Net buying pressure and option informed trading

Transcription

1 Ne buying pressure and opion informed rading Chao-Chun Chen Shih-Hua Wang Absrac To differeniae he impacs of volailiy rading and direcion rading on an opion mare, his sudy develops a mehod o decompose ne buying pressure ino he volailiy-moivaed componen and direcion-moivaed componen. Unlie he oally ne buying pressure adoped in he lieraure, in ha a cancel-ou effec may occur beween volailiy rading and direcion rading and hus bring abou a consequenial muually-exclusive resul when inspecing he wo rading effecs by enire ne buying pressure, he proposed decomposiions in ne buying pressure enable us o examine which ind of informed rading aciviies drive opion price changes by independenly esing he volailiy-learning hypohesis and direcion-learning hypohesis. Empirical evidences show ha he change in implied volailiy of TAIEX OTM pu opions can be accouned for by boh of he wo ne-buying-pressure hypoheses. I indicaes ha rades on OTM pu opions may conain informaion regarding boh fuure volailiy and fuure price movemens of he underlying asse, which is very differen from he findings of he joinly es mehodology adoped in he relaed lieraure. Key words: Learning hypoheses; Ne buying pressure; Volailiy-moivaed rading; Direcion-moivaed rading; Independen es EFM Classificaion Codes: 410, 360 All correspondence o Chao-Chun Chen. Associae Professor. Deparmen of Finance, Tunghai Universiy, Taichung, Taiwan, R.O.C. jawjiun@hu.edu.w Deparmen of Finance, Tunghai Universiy, Taichung, Taiwan, R.O.C. 1

2 1 Inroducion The informaion conen of rading aciviies, especially from informed raders, is a subjec of widespread ineres no maer in soc mares or in derivaive mares. According o he preferred habia of informed invesors, he properies of high financial leverage, low ransacion coss, and few shor-selling resricions in derivaive mares are aracive for informed invesors o exploi heir privae informaion in he opion mare before in he underlying asse mare. According o he asserions in Blac (1975), Easley, O'Hara, and Srinivas (1998), Bollen and Whalley (2004), and Kang and Par (2008), as long as mares are incomplee and here are informed raders aing advanage of privae informaion in opion mares before having a posiion in he underlying securiy mares, opion rades are capable of carrying informaion concerning he subsequen price behavior of he underlying asse. Indeed, here are a leas wo ypes of informed raders paricipaing in an opion mare; hose are volailiy raders and direcion raders. The former aes a posiion in opions when shocs on volailiy of he fuure underlying asse prices occur, while he laer engages in opion rading provided expecaions regarding he fuure price movemens of he underlying asse change. The informaion conen behind opion demands is hus expeced o differ across differen ypes of informed rading, as long as he wo ypes of informed rading relies on differen news. A rich body of lieraure has emerged invesigaing he informaion conen behind opion rades, alhough few documens differeniae he volailiy rading effec and direcion rading effec from opion demands. In he lieraure, Bollen and Whaley (2004) propose a hypohesis o demonsrae he volailiy rading effecs in an opion mare and examine wheher opion price changes resul from volailiy rading by exploring he informaion conen of ne buying pressure. Herein, 2

3 ne buying pressure is defined by he difference beween he number of buyer-moivaed conracs and seller-moivaed conracs muliplied by he absolue value of he opions dela. According o he asserion of his hypohesis, volailiy informed raders buy/sell boh call and pu opions in case of posiive/negaive volailiy shocs arriving. The consequenial order imbalance in opions reflecs he change in mare expecaions abou fuure volailiy, and hus signals o mare maers for updaing opion implied volailiy. I evenually resuls in ne buying pressure having posiive influences on implied volailiy of boh call and pu opions. As suggesed in Kang and Par (2008), we name he hypohesis proposed in Bollen and Whaley (2004) ha concerns he volailiy rading effec as he volailiy-learning hypohesis. By adoping he daily daa in he U.S. opion mare, Bollen and Whaley (2004) provide evidences ha ne buying pressure does maer o he shape of he implied volailiy smile, alhough i canno be concluded o resul from volailiy informed rading. Kang and Par (2008) argue ha opion raders can be direcion raders as well and exend he learning hypohesis o examine he direcion rading effec in opion price changes. They documen ha raders wih opimisic/pessimisic expecaions abou fuure securiy price movemens buy call/pu opions bu sell pu/call opions before aing a posiion in he underlying securiy, provided ha opion mares possess higher financial leverage and lower ransacion coss. Consequenly, ne buying pressure of call/pu opions induced by direcion rading is observed o raise implied volailiy of call/pu opions bu lessen ha of pu/call opions, before informaion is disseminaed o he soc mare. This is he conen of he direcion-learning hypohesis. By exending he empirical es mehodology of Bollen and Whaley (2004), Kang and Par (2008) provide evidences supporing ha price changes in KOSPI 200 opions mainly resul from direcion rading and ne buying pressure conains informaion abou he fuure movemens of he KISPI 200 index. 3

