) (.65) (1.04) (1.60) (1.85) (3.80) TLS ** ** ** 0.076** ** (0.84) (3.60) (-0.09) (5.90) (0.30) (4.1) (3.0) (6.38) WBC * (0.50) (-0.53) (.38) (0.9) (0.61) (-0.47) (0.77) (0.65) WMC * * ** (1.63) (0.85) (-1.13) (.6) (.6) (0.94) (-0.5) (6.09) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he w signed gamma grups are differen. Sub-samples αˆ βˆ βˆ βˆ P vs N

43 Table 11 Cmparing he Bid-Ask Spread Cmpnens f Opins wih Differen Levels f Dela This able presens resuls f he rade and risk indicar mdel applied hree sub-samples: a lw, a medium, and a high dela grup cmprising f u-f-he-mney, a-he-mney, and in-he-mney calls and pus, respecively. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he hree dela grups are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). pin nbs αˆ Lw dela grup (L) Mderae dela grup (M) High dela grup (H) βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R AMP ** ** * (-0.04) (1.0) (-1.3) (3.74) (1.51) (0.3) (1.73) (.91) (0.35) (1.78) (0.0) (.04) ANZ ** ** (1.43) (0.81) (1.0) (.66) (1.9) (1.10) (0.3) (4.51) (1.71) (1.63) (0.50) (1.9) BHP ** ** ** ** (1.91) (1.80) (.87) (4.38) (-0.5) (3.65) (1.40) (5.8) (1.48) (1.89) (1.73) (0.40) CBA * ** ** * ** * (0.53) (.8) (0.) (5.04) (0.0) (3.60) (.35) (4.) (1.88) (1.31) (0.4) (.39) NAB ** * ** ** ** ** (3.70) (-0.18) (0.9) (.0) (1.88) (4.03) (0.74) (4.67) (0.14) (3.55) (-1.09) (4.40) NCP * ** ** * ** ** ** (1.71) (1.61) (.08) (3.19) (3.3) (1.47) (.36) (3.33) (-1.11) (3.65) (0.54) (.75) RIO * * * (.17) (-1.4) (-0.9) (.3) (0.79) (1.68) (1.54) (1.78) (-0.30) (1.9) (1.0) (.18) TLS ** ** * ** ** (1.46) (0.30) (-1.03) (3.97) (0.39) (3.99) (.00) (4.1) (0.89) (3.58) (0.55) (0.06) WBC ** (0.97) (-0.4) (3.4) (-1.47) (-0.78) (-0.18) (1.87) (1.00) (0.86) (0.46) (1.34) (-0.80) WMC ** * * (1.17) (1.40) (-0.35) (1.70) (.78) (0.5) (-0.) (.46) (0.97) (1.9) (-1.) (.06) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he hree dela grups are differen. Sub-samples αˆ βˆ βˆ βˆ L vs M L vs H ** M vs H * 43

44 Table 1 Cmparing he Bid-Ask Spread Cmpnens f Opins wih Differen Levels f Vega This able presens resuls f he rade and risk indicar mdel applied w sub-samples: a lw vega grup cmprising f u-f-he-mney and in-he-mney calls and pus, and a high vega grup f a-he-mney call and pus. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he w vega grups are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). Lw vega grup (L) High vega grup (H) pin nbs αˆ βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R AMP ** ** (0.36) (1.91) (-0.51) (3.9) (1.51) (0.3) (1.73) (.91) ANZ * ** ** (.41) (1.71) (0.77) (.99) (1.9) (1.10) (0.3) (4.51) BHP * ** 0.050* ** ** (1.93) (.40) (3.3) (.10) (-0.5) (3.65) (1.40) (5.8) CBA * ** ** * ** (1.79) (.43) (0.15) (4.59) (0.0) (3.60) (.35) (4.) NAB * ** ** ** ** (.35) (.71) (-0.57) (4.97) (1.88) (4.03) (0.74) (4.67) NCP ** ** ** * ** (0.56) (3.87) (1.38) (4.10) (3.3) (1.47) (.36) (3.33) RIO ** (1.47) (0.43) (0.00) (3.31) (0.79) (1.68) (1.54) (1.78) TLS ** * ** * ** 0.05 (1.71) (3.05) (-0.18) (.19) (0.39) (3.99) (.00) (4.1) WBC * (1.43) (-0.49) (.45) (-0.74) (-0.78) (-0.18) (1.87) (1.00) WMC ** ** * (1.15) (1.77) (-1.39) (.7) (.78) (0.5) (-0.) (.46) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he w vega grups are differen. Sub-samples αˆ βˆ βˆ βˆ L vs H

