The Forecasing Power of he Volailiy Index in Emerging Markes: Evidence from he Taiwan Sock Marke Ming Jing Yang Deparmen and Graduae Insiue of Finance, Feng Chia Universiy 100 Wenhwa Road, Seawen, Taichung 407, Taiwan Tel: 886-4-2451-7250 ex.4158 E-mail: mjyang@fcu.edu.w Meng-Yi Liu (Corresponding auhor) College of Business, Feng Chia Universiy, 100 Wenhwa Road, Seawen, Taichung 407, Taiwan Tel: 886-4-2451-7250 ex.4459 E-mail: mun1212.liu@gmail.com Received: Ocober 11, 2011 Acceped: Ocober 24, 2011 Published: February 1, 2012 doi:10.5539/ijef.v4n2p217 URL: hp://dx.doi.org/10.5539/ijef.v4n2p217 Absrac This paper explores he predicive power of he volailiy index (VIX) in emerging markes from December 2006 o March 2010. The resuls of he sudy show ha he models including boh he volailiy indicaor and he opion marke informaion have a sronger predicive power. The predicive power of he models is improved by 88% in explaining he fuure volailiy of sock markes, much beer han ha of oher models merely considering he volailiy indicaor. Wih respec o he rading informaion from differen ypes of invesors in opion markes, he rading informaion from he foreign insiuional invesors in opion markes demonsraes a significanly posiive relaionship wih he sock marke volailiy. In addiion, he resuls of his paper also reveal ha he volailiy index (TVIX) of Taiwan sock index opions is a srong indicaor of fuure sock marke volailiy. The TVIX ouperforms he hisorical volailiy and he GARCH volailiy forecas in assessing he aciviies of Taiwan s sock marke. Keywords: VIX, Invesor fear gauge, Implied volailiy, Volailiy forecasing, Emerging markes 1. Inroducion The volailiy of financial markes usually demonsraes a coninuous and clusering characer (Poon and Granger, 2005) and has araced widespread aenion. The majoriy of researchers adop he hisorical volailiy, implied volailiy, and ime series volailiy models o conduc differen ypes of volailiy predicion research. However, mos of hem fail o reach a consensus due o he fac ha he marke volailiy has always been unpredicable. Thus, he opimal soluion can be found if he model can achieve he leas predicion error. In 1993, he Chicago Board Opions Exchange (CBOE) launched a volailiy index (VIX) based on he calculaions of he S&P 100 sock index opions. I provides more comprehensive informaion and he rading guidance o invesors by means of observing he changes in he fuure volailiy of he sock marke. The volailiy index has become he leading indicaor for measuring and predicing he performance of sock markes in he U.S. since hen. In 2003, he CBOE adjused is volailiy index by adoping he S&P 500 index opions as he core crieria o provide raders and hedgers wih more accurae figures by broadly analyzing he pu and call opion conracs of he S&P 500 index. Afer he CBOE launched a new version of he volailiy index, i renamed he code of he old version of he volailiy index from 1993 as VXO and reained he VIX for he new version, in order o make a difference. The new mehod is more pracical han he former mehod in he real life scenarios. The VIX uses he curren prices of he S&P 500 index opions o reflec invesors expecaions regarding he sock marke volailiy over he nex 30 days (Whaley, 2009). A higher VIX indicaes ha marke raders are expecing a higher volailiy in he sock index, while a lower VIX suggess ha only a moderae flucuaion is expeced in he sock index. As he VIX is mean o reflec invesors expecaions, i has also been referred o as he invesor fear gauge. As he volailiy index has araced growing aenion in recen years, he CBOE has also launched many differen volailiy indices based on oher underlying arges, such as he NASDAQ-100 Volailiy Index (VXN), he DJIA Volailiy Index (VXD), he Russell 2000 Volailiy Index (RVX), and he S&P 500 3-Monh Volailiy Index (VXV), ec. Neverheless, he VIX sill remains o be he mos widely-used and discussed informaion indicaor in securiy Published by Canadian Cener of Science and Educaion 217
markes. For example, in he 1998 LTCM and he 2002 WorldCom bankrupcy, he VIX rapidly increased o a level over 40. In he 2007 worldwide financial sunami caused by he sub-prime morgage crisis, he VIX even exceeded 80 when he Lehman Brohers filed for bankrupcy. Hence, he research conduced by Aboura and Villa (2003), Majmudar and Banerjee (2004), Corrado and Truong (2007), and Whaley (2009) indicaes ha he VIX serves as a powerful predicive indicaor of he developed derivaive markes. Meanwhile, exploring he predicive power and accuracy of differen models and volailiy indicaors regarding he fuure sock marke volailiy has become one of he major opics in he field of risk managemen of financial markes in recen years. Poon and Granger (2003, 2005) reviewed 93 papers addressing he predicive performances of he volailiy indicaors over he las 20 years and poined ou ha mos papers sugges ha he implied volailiy generaes he greaes predicive power, followed by he volailiy measured by he GARCH family models and he hisorical volailiy. Transacions of index opions in Asia have grown rapidly in recen years. The rading volume of index opions increased from 40 million conracs in 1998 o 3,057 million conracs in 2008, a 54% compound annual growh rae exceeding hose in America and Europe. Taiwan Fuures Exchange (TAIFEX) launched he Taiwan Sock Exchange capializaion weighed sock index (TAIEX) opions in 2001, wih he rading volume increasing very quickly and ranked he sixh place in he world