4 A common feaure sharing wih Bollen and Whaley (2004) and Kang and Par (2008) in inspecing he volailiy rading effec and direcion rading effec is o examine he way how he enire ne buying pressure influences opions implied volailiy. Simply speaing, Bollen and Whaley (2004) examine he volailiy rading effec by looing a wheher ne buying pressure of call and ha of pu opions has equally posiive influences on an opion s implied volailiy, whereas Kang and Par (2008) demonsrae ha a finding regarding ne buying pressure of call and ha of pu opions having opposie influences on an opion s implied volailiy can be aribued o direcion rading. However, as ne buying pressure is an aggregaion of excess opion demands across all opion raders, including volailiy raders and direcion raders, a poenial concern behind he usage of enire ne buying pressure is pars of he volailiy rading effec and direcion rading effec may cancel each oher ou, if opion rades conduced by he wo inds of informed rading are in he opposie posiions. Indeed, his always happens while volailiy shocs and direcion shocs occur a he same ime, in which pu opions may be bough by volailiy raders bu sold by direcion raders, provided ha boh he wo inds of shocs are posiive. As a resul, under he empirical es mehodology adoped in Bollen and Whaley (2004) and Kang and Par (2008), in ha he volailiy rading effec is examined by looing a wheher ne buying pressure of call and pu opions has equal and posiive impacs on an opion s implied volailiy, lile volailiy rading effec can be found ou while a large direcion shoc goes wih a small volailiy shoc. Similarly, enire ne buying pressure canno be found o carry any informaion concerning he direcion rading effec if a wea direcion shoc accompanies wih a large volailiy shoc. The cancel-ou effec behind enire ne buying pressure in case of boh volailiy shocs and direcion shocs happening simulaneously is also he reason why he volailiy-learning and direcion-learning hypoheses are always muual exclusive when adoping enire ne buying pressure, as he way in he empirical es of Kang and Par s (2008), o examine he wo 4

5 hypoheses. In realiy, boh direcion raders and volailiy raders are acive in mos of opion mares, and direcion shocs usually accompany volailiy shocs as well. To avoid he cancel-ou effec in enire ne buying pressure and address he muual-exclusive puzzle beween he volailiy-learning and direcion-learning hypoheses, unlie he way of Kang and Par s (2008) ha sands a an aggregaive perspecive o explore he impac of primarily informed rading aciviies on opion price changes, his research proposes a mehod o decompose he overall ne buying pressure ino he volailiy-moivaed componen and direcion-moivaed componen, and examines he wo ypes informed rading effecs in an opion mare individually based on he proposed mehod. Wih he decomposiions of ne buying pressure, he volailiy-learning hypohesis and direcion-learning hypohesis are able o be esed independenly, and, as a resul, he changes in opions implied volailiy are allowed o be accouned for by boh he wo hypoheses, which is very differen from he joinly es mehodology adoped in he lieraure. We apply he proposed approach o invesigae he impacs of he wo ypes informed rading on prices of he Taiwan Soc Exchange Capializaion Weighed Soc Index opions (TAIEX opions, hereafer), and explore wheher he informaion conen behind he decomposed ne buying pressure changes afer he onse of he U.S. deb-ceiling crisis in The TAIEX opion, in which he underlying asse is he Taiwan Capializaion Weighed Soc Index (TAIEX), is in a mare wih high individual paricipaion and is one of he mos liquid index opions in he world. As he saisics in WFE/IOMA Derivaives Mare Survey 2013, he number of TAIEX opion conracs raded accrued in 2013 reach o 109 million conracs, raning i sixh among he mos acively raded index opion in he world. Based on he empirical evidences, he change in implied volailiy of TAIEX opions is accouned for 5

6 by he direcion-learning hypohesis across all models, regardless of moneyness and sample periods, while he volailiy rading effec is only found in OTM pu opions. These empirical evidences are very differen from ha of Kang and Par (2008), in which he wo learning effecs are resrics o be muually exclusive under he adopion of enire ne buying pressure. The remaining pars of his paper are arranged as follows. Secion 2 proposes a mehod o decompose ne buying pressure. Secion 3 describes our daa. The empirical specificaions in invesigaing he relaionship beween he decomposed ne buying pressure and opions implied volailiy are provided in Secion 4. Secion 5 is empirically resuls. Concluding remars are given in he las secion. 2 Decomposiions of ne buying pressure The classical ne buying pressure adoped in Bollen and Whaley (2004) and Kang and Par (2008) is defined by he difference beween he number of buyer-moivaed conracs and seller-moivaed conracs muliplied by he absolue value of opions dela. Herein, he difference is compued on a series-by-series basis, and is muliplied by he absolue value of he opion s dela o express demand in index equivalen unis. As we menioned above, ne buying pressure is comprised of excess opion demands from boh direcion raders and volailiy raders. As he enire ne buying pressure includes ne opion demands from direcion rading and volailiy rading, i can be displayed as: NBP = NBPD + NBPV (1) C, C, C,, and NBP = NBPD + NBPV (2) P, P, P,, 6

7 where {DOTM, OTM, ATM, ITM, DITM} and i { C, P}. Moreover, NBP i, displays ne buying pressure summed across he ime inerval for call/pu opions caegorized in he moneyness caegory, NBPD i, denoes he direcion-moivaed ne buying pressure for he -caegory call/pu opions, and NBPV i, represens he volailiy-moivaed ne buying pressure for he -caegory call/pu opions. We follow Bollen and Whaley (2004) and Kang and Par (2008) o measure moneyness of an opion by opions dela and group opions ino five differen moneyness caegories, hose are he DOTM-, OTM-, ATM-, ITM-, and DITM-caegory, based on dela, since dela can be inerpreed as he lielihood of being in he money a expiraion. The upper and lower bounds of each moneyness caegory are lised in Table 1. As in he prior sudies, his research focuses on invesigaing he informaion conen of ne buying pressure in he OTM- and ATM-caegory opions, because hese opions are more liquid and expeced o convey abundan informaion concerning opion informed rading. The direcion informed rading and volailiy informed rading is sensiive o differen ypes of news. Specifically, volailiy informed raders ener ino opion posiions while a volailiy shoc his mares and induces he expecaion abou volailiy changes, whereas he direcion informed raders are nown o be occupied in opion rading while a direcion shoc occurs and leads o he expecaion concerning he fuure asse price change. Thus, for an opion wihin moneyness caegory, he volailiy-moivaed ne buying pressure and direcion -moivaed ne buying pressure can be defined as: and NBPV NBPD NBP i, E i, = σ, σ NBP i, E i, = S, S (3) (4) 7