45 Table 13 Cmparing he Bid-Ask Spread Cmpnens f Shr Mauriy Opins wih Differen Levels f Gamma This able presens resuls f he rade and risk indicar mdel applied w sub-samples f pins wih up 14 days mauriy: a lw gamma grup cmprising f u-f-he-mney and in-he-mney calls and pus, and a high gamma grup f a-he-mney call and pus. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he w gamma grups are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). Lw gamma grup (L) High gamma grup (H) pin nbs αˆ βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R AMP ** ** (0.50) (-0.16) (-1.54) (3.3) (1.4) (0.30) (-0.4) (3.15) ANZ ** (1.08) (1.1) (-1.1) (1.76) (1.0) (1.84) (-1.9) (3.88) BHP ** ** 0.00 (.7) (-0.4) (0.8) (1.40) (-0.) (1.4) (-0.59) (5.16) CBA ** ** (0.16) (1.79) (-1.87) (4.39) (0.53) (1.03) (0.07) (3.6) NAB * ** ** (.46) (1.53) (-1.40) (.65) (1.44) (1.9) (-1.17) (6.3) NCP * ** * ** (-0.17) (.4) (-1.74) (4.91) (.41) (-0.15) (0.7) (3.66) RIO * * * (0.34) (1.50) (0.03) (1.99) (-0.34) (.0) (-0.44) (.04) TLS ** ** (0.67) (1.55) (-0.8) (1.63) (-1.04) (.7) (-0.76) (6.05) WBC (-0.4) (1.4) (1.55) (-0.8) (-.8) (1.7) (0.51) (1.67) WMC (-0.3) (0.49) (-.51) (0.70) (1.83) (0.90) (-1.89) (0.0) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he w gamma grups are differen. Sub-samples αˆ βˆ βˆ βˆ L vs H * 45

46 Table 14 Cmparing he Bid-Ask Spread Cmpnens f Medium Mauriy Opins wih Differen Levels f Gamma This able presens resuls f he rade and risk indicar mdel applied hree sub-samples f pins wih days mauriy: a lw gamma grup cmprising f in-hemney calls and u-f-he-mney pus, and medium gamma grup f u-f-he-mney calls and in-he-mney pus, and a high gamma grup f a-he-mney call and pus. The numbers in parenheses belw he esimaed cefficiens f he rade and risk indicar variables are he -values f he esimaes. The Chi-square saisics f he Kruskal-Wallis es are used deermine if he esimaed cefficiens f each f he fur indicar variables frm he hree gamma grups are differen. Esimaed cefficiens and Chi-square saisics ha are differen frm zer a he 5% (1%) significance level are highlighed wih ne (w) aserisk(s). pin nbs αˆ Lw gamma grup (L) Mderae gamma grup (M) High gamma grup (H) βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R nbs αˆ βˆ βˆ βˆ R AMP * * (-0.11) (1.89) (0.84) (1.54) (0.) (1.39) (-0.33) (.11) (1.13) (0.13) (.3) (1.67) ANZ ** ** ** (0.13) (.64) (1.56) (1.5) (3.9) (-1.11) (1.47) (1.9) (1.10) (0.48) (0.96) (3.) BHP * ** 0.093* ** * ** (0.5) (1.6) (.44) (1.64) (0.4) (.89) (.38) (0.55) (-0.8) (3.37) (.01) (.91) CBA * ** ** ** ** (1.13) (1.3) (.18) (0.75) (1.78) (1.39) (-0.9) (3.18) (-0.06) (3.55) (.93) (.78) NAB ** * * ** ** * (-0.61) (.78) (1.43) (.3) (.11) (0.98) (-1.43) (3.45) (1.5) (3.91) (1.64) (.11) NCP ** ** * ** (-0.4.0) (3.00) (1.09) (1.31) (1.10) (1.66) (.8) (1.00) (.47) (1.7) (.55) (1.7) RIO ** (1.65) (-0.6) (-0.14) (1.35) (1.15) (-0.7) (-0.11) (.61) (1.41) (0.5) (1.86) (0.9) TLS ** * ** 0.089** (-0.09) (3.18) (0.87) (0.60) (.08) (0.81) (-0.68) (1.64) (0.91) (.79) (.81) (1.93) WBC * (1.39) (-1.49) (.3) (-1.57) (1.35) (0.7) (0.6) (0.59) (0.9) (-1.01) (1.80) (0.37) WMC * ** * ** (1.33) (1.86) (1.85) (0.70) (0.64) (1.5) (-.07) (.81) (.13) (0.11) (0.51) (.43) Average Kruskal-Wallis es: Chi-square saisics wih ne degree f freedm are repred belw deermine if he esimaed cefficiens frm he hree gamma grups are differen. Sub-samples αˆ βˆ βˆ βˆ L vs M * L vs H M vs H