financial markes in 2008, behind only Korea and India among he Asian counries (Noe 1). Therefore, in his sudy, we inend o compare he predicive performance of he hisorical volailiy, he implied volailiy, he volailiy index (TVIX) of Taiwan sock index opions, and he GARCH volailiy forecass, regarding he fuure sock price movemens in Taiwan. Besides, he valuable deailed rading informaion wih respec o TAIEX opions for differen ypes of invesors recorded in TAIFEX daabase is also included, such as he rading daes, invesor codes, rading posiions, pu or call opions, rading volumes, opening or closing posiions, ec. Addiionally, he pu-call raio inroduced by Pan and Poeshman (2006) is also employed o analyze he impac of opion marke informaion on he volailiy of an emerging sock marke, namely he Taiwan sock marke. According o he comparison of he empirical resuls wih he models merely considering he volailiy indicaor, he predicive performance of he models ha incorporae boh he volailiy indicaor and opion marke informaion is improved subsanially. (The adjused R 2 of he models is increased by 88%). Among all of he volailiy indicaors, he average implied volailiy of pu and call opions has he greaes predicive power, followed by he implied volailiy of he pu opions and he TVIX. The empirical resuls of his paper show ha he predicive power of he TVIX remains fairly close o ha of he implied volailiy, irrespecive of he models adoped. Is performance exceeds ha of he implied volailiy of he call opions in some scenarios. The resuls are consisen wih he findings of Majmudar and Banerjee (2004), Corrado and Truong (2007), and Whaley (2009). Therefore, he resuls of our sudy show ha he VIX is a powerful predicive indicaor for he sock marke volailiy in he emerging markes, as documened in Taiwan. Invesors can hus make use of he volailiy index o furher undersand he sock marke movemen and adjus heir inernaional porfolios accordingly. In addiion, he informaion variables from opion marke in his research are divided ino four componens, which are consruced by he Pu-Call raios from four differen ypes of invesors rading in opion marke, including he foreign insiuional invesors, domesic insiuional invesors, individual invesors, and marke makers. The resuls of he sudy also reveal ha he informaion flows from foreign insiuional invesors have significan predicive power in erms of fuure volailiy of TAIEX spo index, as documened in Chang e al. (2010). 2. Background and Relaed Work In he 1987 U.S. sock marke crash, he New York Sock Exchange (NYSE) launched he Circui Breakers mechanism, which can manually suspend sock rading if sock prices flucuae abnormally, in order o sabilize sock markes and proec invesors. This mechanism has been used o reduce abnormal flucuaions in he sock marke, sabilize marke orders, and reassure invesors since hen. In 1993, he CBOE launched a volailiy index o observe marke volailiy by using he prices of he mos heavily-raded S&P 100 index opions (OEX) (Noe 2). In 2003, he CBOE adjused is original volailiy index and swiched he measuremen arge o he S&P 500 index opions in aemps o deliver he informaion for he sock marke volailiy over he nex 30 rading days. Whaley (2009) poined ou ha here are wo imporan implicaions of promoing he VIX. Firs, he VIX can provide a crierion for measuring he shor-erm marke volailiy. Second, is relaed derivaives can also offer invesors more choices, for insance, in invesmen porfolio managemen and risk managemen. Therefore, he CBOE launched fuures and opions based on he VIX in May 2004 and February 2006, respecively. The difference beween he VXO and he VIX has been invesigaed exensively by academics, researchers, and invesors. Mark (2003) indicaed ha he VIX is generally 3.8% lower han he VXO. The VIX and VXO have been shown o have similar analyical capabiliies in predicing he fuure marke volailiy. Mayhew and Sivers (2003) sudied he op 50 mos heavily-raded opions of he CBOE and demonsraed ha he VXO conains more 218 ISSN 1916-971X E-ISSN 1916-9728
informaion. However, no consensus was reached wih respec o he lighly-raded opions. Whaley (2000) analyzed he S&P 100 index and he VXO and suggesed ha he relaion beween sock marke reurns and VXO variaion is asymmeric. Aboura and Villa (2003) analyzed and compared he volailiy indices of he U.S. (VXO), France (VXI), and Germany (VDAX) and poined ou ha he VXO, he VXI, and he VDAX are useful ools o predic he fuure volailiy. Whaley (2009) sudied he connecion beween he VIX and he sock markes and indicaed ha he movemen rends in he VIX exhibis a raher powerful explanaion for he change in he performance of S&P 500 index porfolio. Some oher sudies focused on he informaion conen of VIX derivaives. Becke e al. (2009) and Chung e al. (2011) suggesed ha VIX opions essenially possess he incremenal informaion abou he fuure dynamics of he S&P 500 index. The resuls of heir sudies show ha he predicions of reurns, volailiy, and densiy in he S&P 500 index are improved significanly by using he informaion embedded in he VIX opions for various measures of realized volailiy. Chen e al. (2011) demonsraed ha adding he VIX-relaed asses can enlarge he invesor s invesmen opporuniy se. Daigler and Rossi (2006) and Szado (2009) repored ha he poenial diversificaion benefis of adding a long VIX and VIX fuures o he base porfolio are significan. Alhough he VIX derivaives have achieved widespread recogniion, i is sill challenging on he