8 where NBPi, σ represens sensiiviies of enire ne buying pressure o changes in volailiy, NBPi, S displays sensiiviies of enire ne buying pressure o changes in he underlying asse price, and E σ and E S sand for changes in he expecaion of asse volailiy and asse prices, respecively. Wihou loss of generaliy, he excess opion demand is se o be a funcion of he opion s price. By applying Chain rule o Equaions (3) and (4) and subsiuing he resuls ino Equaions (1) and (2), enire ne buying pressure can be displayed as: NBP = NBPD + NBPV C, C, C, NBP NBP = C S C NBP C, C E C, C E S + σ σ NBP C, E C, E = C S + νc σ, C C (5) and NBP = NBPD + NBPV P, P, P, NBP NBP = P S P P, P E P, P E S + σ σ ' E E ' E E = f ( P, ) P S + f ( P, ) νp σ, (6) where C and P are he ime prices of call and pu opions classified in moneyness caegory, respecively. Moreover, boh i and ν, where i { C, P} i and {DOTM, OTM, ATM, ITM, DITM}, are he opion s Gree leers defined as: = C / S, = P / S, ν = C / σ, and ν = P / σ. P C The properies of vega, ν C and P ν P, and dela, C and P, play imporan roles in refining he direcion-moivaed and volailiy-moivaed componens from enire ne buying pressure. According o he Blac and Scholes opion pricing model, variaion of vega wih C 8

9 soc prices is idenical o a symmerically normal disribuion, indicaing ha he vega of a -caegory call opion is idenical o ha of a -caegory pu opion: ν C = ν. (7) P On he oher hand, according o he moneyness caegory definiion lised in Table 1, a definiely propery concerning dela ha can be observed from Table 1 is: =, (8) C P where { DOTM, OTM, ATM, ITM, DITM}. I indicaes ha dela for -caegory call opions and dela for -caegory pu opions has equivalen values bu in differen signs. Combining hese imporan properies of Gree Leers displayed in Equaions (7) and (8) wih Equaions (5)-(6), he direcion-moivaed ne buying pressure of he -caegory call opions can be solved by: NBPD NBP NBP C, P, C, =, while he volailiy-moivaed ne buying pressure of call opions can be sized by: 2 (9) NBPV NBP + NBP C, P, C, =. Similarly, ne buying pressures of pu opions induced by direcion rading and volailiy rading are measured respecively by: 2 (10) and NBPD NBP NBP P, C, P, =, 2 (11) NBPV NBP + NBP P, C, P, =. As shown in Equaions (9) and (11), direcion-moivaed ne buying pressure of -caegory 2 (12) call opions, NBPD C,, is symmeric o ha of pu opions, NBPD P,, in ha he wo variables are idenical in values bu in differen signs. This feaure is convincing since he degree of 9

10 informaion conen behind direcion-moivaed rading canno change, no maer ha is measured from a viewpoin of call opions or from a pu opion s perspecive. The only difference is he signal concerning he fuure price movemens is opposie, where direcion-moivaed ne buying pressure on call/pu opions is expeced o resul in a higher/lower asse price, because he opion s dela is posiive for call opions bu negaive for pu opions. Equaions (10) and (12) also show ha volailiy-moivaed ne buying pressure of -caegory call opions, NBPV C,, is idenical o ha of he corresponding pu opions, NBPV P,, in erms of boh he magniude and sign. Similarly, i is convincing since he degree of informaion conen embedded in volailiy-moivaed rading does no change, no maer i is measured from he call opion s viewpoin or from he pu opion s perspecive. Moreover, he wo variables are in he same signs because boh of call and pu opions have posiive vega, indicaing ha an increase in ne demands for volailiy, regardless of opion ypes, is expeced o enlarge realized volailiy. 3 Sample Descripion This secion displays he daa adoped in his research and he way o generae opion s implied volailiy and he classical ne buying pressure. The sample saisics and empirical properies of implied volailiy and ne buying pressure are analyzed in he secion as well. 3.1 Daa This research applies he proposed decomposiions of ne buying pressure o analyze he price changes of TAIEX opions in The TAIEX opion, raded on Taiwan Fuures Exchange, is European-syle and maures on he hird Wednesday of he expiraion monh. 10