pricing of VIX opions and fuures. Several sudies have explored he pricing of VIX opions and fuures under various approaches (see Zhang and Zhu, 2006; Seep, 2008; Lin and Chang, 2009; Zhang e al., 2010; Wang and Daigler, 2011). In conras o he sudies of he heoreical models, Konsaninidi e al. (2008) and Konsaninidi and Skiadopoulos (2011) invesigaed he informaion efficiency of he VIX fuures. Shu and Zhang (2011) suggesed ha alhough he VIX fuures have some price-discovery funcion, overall he VIX fuures marke is sill considered informaionally efficien. Addiionally, he predicion of marke volailiy has been a research focus in he fields of invesmen decisions and porfolio managemen. Day and Lewis (1992) and Canina and Figlewski (1993) conduced sudies on S&P 100 index opions and individual sock opions and repored ha he hisorical volailiy is beer han he implied volailiy in predicing he fuure volailiy of sock markes. However, he resuls of heir sudies may be aribued o he overlapping samples seleced in he research and he mauriy mismaches of he samples (Yu, Lui, and Wang, 2010). Chrisensen and Prabhala (1998) uilized he non-overlapping samples o resudy S&P 100 index opions and documened ha he implied volailiy is superior o he hisorical volailiy in predicing he fuure marke volailiy. Szakmary e al. (2003) explored 35 major fuures and opions markes in he U.S., and heir findings corroboraed he fac ha he implied volailiy predics he fuure marke volailiy beer han he hisorical volailiy. Similar resuls were also found by Corrado and Miller (2005) and Carr and Wu (2006), who showed ha he VIX ouperforms he hisorical volailiy and he volailiy esimaed from GARCH models in forecasing he S&P 500 index volailiy. Yu e al. (2010) sudied he exchanges and OTC markes in Hong Kong and Japan and concluded ha he implied volailiy is a beer predicor of he fuure volailiy in he exchanges and OTC markes han he GARCH volailiy forecass and he hisorical volailiy. Poon and Granger (2003, 2005) reviewed he volailiy predicion research papers of he pas 20 years. In hese papers, he implied volailiy achieves he bes predicive power, followed by he volailiy from GARCH models, he hisorical volailiy, and he volailiy from sochasic models. The research discussed above mainly focused on he U.S. markes. Afer he CBOE launched he new volailiy index in 2003, he findings of mos empirical sudies indicae ha he VIX is an excellen predicor for he fuure volailiy of well-developed securiy markes. Nowadays he inernaional financial markes have become closely conneced, and he empirical sudies from oher securiy markes ouside he U.S. should also be performed, especially hose from he emerging markes. For insance, Taiwan also consruced he volailiy index of Taiwan sock index opions in 2006. Thus, his sudy aims o fill a gap in he research by exploring he predicive power of he volailiy index in one of he emerging markes, Taiwan. The calculaion of he volailiy index is performed independenly of he derivaive pricing models and enails a kind of forward-looking concep, which is differen from he implied volailiy derived from he opion pricing model. Based on he research design of Corrado and Miller (2005) and Yu e al. (2010), he volailiy index is firs included in he analysis model of he sudy. Then, he informaion ses of opions are furher included, such as he rading volume for index opions and for differen ypes of invesors, o examine he explanaory power of he volailiy index in predicing he fuure volailiy in he emerging sock markes. Finally, he empirical resuls of he sudy are also compared wih hose measured by he hisorical volailiy, he implied volailiy, and he volailiy esimaed from GARCH models. The findings of he sudy will provide invesors wih more comprehensive informaion abou he fuure marke volailiy and hus improve heir invesmen decisions and porfolio performance. 3. Mehodology and Research Models 3.1 Daa Source The daa sources of our empirical sudy are saed as follows. (1) The daily daa of he implied volailiy, rading Published by Canadian Cener of Science and Educaion 219
volume, and open ineres of Taiwan sock index opions are colleced from he Taiwan Economic Journal daabase. (2) The valuable deailed ransacion daa of Taiwan sock index opions for differen ypes of invesors are colleced from TAIFEX daabase, including he rading daes, invesor codes, rading posiions, pu or call opions, rading volumes, opening or closing posiions, ec. The volailiy index (TVIX) of Taiwan sock index opions and he rading informaion for he differen ypes of invesors in opion markes are also provided by TAIFEX, including he foreign insiuional invesors, domesic insiuional invesors, individual invesors, and marke makers. This sudy analyzes he ime period beween December 1, 2006 and March 31, 2010, maching he period in which he TAIFEX aggressively promoed he volailiy index. 3.2 The Research Models This sudy follows he mehods of Alizadeh e al. (2002), Szakmary e al. (2003), Covrig and Low (2003), Chang e al. (2010), and Yu e al. (2010) in measuring he relaed volailiies and building he research models. The research mehods of Ni e al. (2008) and Chang e al. (2010) are employed o measure he daily realized volailiy of Taiwan sock marke. As he volailiy index and implied volailiy are boh annualized figures, his sudy also adops he mehods of Claessen and Minik (2002) and Yu e al. (2010) o annualize he volailiy measures by using 250 rading days, so as o reconcile he daa periods. The formulas for esimaing he realized volailiy and he hisorical volailiy are lised below: H L 250 (1) C H i L i HV 250 (2) C i where and HV are he realized volailiy (annualized) and he hisorical volailiy (annualized) of he TAIEX on day, respecively. H and L are he highes and he lowes prices of daily TAIEX on day, respecively. C is he closing price of daily TAIEX on day, and i is he lag lengh (i = 1, 5, 10, 20). In order o invesigae wheher he volailiy index is an unbiased esimaor of he fuure marke volailiy and wheher he volailiy index is beer in predicing he fuure marke volailiy han he implied volailiy, he hisorical volailiy, and he GARCH forecas volailiy, he research models are furher buil up as follows: o o o 1 HV i (3) 2 IV i (4) 3 TVIX i (5) o where TVIX denoes he volailiy index derived from he TAIEX opions on day. IV is he implied volailiy on day. GFV is he volailiy forecas by he GARCH model on day. The equaions of Black-Scholes are used o inversely derive he annual volailiy implied from he marke prices of opions. The implied volailiy represens invesors expecaions of he fuure volailiy of sock reurns and helps invesors deermine wheher he opion prices are reasonable. The implied volailiies of pu and call opions may differ because of he differences in moneyness beween he call and pu opions. To miigae he problems in measuring he implied volailiy, his research adops hree differen measures of he implied volailiy in our analysis, including he implied volailiy of he (neares) a-he-money call opion (IV_C), pu opion (IV_P), and he averages of boh (IV_A) wih he shores mauriy (of a leas five rading days) (Noe 3). As he calculaion procedures are quie complicaed, his sudy uses he Newon-Raphson approximaion mehod o measure he implied volailiy. To avoid he observaion errors generaed by he implied volailiy when i is an independen variable ha may affec he resuls of regression, his sudy adops he unransformed and he log-ransformed daa of he volailiy measures, as in Corrado and Miller (2005). 4 GFV i (6) This sudy is designed primarily o es he predicive power of he volailiy index in erms of he fuure marke volailiy in one of he emerging markes. The volailiy index, consruced according o he new version of he CBOE VIX compuaion formulas in 2003, is based on a series of differen exercise prices of he TAIEX opions. Such a volailiy index is no derived from any specific opion pricing model, and is calculaion is also irrelevan o any oher opion pricing models. Insead, i is derived from he weighed average of he pu and call opion premiums. In order o reconcile he volailiy measures across differen models, he volailiy index (TVIX) used in his sudy is calculaed as follows (Noe 4). 220 ISSN 1916-971X E-ISSN 1916-9728
2 2 K i RT 1 F 2 e Q( K i ) [ 1] 2 (7) T K T K i i TVIX (8) where T refers o he ime o expiraion. F is he forward index level derived from he index opion prices. K i is he srike price of i h ou-of-he-money opion. K i denoes he inerval beween wo srike prices, measured by half he difference beween he srike prices on eiher side of K i. K for he lowes srike price is simply he difference beween he lowes srike price and he nex higher srike price. Likewise, K for he highes srike price is he difference beween he highes srike price and he nex lower srike price. K 0 is he firs srike price below he forward index level F. R is he risk-free ineres rae o expiraion. Q(K i ) is he midpoin of he bid-ask spread for each opion wih srike price K i. The TVIX measures he 30-day expeced volailiy of he TAIEX. I uses he pu and call opions wih he wo neares expiraion erms (near-erm and nex-erm). In order o minimize pricing anomalies ha migh occur close o expiraion, he near-erm opions mus have a mauriy in excess of one week. When he near-erm opions have less han one week unil expiraion, he TVIX rolls o he second and hird TAIEX opions conrac monhs. T is calculaed in minues raher han days in order o assure he precision. The ime o expiraion is calculaed by he following formula: T M M M Minues in a year Curren day Selemen day Oher days / where M Curren day, M Selemen day and M Oher days are he minues remaining unil midnigh of he curren day, he minues from midnigh unil 8:30 a.m. on he selemen day of TAIEX opions, and he oal minues in he days beween he curren day and he selemen day, respecively. Furhermore, Engle (1993) claimed ha he condiional variance in he GARCH model is more effecive in predicing he volailiy of sock reurns han he hisorical volaily. Based on he mehods proposed by Brailsford and Faff (1996), Covrig and Low (2003), and Yu e al. (2010), his sudy also uses he volailiy esimaed from he GARCH model o forecas he fuure volailiy of sock markes. The condiional mean and condiional variance equaions of sock reurns are defined below. h R 0 0 1R 1 (9) 2 0 1 1 2h 1 (10) where R, h, and are he daily reurn, he condiional variance of reurns, and he residual of reurns on he weighed average sock index on day, respecively. According o Engle and Bollerslev (1986) and Yu e al. (2010), a rolling-over mehod is adoped o obain he volailiy esimaed from he GARCH model in equaion (11). h ˆ 1 is he volailiy in period (+1), which is derived from he parameer esimaes of β 1 and β 2 for -250~ days. Similarly, h ˆ is he volailiy in period (+2) derived from he parameer esimaes of β 2 1 and β 2 for -249~+1 days. In order o reconcile he comparaive bases, he variance ĥ esimaed by he GARCH model