11 The asse underlying TAIEX opions is he Taiwan Capializaion Weighed Soc Index (TAIEX), which is repored based on 1-min frequency in our daa se. For TAIEX opions, here are five expiraion monhs lised in he exchange, including he spo monh, he nex wo calendar monhs, and he nex wo quarerly monhs. As we menioned above, he TAIEX opions have been one of he mos frequenly raded and imporan index opions in he world. The TAIEX opion ransacion daa ha we adop are drawn from he daabase of CMoney-Insiuional Invesor Invesmen Decision Suppor Sysem and comprises he rading ime, including he rading dae, hour, minue, and second, bid price, as price, rading price, srie price, expiraion monh, opion ype, and rading volume for each ransacion of TAIEX opions in As well nown, he U.S. deb-ceiling crisis is one of he mos impressively caasrophic even happened in 2011, in ha he delay in raising he deb ceiling by Republicans in Congress almos causes he U.S. governmen shudown in he beginning of Augus I also resuls in he firs downgrade in he U.S. credi raing and a consequenly sharp drop in he soc mare. To analyze he impac of he U.S. sovereign deb crisis on he TAIEX opion mare, we adop July 31, 2011 as he cuoff poin and divide he whole sample period ino wo subperiods: Subperiod I and II, represening he subperiods before and afer he onse of he U.S. sovereign deb crisis, individually. Summarily, subperiod I ranges from January 2011 o July 2011, while Subperiod II covers from Augus 2011 o December In order o calculae opions implied volailiy and heirs ne buying pressure, we merge he ime-samp TAIEX opion ransacion daa wih he inraday TAIEX index daa by rading ime, and calculae implied volailiy for each ransacion based on is synchronic TAIEX index. Denoe he rading prices of call and pu opions a ime are C and P, respecively. Implied volailiy can be calculaed by he following Blac and Scholes model: 11

12 C= Se Nd ( ) Ke Nd ( ), (13) q( T ) r( T ) 1 2 and P = Ke N( d ) Se N( d ), (14) r( T ) q( T ) 2 1 where d 1 = ln( S / K) ( r q 0.5 σ )( T ), σ ( T ) (15) and d2 = d1 σ ( T ). (16) Herein, S denoes he index level a ime, K is he opion s srie price, T displays he ime o expiraion, r sands for he ris-free ineres rae, q represens he dividend yield of he index, N () is he normal cumulaive densiy funcion, and σ denoes he volailiy. We adop he average of one-monh ime deposi ineres raes of five major bans in Taiwan as he ris-free ineres rae, r, which are colleced from he websie of he Cenral Ban of he Republic of China. Moreover, according o he saisics of Taiwan Soc Exchange, he TAIEX dividend yield, q, is equal o 5.83% in Transacions wih he non-synchronic problem and wih possible price disorions are removed from our daa se. The non-synchronic problem resuls from he design of he mare mechanism, whereas he price disorions usually happen in very DITM or DOTM opions. Specifically, Taiwan Soc Exchange, in which TAIEX index liss, operaes from 9:00 o 13:30 each rading dae, while he rading hour for TAIEX opions lis in Taiwan Fuures Exchange is from 8:45 o 13:45 for each rading dae. According o TWSE informaion disclosure mechanism during he closing session, orders made will no be mached bu only be acceped from 13:25 o 13:30, and no informaion is disclosed during his las five minues 12

13 unil closing. I indicaes ha soc prices say a 13:25 and will no updae unil 13:30. Alhough he TWSE launches a new order-maching simulaion mechanism five minues during he closing session from February 20, 2012, and release informaion on he highes bid price and he lowes as price approximaely every weny seconds a he las five minues during he closing session, here is no acual mached rade informaion available. Accordingly, i is impossible o mach he synchronic underlying asse price afer 13:25 on each rading day. For TAIEX opion ransacions execued before 9:00 and afer 13:30, here exiss even more serious nonsynchronic problem. To be wihou in he nonsynchronic problem, we delee ransacions of TAIEX opions raded before 9:00 and afer 13:25 on each rading day. Implied volailiy execued in each ransacion canno be analyzed by he regression mehod ye. We follow Bollen and Whaley (2004) and Kang and Par (2008) o group opions ino five differen moneyness caegories and compue an average implied volailiy for each of he opion caegories over a five-minue ime inerval. The moneyness caegories are classified by opion s dela, 2 ln( S / K) + ( r q+ 0.5 σ )( T ) C = N σ ( T ), (17) and 2 ln( S / K) + ( r q+ 0.5 σ )( T ) P = N 1, (18) σ ( T ) in which opion s dela, C and P, can be regarded as he probabiliy of he opion being in he money a mauriy. Herein, he proxy for he volailiy rae in calculaing opion s dela is realized reurn volailiy of he underlying asse over he mos recen sixy rading days, as 13

14 in he mehod of Bollen and Whaley (2004). Upper and lower bounds for each caegory are displayed in Table 1. Finally, as in Bollen and Whaley (2004) and Kang and Par (2008), ransacions of opions wih absolue delas below 0.02 or above 0.98 are excluded because he value of DITM and DOTM opions are exraordinarily insensiive o volailiy changes and may have disorions due o price discreeness. The ransacions wih a rading price above is heoreically upper bound or below is heoreically lower bound are also excluded from our daa se, since implied volailiy canno be esimaed reasonably in hese cases. Herein, he heoreically boundary of call prices is: Max S e Ke C S q( T ) r( T ) (,0), and ha of pu prices is: r( T ) q( T ) r( T ) (,0). Max Ke S e P Ke 3.2 Empirical Properies of Implied Volailiy Figure 1 plos he ime series properies of he TAIEX closing price and average implied volailiy of TAIEX opions over he whole sample period. A salien feaure observed in Figure 1 is a significan jump in TAIEX implied volailiy afer he onse of he 2011 U.S. deb-ceiling crisis, indicaing ha rading aciviies on TAIEX opions are subsanially affeced by his crisis. This is he reason why we chose July 31, 2011 as he cuoff poin o divide he whole sample period ino wo sub-periods. The implied volailiy funcions for he whole sample period and wo sub-periods are ploed in Figure 2. As expeced, he implied volailiy curve for Subperiod II is no only higher bu also seeper han ha from he Subperiod I, indicaing ha he occurrence of he 2011 U.S. deb-ceiling crisis affecs boh he level and shape of implied volailiy curve. This phenomenon is very similar o he findings in he lieraure, in which he shape of he implied 14

15 volailiy curve are observed o change from a smile o smir afer Ocober 1987 mare crash. 3.3 Ne Buying Pressure Table 2 repors he summary for he number of conracs raded and ne purchases of conracs in TAIEX opions, respecively. As shown in Panel A of Table 2, 55 percen of all conracs raded were call opions, wih only 45 percen being pu opions. There are similar resuls observed in Subperiod I and Subperiod II. I implies ha TAIEX opion raders prefer call opions o pu opions. This phenomenon is differen from he U.S. index opion mare repored in lieraure, where he percenage of pu opions raded was usually more han he proporion of call opions. Afer aing he rading moivaion ino accoun, Panel B of Table 2 shows ha he rading moivaion for mos TAIEX opions belongs o seller-moivaed. Table 3 summarizes ne buying pressure of call opions and pu opions. The resul is similar o wha observed in he saisics of ne-purchases conracs, because ne buying pressure is generaed by he number of ne-purchases conracs muliplying he absolue value of he opion s dela so as o express demand in index equivalen unis. For he whole sample period, Table 3 repors ha TAIEX opion raders generally have ne selling posiions excep for DOTM call opions. To compare across he resuls in Subperiod I and Subperiod II, he ne buying pressure of call opions was 1.36 imes ha of pus during Subperiod I, while he proporion lessened o 1.13 in Subperiod II. This resul suggess ha he 2011 U.S. deb-ceiling crisis changed invesors rading behavior on TAIEX opions again. 4 Empirical Specificaions This sudy examines he wo informed rading effecs in he TAIEX opion mare wih he proposed decomposiions of ne buying pressure, and explores wheher he impacs of he 15

16 wo informed rading on opions implied volailiy aler afer he onse of he 2011 U.S. sovereign deb crisis. The model specificaions for he cases of call and pu opions across various moneyness caegories are as follows: σ = β + β + β + β + β + β σ + ε (19) ATM ATM ATM ATM i, 0 1RS 2VS 3 NBPVi, 4 NBPDi, 5 i, 1, σ = β + β + β + β + β + β σ + ε (20) OTM OTM OTM OTM i, 0 1RS 2VS 3 NBPVi, 4 NBPDi, 5 i, 1, where i { C, P}. Herein, as in Equaions (9-12), NBPV = ( NBP + NBP ) 2, i, C, P, NBPD = ( NBP NBP ) 2, C, C, P, and NBPD = ( NBP NBP ) 2. P, P, C, Moreover, σ i, ATM, where i { C, P}, denoes he change in he average implied volailiy of OTM ATM call/pu opions, while σ i represens he analogous quaniy for OTM opions. RS, displays TAIEX reurns during he ime inerval, and VS sands for he summed rading volume of he TAIEX over he ime inerval, expressed in millions of New Taiwan (NT) ATM dollars. As menioned above, NBPV and i, i, OTM NBPV, where i { C, P}, are he volailiy-moivaed ne buying pressure of ATM and OTM call/pu opions, whereas ATM OTM NBPD and i, i, NBPD denoe he direcion-moivaed ne buying pressure of ATM and OTM call/pu opions. All variables are calculaed across five-minue ime inerval. Similar o he way adoped in Kang and Par (2008), we conduc he regression analysis wih 5-min inraday daa, in order o focus more on he informaion effec of ne buying pressure on opions prices. 16

17 The regression specificaion in Equaions (19) and (20) is idenical o he ones adoped in he relaed lieraure, excep for wo adjusmens in explanaory variables, in ha we replace enire ne buying pressure wih he proposed decomposiions of ne buying pressure, as suggesed in his research, and exclude he variable on ATM opions ne buying pressure from he regression of OTM opions implied volailiy. In he lieraure, ATM opions ne buying pressure is included in he regressions of OTM opions implied volailiy in order o differeniae he volailiy-learning hypohesis from he limi of arbirage hypohesis. Unlie he empirical es mehodology adoped in Kang and Par (2008) ha aims o examine hree ne-buying-pressure hypoheses, including he limi of arbirage hypohesis, volailiy-learning hypohesis, and direcion-learning hypohesis, he proposed approach focuses on independenly examining he wo learning hypoheses. We do no include any variables abou ne buying pressure of ATM opions in he regressions of changes in implied volailiy of OTM call/pu opions, because examining he limi of arbirage hypohesis is no a purpose of he proposed mehod and hus disinguishing his hypohesis from he volailiy-learning hypohesis by comparing he coefficien of ATM opions ne buying pressure and ha of OTM opions ne buying pressure, as done in he relaed lieraure, needs no o be aen ino accoun in his sudy. Similar o he seing in Bollen and Whalley (2004) and Kang and Par (2008), our regression model includes he conemporaneous index reurn RS and is rading volume VS as conrol variables for leverage and informaion flow effecs. According o Blac (1976) and Anderson (1996), soc reurn volailiy is negaively associaed wih soc reurns due o leverage effecs, bu is posiively relaed o rading volume due o informaion flow effecs. We hus expec he coefficien on TAIEX reurn, β 1, o be negaive, whereas he coefficien on he rading volume of he TAIEX, β 2, is expeced o be posiive. 17