is also adjused and annualized according o equaion (12). We incorporae he resuls of he esimaed GFV ino equaion (6) o compare is predicive power wih he volailiy index, hisorical volailiy, and implied volailiy. hˆ i 2 ˆ ˆ ˆ j ˆ ˆ i 1 ˆ i 0 ( 1 2 ) ( 1 2 ) h 1 j 0 (11) GFV ˆ h 250 (12) Differen from he index spo markes, he index opion markes are highly-leveraged securiy markes. Afer invesors pay he opion premium, hey are eniled o purchase or sell a cerain amoun of he underlying asses from or o he sellers of conracs based on he exercise prices sipulaed on he opion conracs. If invesors expec fuure sock prices o be on he rising rend, hey would end o buy call opions or sell pu opions. On he conrary, if hey predic fuure sock prices o be on he downward rend, hey would end o buy pu opions or sell call opions in order o make profis. Jayaraman e al. (2001), Kawaller e al. (2001), Pand and Poeshman (2006), and Fung (2007) found ha he rading volume and open ineres of opion markes possess he explanaory power regarding he fuure volailiy of sock prices. The rading volume and open ineres of opion markes may reflec invesors expecaions of fuure movemen in sock markes. Thus, he paper furher incorporaes he marke informaion from he opion ransacions, including he rading volume and open ineres of opion markes, ino our models for analysis. The realized volailiies of he pas five days ( -1 ~ -5 ) are also included as he conrol variables (Noe 5). The model is defined below. Published by Canadian Cener of Science and Educaion 221
b o b 1 b Volailiy 6 1 b i 2 2 b VOL 7 i b 3 b OI 8 3 i where Volailiy -i in equaion (13) represens IV_A -i, IV_C -i, IV_P -i, TVIX -i, or GFV -i on day -i. VOL -i sands for he rading volume of opions on day -i, and OI -i represens he open ineres of opions on day -i. In addiion, our models furher analyze he valuable daase provided by he TAIFEX, which classifies he relaed informaion of opion ransacions (such as he rading daes, rading ime, invesor IDs, ypes of opions, selemen daes, srike prices, number of conracs, and opening/closing posiions) by differen ypes of invesors (such as he foreign insiuional invesors, domesic insiuional invesors, individual invesors, and marke makers). The rading informaion from differen ypes of invesors is furher included o analyze he predicive power of each model for fuure sock marke movemen. According o he definiions inroduced by Pan and Poeshman (2006), his sudy adops he informaion variables of he pu-call raios for differen ypes of invesors. The pu-call raio is measured as follows: Pu P b 4 4 b 5 5 (13) Call raio (14) P C P and C are he number of pu and call opion conracs purchased by differen ypes of invesors o open new posiions on day. If an invesor is informed of negaive privae informaion on an underling sock and acs on his informaion by building new long pu opion posiions, he pu-call raio would increase. On he oher hand, building new long call opion posiions based on posiive privae informaion would lower he pu-call raio. To srenghen our analysis, his sudy also uilizes he public informaion variables of he rading volumes of pu and call opions. The pu-call raio of public informaion is deermined from he volume of pu and call opions purchased by differen ypes of invesors. Thus, he models highligh he disincive influences of privae and public informaion. The informaion-based model is described as follows (Noe 6): o 1 1 2 2 3 3 4 4 5 5 (15) i 7 FI i 8 II i 9 DI i 10 MM i Volailiy 6 where FI, II, DI, and MM are he Pu-Call raios of he foreign insiuional invesors, individual invesors, domesic insiuional invesors, and marke makers on day, respecively. The predicive power of differen volailiy indicaors and differen ypes of invesors oward fuure marke volailiy can be deermined in equaion (15). 4. Empirical Resuls 4.1 Summary Saisics Table 1 summarizes he descripive saisics of he realized volailiy (), implied volailiy (IV_A, IV_C, IV_P), volailiy index (TVIX), and GARCH forecas volailiy (GFV). Among he volailiy indicaors, he IV_P has he highes mean value, followed by TVIX and IV_A, and GFV has he lowes mean value. The values of skewness are posiive for all variables, indicaing he daa disribuions are skewed o he righ. Moreover, he saisics of kurosis show ha he disribuions of all variables appear o be lepokuric excep he GFV. Table 2 repors he correlaion coefficiens for he main variables used in our empirical analysis. The correlaion marix demonsraes a posiive correlaion coefficien of abou 0.5 beween he realized volailiy and oher volailiy indicaors. Furhermore, he correlaion beween IV_A, IV_P, and TVIX is as much as 0.95, implying ha he implied volailiy and he volailiy index may have a very similar capaciy o predic he realized volailiy. Figure 1 shows he rends of he TAIEX and differen volailiy indicaors. Sruck by he worldwide financial sunami of he cenury caused by he U.S. sub-prime morgage crisis, he TAIEX fell around 58%, from 9,809 o 4,089. The realized volailiy calculaed for his period reached a peak of 113.49% on Ocober 27, 2008. The TVIX reached 60.41%, which is he highes level of TVIX during he research period. I indicaes ha invesors were panicky. Therefore, he selling pressure was amplified and refleced in he TVIX. I is imporan o noe ha he rends of he TVIX and he IV_A are very close o ha of he realized volailiy. Thus, we expec ha he predicive power of boh volailiy indicaors would be very similar. 4.2 Comparison of Differen Volailiy Indicaors The empirical resuls for he predicive power of each ype of volailiy indicaor regarding he fuure marke volailiy are shown in Table 3 (Noe 7). Panel A is for he unransformed daa and Panel B is for he log-ransformed daa. The regression coefficiens, -saisics, R 2, adjused R 2, and F Value from all models are recorded in he Table. The empirical resuls reveal ha when differen volailiy indicaors are used as a single independen variable, he regression coefficiens of he volailiy indicaors are significanly posiive a he 1% level, regardless of wheher he 222 ISSN 1916-971X E-ISSN 1916-9728