18 The volailiy-learning hypohesis and direcion-learning hypohesis for opions wihin a paricular moneyness caegory can be examined by he coefficiens of he wo decomposed ne buying pressure, i.e., β 3 and β 4, respecively, in erms of he sign and significance. Under he volailiy-learning hypohesis, new informaion abou fuure volailiy causes an order imbalance in opion conracs and hen signals mare maers o change implied volailiy. I indicaes ha volailiy-moivaed ne buying pressure of a call/pu opion, NBPV, has a posiive impac on changes in he opion s own implied volailiy, no maer i, wha moneyness caegory he opion is in. Conrarily, under he opinion of he direcion-learning hypohesis, in ha he opion order imbalance induced by direcion shocs changes he mare expecaions abou he fuure price movemens of he underlying asse and opion prices correspondingly, he impac of direcion-moivaed ne buying pressure of a call/pu opion, NBPD, on changes in he opion iself implied volailiy is expeced o be i, posiive, regardless of moneyness. Consequenly, he volailiy-learning hypohesis predics he coefficien of volailiy-moivaed ne buying pressure, β 3, in he regressions of changes in implied volailiy o be significanly posiive, whereas he direcion-learning hypohesis argues ha he coefficien on direcion-moivaed ne buying pressure, β 4, should be significan and posiive. Among he coefficiens of he wo decomposed ne buying pressure, he coefficien on NBPV is only relaed o he examinaion of he volailiy-learning hypohesis and does no i, maer o he direcion-learning hypohesis a all. Similarly, he direcion-learning hypohesis canno accoun for he coefficien on NBPV any more. The properies behind he proposed i, decomposiions of ne buying pressure enable us o independenly inspec he volailiy-learning hypohesis and direcion-learning hypohesis by he esimaes of β 3 and 18

19 β 4, respecively, and hus allows he possibiliy of boh he wo learning hypohesis being correc, which is very differen from he joinly es mehodology adoped in he lieraure. The coefficien of lagged change in implied volailiy, β 5, plays an assisan role in differeniaing he wo learning hypoheses as well. Specifically, he volailiy-learning hypohesis predics he coefficien of lagged change in implied volailiy being no differen from zero, because shifs in mare expecaions abou volailiy drives permanen changes in opions implied volailiy and lead hese unpredicable volailiy shocs as well as he change in implied volailiy o be serially uncorrelaed. Conrarily, under he direcion-learning hypohesis he lagged change in implied volailiy is expeced o be negaively correlaed wih he curren one. Recall ha direcion informed raders prefer o exploi heir privae informaion abou he fuure price movemens in he opion mare before in he soc mare, resuling in opion prices leading heir underlying asse price. The opion s implied volailiy changes a once when a direcion shoc his he mare and hen reversely reurns o is previous level as he price of he opion s underlying asse reflecs he new informaion, provided ha mare volailiy does no change. To briefly summarize, he regression coefficien of he lagged change in implied volailiy is expeced o be insignifican under he volailiy-learning hypohesis, whereas i is prediced o be significanly negaive under he direcion-learning hypohesis. 5 Empirical analysis This secion displays empirical resuls in erms of he relaionship beween decomposed ne buying pressure and changes in opion s implied volailiy and provides evidences for he wo learning hypoheses in he TAIEX opion mare. Table 4 exhibis he regression resuls 19

20 for changes in implied volailiy of ATM opions across various sample periods, while he resuls for OTM opions are displayed in Table 5. As expeced, he coefficiens on TAIEX reurns are negaive and saisically significan a he 1% level no maer wha opion caegory and sample period he model is specified, srongly suggesing he leverage effec of Blac (1976). Being as he second conrolled variable, he TAIEX rading volume is found o have posiive impacs on changes in implied volailiy regardless of moneyness, confirming he informaion flow effec proposed in Andersen (1996) ha rading volume is driven by he idenical facors generaing reurn volailiy. Ineresingly, he informaion flow effec is no consisenly found across he wo subperiods. The coefficiens of NBPV and NBPD play imporan roles in exploring he wo i, i, ypes informed rading effecs in he TAIEX opion mare. Tables 4 and 5 show ha he coefficien on NBPD is posiive and saisically significan a 1% significance level across i, all cases, including cases for various opion ypes, opion moneyness, and sample periods, apparenly supporing he direcion-learning hypohesis. On he conrary, only he change in implied volailiy of OTM pu opions is consisen wih he volailiy-learning hypohesis, as OTM he coefficien on NBPV is posiive and saisically significan a 1% significance level P, no maer wheher he 2011 U.S. deb-ceiling crisis happens. Recognized ha he OTM pu opion is he mos popular ool for hedging he downside ris of he underlying asse, i may be he reason why rades on OTM pu opions carry more informaion regarding volailiy ATM shocs han hose of oher opions. I is also observed ha he coefficien on NBPV is C, negaive, indicaing ha changes in implied volailiy of ATM call opions, which is rarely adoped in volailiy informed rading in pracices, canno be accouned for by he volailiy-learning hypohesis any more. Combined wih hese evidences, boh he 20

21 volailiy-learning hypohesis and direcion-learning hypohesis are able o accoun for he change in implied volailiy of OTM pu opions. 6 Conclusions One poenial concern behind oally ne buying pressure is pars of he demand from direcion rading may offse he demand of he volailiy rading, especially when he direcion shoc and volailiy shoc arrive simulaneously. To avoid his cancel-ou effec, his sudy develops a mehod o decompose ne buying pressure of opions ino he volailiy-moivaed componen and direcion-moivaed componen, and re-invesigaes he wo informed rading effecs in he TAIEX opion mare. The empirical evidences show ha implied volailiy of OTM pu opions is driven by boh of he wo decomposed ne buying pressure, indicaing ha raders of OTM pu opions are boh direcion raders and volailiy raders. We noe ha his empirical finding is very differen from ha in he lieraure, where he wo learning effecs are resrics o be muually exclusive under he adopion of enire ne buying pressure. 21