unransformed daa or he log-ransformed daa are used. The highes -saisic is 21.7287 for IV_A, followed by 20.6674 for IV_P and 20.2658 for TVIX, based on he log-ransformed daa wih he lag lengh equal o 1 (i=1). The values of he adjused R 2 are 0.3641, 0.3411 and 0.3324, respecively. In addiion, we furher include HV -i in equaions (4)~(6) o deermine wheher he model simulaneously combining he hisorical volailiy and oher ypes of volailiy indicaors could enhance he explanaory power. The empirical resuls show ha he coefficiens of volailiy indicaors in each model are all significanly posiive a he 1% level. Afer including HV -i in he regression, mos of he models show higher values of adjused R 2. The highes value of model adjused R 2 is 0.3946 (HV+IV_A), followed by 0.3828 (HV+IV_P) and 0.3731 (HV+TVIX). In general, when a single volailiy indicaor is adoped as an independen variable in he model, regardless of he lag periods (i = 1, 5, 10, or 20), IV_A generaes he bes predicaive performance, followed by IV_P, TVIX, GFV, IV_C, and HV. As documened in Chrisensen and Prabhala (1998), Szakmary e al. (2003), and Yu e al. (2010), he predicive performance of he implied volailiy is beer han ha of he hisorical volailiy. Meanwhile, he predicive power of he TVIX is very close o ha of he implied volailiy. As repored in Aboura and Villa (2003) and Whaley (2009), he volailiy index is an effecive predicive indicaor of he fuure marke volailiy. In addiion, he resuls sugges ha he explanaory power (adjused R 2 ) of all models is reduced when he number of lag periods i increases. The models wih he lag period equal o 1 (i=1) have he higher explanaory power. I implies ha he abiliy of volailiy indicaor o reflec marke informaion is beer in shorer ime periods. Regardless of wheher he sample daa are log-ransformed, he empirical resuls are idenical and he ranking of he predicive performance of volailiy indicaors is no affeced. Afer HV is incorporaed ino equaions (4)~(6), he resuls remain he same and he values of adjused R 2 in mos models slighly increase. Overall, he resuls sugges ha he volailiy indicaors adoped in his sudy have significan impacs in deermining he fuure realized volailiy. 4.3 Incorporaion of he Conrol Variables From he resuls of he above analysis, we found ha each ype of volailiy indicaor is able o reflec he marke informaion of recen periods. Thus, his paper incorporaes he realized marke volailiy of he pas 5 days ino he models as he conrol variables o observe wheher he resuls would be affeced by including he recen realized volailiy. The empirical resuls are lised in Table 4. The resuls show ha he explanaory power of he models including he conrol variables ( -1 ~ -5 ) is significanly enhanced, compared wih ha of he models wih one single volailiy indicaor. The maximum value of model adjused R 2 is 0.4020 (based on he log-ransformed daa wih he lag lengh equal o 1 (i=1)). The coefficiens of IV_A, IV_C, IV_P, TVIX, and GFV are all significanly posiive a he 1% level. When he -1 ~ -5 are added ino he regression models, he coefficiens of he -1 and -2 are all significanly posiive a he 1% level, whereas mos coefficiens of he -5 are significanly posiive a he 10% level. These resuls are in line wih he expecaion ha marke informaion from he recen periods can effecively reflec he fuure volailiy. The overall resuls of Table 4 are similar o hose previously analyzed. The model adoping IV_A as an independen variable achieves he greaes predicive performance, and he performance of TVIX is quie close o ha of IV_A, suggesing ha he implied volailiy and he volailiy index are good indicaors in predicing he fuure volailiy of sock markes. Furhermore, he resuls also sugges ha he models including -1 ~ -5 perform beer han hose wihou -1 ~ -5 in erms of predicing he fuure realized volailiy. 4.4 Inclusion of he Opion Marke Informaion Pan and Poeshman (2006) and Fung (2007) addressed ha he opion marke informaion may reflec he fuure marke volailiy. Table 5 repors he empirical resuls generaed upon he inclusion of opion marke informaion, such as he rading volume and open ineres of opion markes. The empirical resuls show ha he coefficien of each volailiy indicaor is saisically significan a he 1% level. The coefficiens of VOL in mos of he models are saisically significan a he 10% level. I proves ha he opion rading volume can indeed reflec he fuure marke volailiy. The resuls coincide wih he findings in Jayaraman e al. (2001), Kawaller e al. (2001), Pan and Poeshman (2006), and Fung (2007). As he empirical resuls of he open ineres are no he same as hose of he opion rading volume, he informaion covered in he opion rading volume may have included he informaion se covered in he open ineres. Incorporaing he opion marke informaion in he model can slighly enhance he explanaory power of he models. The maximum value of model adjused R 2 is 0.4043 (based on he log-ransformed daa wih he lag lengh equal o 1 (i=1)). Finally, among all he models, he model using he IV_A as an independen variable achieves he greaes predicive performance, followed by he models using he TVIX and IV_P. 4.5 Incorporaion of he Informaion from Differen Types of Invesors The TAIFEX launched TAIEX opions in December 24, 2001 and recorded he deailed informaion of each Published by Canadian Cener of Science and Educaion 223
ransacion. The rading volume of pu and call opions will affec he volailiy of sock markes. The valuable daase provided by he TAIFEX enables us o furher classify he ypes of opion ransacions. By adoping he approach repored in he prior sudies of Pan and Poeshman (2006) and Chang e al. (2009), we divide he invesors ino four ypes: he foreign insiuional invesors, domesic insiuional invesors, individual invesors, and marke makers. We also use he informaion variables of pu-call raios developed by Pan and Poeshman (2006) o conduc our analysis. In order o srenghen our analysis, we adop he public informaion variables and privae informaion variables in our empirical analysis. For he public informaion variables, he pu-call raios of differen ypes of invesors are measured based on he volume of long call and long pu opion conracs. For he privae informaion variables, he P and C are he number of pu and call opion conracs purchased by differen ypes of invesors o open new posiions on dae. Table 6 liss he empirical resuls of he equaion (15) for he models including he public informaion variables (in Panel A) and he privae informaion variables (in Panel B). The empirical resuls are similar beween he models including he public informaion variables and privae informaion variables. The posiive relaionship is found beween he volailiy indicaors (IV_A, IV_C, IV_P, TVIX, and GFV) and he realized volailiy (), and he coefficiens are significan. The rading informaion from differen ypes of invesors is likely o generae differen resuls. Mos coefficiens of he pu-call raios of foreign insiuional invesors (FI ) are significanly posiive a he 5% level, whereas mos coefficiens of he pu-call raios of marke makers (MM ) are negaive and significan. However, he informaion variables of individual invesors and domesic insiuional invesors are no saisically significan. The resuls indicae ha foreign insiuional invesors are able o predic he marke volailiy more precisely han he oher hree ypes of invesors. The resuls are consisen wih he findings of Chang e al. (2009), who poined ou ha foreign insiuional invesors have he significan predicive power in he Taiwan sock marke. Meanwhile, marke makers consisenly play he role of machmaking or revising quoes. When marke volailiy is high, he need for machmaking or revising quoes would end o be reduced. Therefore, he coefficiens of MM are significanly negaive wih respec o. Finally, we found ha he explanaory power of he models is significanly enhanced hrough he incorporaion of he rading informaion variables (pu-call raios) of differen ypes of invesors. The adjused R 2 values of he models adoping boh he opion informaion variables and he volailiy indicaor are enhanced by 88% (from 0.2373 o 0.4457), compared wih hose of he models adoping he single volailiy indicaor. When he privae informaion erms are included, he explanaory power (adjused R 2 ) of he models is able o reach a maximum of 0.4457. Excep for he models using IV_C and GFV as an independen variable, he adjused R 2 values of oher models all exceed 0.40, indicaing ha he models including he IV_A, IV_P, or TVIX, as well as he invesors opion rading informaion variables, can significanly enhance he explanaory power in erms of he fuure volailiy of Taiwan s sock marke. Similar o he findings previously menioned, he models incorporaing IV_A as an independen variable perform he bes, followed by he models including TVIX and IV_P, whose resuls are very close o hose of IV_A. 5. Conclusions This paper invesigaes he predicive power of differen ypes of volailiy indicaors in Taiwan s sock marke, including he hisorical volailiy, he implied volailiy, he TVIX, and he GARCH forecas volailiy. Differen models are developed o examine he explanaory power of he volailiy indicaors in predicing he sock marke volailiy. Furhermore, he deailed rading informaion compiled in he daase of he TAIFEX is used o explore he influence of he informaion from opion markes on he sock marke volailiy. Finally, our sudy compares he various models of volailiy indicaors, incorporaing he rading informaion of differen ypes of invesors from opion markes ino he models and verifying he applicabiliy of he volailiy index o he emerging markes, in an aemp o fill he gap in he research. The empirical resuls of our sudy sugges ha he models including he opion marke informaion perform beer han he models merely adoping a single volailiy indicaor. As for he predicive power of he volailiy indicaors, he implied volailiy is demonsraed o have he bes predicive power, followed by he TVIX, wih boh generaing he similar resuls. However, he performance of he hisorical volailiy and he GARCH forecas volailiy is inferior o ha of he implied volailiy and he TVIX in deermining he fuure realized volailiy. The conclusions generaed by his sudy conduced on he implied volailiy and hisorical volailiy coincide wih he findings of Chrisensen and Prabhala (1998), Szakmary e al. (2003), and Yu e al. (2010). Compared wih he implied volailiy derived from he Black-Scholes opion pricing model, he volailiy index is an indicaor independen of any opion pricing model. I is calculaed by he daily informaion released by he opion markes and does no rely on he complicaed calculaions and assumpions. Therefore, he TVIX is more accessible o invesors. The empirical resuls of our sudy indicae ha he abiliy of he TVIX o predic he fuure marke volailiy is very similar o ha of he implied volailiy of pu opions. In various ypes of models, he predicive 224 ISSN 1916-971X E-ISSN 1916-9728