22 References 1. Anderson, T.G., L. Benzoni, and J. Lund, 2002, An empirical invesigaion of coninuous-ime equiy reurn models, Journal of Finance, 57, Bashi, G., C. Cao, and Z. Chen, 1997, Empirical performance of alernaive opion pricing models, Journal of Finance, 52, Blac, F., and M. Scholes, 1973, The pricing of opions and corporae liabiliies, Journal of Poliical Economy, 81, Bollen, N. P. B., and R.E.Whaley, 2004, Does ne buying pressure affec he shape of implied volailiy funcion?, Journal of Finance, 59, Chan, K.C., L.T.W. Cheng, and P.P. Lung, 2004, Ne buying pressure, volailiy smile, and abnormal profi of Hang Seng Index Opions, Journal of Fuures Mares, 24, Chernov, M., A.R. Gallan, E. Ghysels, and G. Tauchen, 2003, Alernaive models of soc price dynamics, Journal of Economerics, 116, Cox, J.C., and S.A. Ross, 1976, The valuaion of opions for alernaive sochasic processes, Journal of Financial Economics, 3, Derman, E., and I. Kani, 1998, Sochasic implied rees: arbirage pricing wih sochasic erm and srie srucure of volailiy, Inernaional Journal of Theoreical and Applied Finance, 1, Ederingon, L., and W. Guan., 2002, Why are hose opions smiling?, Journal of Derivaives, 10, Emanuel, D.C., and J.D. MacBeh, 1982, Furher resuls on he consan elasiciy of variance call opion pricing model, Journal of Financial and Quaniaive Analysis, 4,

23 11. Garleanu, N., L.H. Pedersen, and A.M. Poeshman, 2009, Demand-Based Opion Pricing, Review of Financial Sudies, 22, Sephen S., 1989, Opion arbirage in imperfec mares, Journal of Finance, 44, Fleming, J., 1998, The qualiy of mare volailiy forecass implied by S&P 100 index opions prices, Journal of Empirical Finance, Fleming, J., 1999, The economic significance of forecas bias of S&P 100 index opion implied volailiy, Advances in Fuures and Opion Research, 10, George, J.J., and Y.S. Tian, 2005, The model-free implied volailiy and is informaion conen, Review of Financial Sudies, 18, Green, T.C., and S. Figlewsi. 1999, Mare ris and model ris for a financial insiuion wriing opions, Journal of Finance, 54, Kang, J., and H. J. Par, 2008, The Informaion conen of ne buying pressure: evidence from ospi 200 index opion mare, Journal of Financial Mare, 11, Liu, J, and F. A. Longsaff, 2004, Losing money on arbirages: Opimal dynamic porfolio choice in mares wih arbirage opporuniies, Review of Financial Sudies, 17, Shiu, Y. M., G. G. Pan, S. H. Lin, and T. C. Wu, 2010, Impac of ne buying pressure on changes in implied volailiy: before and afer he onse of he subprime crisis, Journal of Derivaives, 17,

24 Table 1. Moneyness caegory definiions Caegory for calls Dela range Caegory for pus Dela range DITM 0.875< Δ C DOTM 0.125< Δ P ITM 0.625< Δ C OTM 0.375< Δ P ATM 0.375< Δ C ATM 0.625< Δ P OTM 0.125< Δ C ITM 0.875< Δ P DOTM < Δ C DITM < Δ P Noes: (1). This paper measures moneyness of an opion by using opion s dela, since i can be regarded as he possibiliy of opions being in he money a mauriy. (2). Transacions for call opions wih dela below 0.02 and above 0.98 are excluded. Similarly, ransacions for pu opions wih dela below and above are excluded as well. (3). The moneyness caegory definiion adoped in his research is he same as ha used in Bollen and Whaley (2004) and Kang and Par (2008).

25 Dela value caegory No. of conracs Whole period January 2011-December 2011 Table 2. The number of TAIEX opions raded in 2011 Subperiod I January 2011-July 2011 Subperiod II Augus 2011-December 2011 Call Pu Call Pu Call Pu Prop. of oal Panel A. Number of conracs raded No. of conracs Prop. of oal No. of conracs Prop. of oal No. of conracs Prop. of oal No. of conracs Prop. of oal No. of conracs Prop. of oal DITM 214, % 290, % 162, % 167, % 4,045, % 122, % ITM 1,974, % 1,732, % 1,482, % 1,115, % 8,530, % 616, % ATM 9,290, % 6,644, % 6,025, % 3,743, % 3,265, % 2,900, % OTM 20,584, % 13,450, % 12,053, % 7,808, % 492, % 5,642, % DOTM 9,405, % 11,278, % 5,360, % 6,857, % 51, % 4,420, % Toals 41,469, % 33,396, % 25,084, % 19,693, % 16,385, % 13,702, % Panel B. ne purchases of conracs DITM -5,849-23,475-7,370-7,931 1,521-15,544 ITM -1,090-11,861-1, ,293 ATM -280,033-64, ,892-24, ,141-39,555 OTM -172, ,142 57, , , ,687 DOTM 1,603-8, ,155 96, , ,721 Toals -458, ,944-5, , , ,800 Noe: (1). The whole sample period ha ranges from January 2011 o December 2011 is divided ino wo subperiods. Subperiod I is from January 2011 o July 2011, whereas Subperiod II sars from Augus 2011 and ends in December (2). The ne purchases of conracs displayed in Panel B are calculaed as he number of buyer-moivaed conracs minus he number of seller-moivaed conracs.

26 Dela value caegory Table 3. Ne buying pressure Whole period Subperiod I Subperiod II Call Pu Call Pu Call Pu DITM -5,467-21,783-6,839-7,469 1,372-14,314 ITM -2,032-10,941-2,799-1, ,511 ATM -127,213-27,299-82,959-7,981-44,254-19,318 OTM -58,849-90,409-5,400-48,779-53,449-41,630 DOTM 2,346-5,451 11,053 1,650-8,708-7,101 Toals -191, ,883-86,944-64, ,271-91,874 Noe: (1). The whole sample period ha ranges from January 2011 o December 2011 is divided ino wo subperiods. Subperiod I is from January 2011 o July 2011, whereas Subperiod II sars from Augus 2011 and ends in December (2). The ne buying pressure is defined as he number of conracs raded above he prevailing bid/as midpoin less he number of conracs raded below he prevailing bid/as midpoin imes he absolue value of he opion's dela.

27 Table 4. Regression resuls for he impac of he ne buying pressure on he changes of ATM implied volailiy Parameer esimaes ATM σ i, β 0 β 1 β 2 β 3 β 4 β 5 ( 10 4 ) ( 10 3 ) ( 10 3 ) Panel A. Whole Period: January 2011-December 2011 Call ** *** *** *** 1.44 *** *** Pu *** *** ** *** *** Panel B. Subperiod I: January 2011-July 2011 Call *** *** *** Pu *** ** *** *** *** Panel C. Subperiod II: Augus 2011-December 2011 Call *** *** *** ** 1.82 *** *** Pu *** *** *** Noes: The regression model is displayed as follows: σ ATM i, = β 0 + β 1 RS + β 2 VS + β 3 NBPV ATM i, + β 4 NBPD ATM i, + β 5 σ ATM i, 1 + ε, i {C, P}, (19) where σ ATM i,, i {C, P}, denoes he change in he averaged implied volailiy of ATM call/pu opions, RS indicaes he index reurns over he ime inerval, and VS is he rading volume of he TAIEX index expressed in billions of New Taiwan Dollars for he ime inerval. All variables are calculaed a a five-minue ime inerval. Moreover, for ATM opions, he volailiy-moivaed ne buying pressure, NBPV i, ATM, and he direcion-moivaed ne buying pressure, NBPD ATM i,, are measured by: NBPV ATM i, = NBP ATM C, + NBP ATM P, 2, where i {C, P}, and NBPD C, ATM = NBP ATM C, NBP ATM P, 2 ; NBPD ATM P, = NBP ATM P, NBP ATM C, 2. Finally, one, wo and hree aseriss indicae he 10%, 5%, and 1% significan levels, respecively.

28 Table 5. Regression resuls for he impac of he ne buying pressure on he changes of OTM implied volailiy Parameer esimaes OTM σ i, β 0 β 1 β 2 β 3 β 4 β 5 ( 10 4 ) ( 10 3 ) ( 10 3 ) Panel A. Whole Period: January 2011-December 2011 Call *** *** *** *** *** Pu *** *** ** *** *** *** Panel B. Subperiod I: January 2011-July 2011 Call *** *** *** Pu *** *** *** *** 1.05 *** *** Panel C. Subperiod II: Augus 2011-December 2011 Call *** *** *** *** *** Pu *** *** *** *** Noes: The regression model is displayed as follows: σ OTM i, = β 0 + β 1 RS + β 2 VS + β 3 NBPV OTM i, + β 4 NBPD OTM i, + β 5 σ OTM i, 1 + ε, i {C, P}, (20) where σ OTM i,, i {C, P}, denoes he change in he average implied volailiy for OTM call/pu opions, RS indicaes he index reurns over he ime inerval, and VS is he rading volume of he TAIEX index expressed in billions of New Taiwan Dollars for he ime inerval. All variables are calculaed a a five-minue ime inerval. Moreover, for OTM opions, he volailiy-moivaed ne buying pressure, NBPV i, OTM, and he direcion-moivaed ne buying pressure, NBPD OTM i,, are measured by: NBPV OTM i, = NBP OTM C, + NBP OTM P, 2, where i {C, P}, and NBPD C, OTM = NBP OTM C, NBP OTM P, 2 ; NBPD OTM P, = NBP OTM P, NBP OTM C, 2. Finally, one, wo and hree aseriss indicae he 10%, 5%, and 1% significan levels, respecively.

29 Index level Implied volailiy Index level /1/3 2011/2/3 2011/3/3 2011/4/3 2011/5/3 2011/6/3 2011/7/3 2011/8/3 2011/9/3 2011/10/3 2011/11/3 2011/12/ Implied volailiy of TAIEX opions Time Figure 1. Implied volailiy of TAIEX opions and TAIEX closing prices in 2011

30 Whole period Subperiod II Subperiod I Implied volailiy Moneyness Caegory Figure 2. Esimaed implied volailiy funcions of TAIEX opions in 2011 As in Bollen and Whaley (2004), caegory 1 comprises DITM calls and DOTM pus, caegory 2 conains ITM calls and OTM pus, caegory 3 are ATM calls and ATM pus, caegory 4 includes OTM calls and ITM pus, and caegory 5 consiss of DOTM calls and DITM pus.