power of TVIX is superior o ha of he implied volailiy of call opions. Thus, he volailiy index is an effecive predicive indicaor in he emerging markes, as documened in Taiwan s sock marke. Especially afer incorporaing he opion marke informaion ino he models, he explanaory power of our models can even exceed 40%. I proves ha he TVIX is effecive in predicing he fuure realized volailiy of Taiwan s sock marke. Finally, we furher analyze he influence of opion marke informaion variables, provided by Pan and Poeshman (2006), on he fuure marke volailiy. We found ha he rading informaion of foreign insiuional invesors from he opion markes provides srong predicive power in explaining he fuure volailiy of sock markes. References Aboura, S., & Villa, C. (2003). Inernaional Marke Volailiy Indexes: A Sudy on VX1, VDAX, and VIX. Working paper. Paris Dauphine Universiy and Audencia Nanes School of Managemen. Alizadeh, S., Brand, M. W., & Diebold, F. X. (2002). Range Based Esimaion of Sochasic Volailiy Models. Journal of Finance. 57. 1047-1091. hp://dx.doi.org/10.1111/1540-6261.00454 Brailsford, T. J., & Faff, R. W. (1996). An Evaluaion of Volailiy Forecasing Techniques. Journal of Banking and Finance, 20. 419-438. hp://dx.doi.org/10.1016/0378-4266(95)00015-1 Canina, E. C. and Figlewski, S. (1993). The Informaion Conen of Implied Volailiy. Review of Financial Sudies, 6(3). 659-681. hp://dx.doi.org/10.1093/rfs/6.3.659 Carr, P., & Wu, L. R. (2006). A Tale of Two Indices. Journal of Derivaives, 13. 13-29. hp://dx.doi.org/10.3905/jod.2006.616865 Chang, C. C., Hsieh, P. F., & Lai, H. N. (2009). Do Informed Opion Invesors Predic Sock Reurns? Evidence from he Taiwan Sock Exchange, Journal of Banking and Finance, 33. 757-764. hp://dx.doi.org/10.1016/j.jbankfin.2008.11.001 Chang, C. C., Hsieh, P. F., & Wang, Y. H. (2010). Informaion Conen of Opions Trading Volume for Fuure Volailiy: Evidence From he Taiwan Opions Marke. Journal of Banking and Finance, 34. 174-183. hp://dx.doi.org/10.1016/j.jbankfin.2009.07.015 Chen, H. C., Chung, S. L., & Ho, K. Y. (2011). The Diversificaion Effecs of Volailiy-Relaed Asses. Journal of Banking and Finance, 35. 1179-1189. hp://dx.doi.org/10.1016/j.jbankfin.2010.09.024 Chung, S. L., Tsai, W. C., Wang, Y. H., & Weng, P. S. (2011). The Informaion Conen of he S&P 500 Index and VIX Opions on he Dynamics of he S&P 500 Index. Journal of Fuures Markes, 31(12). 1170 1201. hp://dx.doi.org/10.1002/fu.20532 Chrisensen, B. J., & Prabhala, N. R. (1998). The Relaion beween Implied and Realized Volailiy. Journal of Financial Economics, 50. 125-150. hp://dx.doi.org/10.1016/s0304-405x(98)00034-8 Claessen, H., & Minik, S. (2002). Forecasing Sock Marke Volailiy and he Informaional Efficiency of he DAX-Index Opions Marke. European Journal of Finance, 8. 302-321. hp://dx.doi.org/10.1080/13518470110074828 Corrado, C. J., & Miller, T. W. (2005). The Forecas Qualiy of CBOE Implied Volailiy Indexes. Journal of Fuures Markes, 25(4). 339-373. Corrado, C., & Truong, C. (2007). Forecasing Sock Index Volailiy: Comparing Implied Volailiy and he Inraday High-Low Price Range. Journal of Financial Research, 30(2). 201-215. hp://dx.doi.org/10.1111/j.1475-6803.2007.00210.x Covrig, V., & Low, B. S. (2003). The Qualiy of Volailiy Traded on he Over-he-Couner Currency Marke: A Muliple Horizon Sudy. Journal of Fuures Markes, 23(3). 261-285. hp://dx.doi.org/10.1002/fu.10066 Daigler, R. T., & Rossi, L. (2006). A Porfolio of Socks and Volailiy. Journal of Invesing, Summer. 99-106. hp://dx.doi.org/10.3905/joi.2006.635636 Day, T. E., & Lewis, C. M. (1992). Sock Marke Volailiy and he Informaion Conen of Sock Index Opions. Journal of Economerics, 52. 267-287. hp://dx.doi.org/10.1016/0304-4076(92)90073-z Ederingon, L. H., & Guan, W. (2002). Measuring Implied Volailiy: Is an Average Beer? Which Average? Journal of Fuures Markes, 22. 811-837. hp://dx.doi.org/10.1002/fu.10034 Engle, R. F. (1993). Saisical Models for Financial Volailiy. Financial Analys Journal, 49. 72-78. hp://dx.doi.org/10.2469/faj.v49.n1.72 Engle, R. F., & Bollerslev, T. (1986). Modelling he Persisence of Condiional Variances. Economeric Reviews, 5. Published by Canadian Cener of Science and Educaion 225
1-50. hp://dx.doi.org/10.1080/07474938608800095 Fung, J. K. W. (2007). The Informaion Conen of Opion Implied Volailiy Surrounding he 1997 Hong Kong Sock Marke Crash. Journal of Fuures Markes, 27(6). 555-574. hp://dx.doi.org/10.1002/fu.20259 Jayaraman, N., Frye, M. B., & Sabherwal, S. (2001). Informed Trading around Merger Announcemens: An Empirical Tes Using Transacion Volume and Open Ineres in Opions Marke. Financial Review, 36. 45-74. hp://dx.doi.org/10.1111/j.1540-6288.2001.b00010.x Kawaller, I. G., Koch, P. D., & Peerson, J. E. (2001). Volume and Volailiy Surrounding Quarerly Redesignaion of he Lead S&P 500 Fuures Conrac. Journal of Fuures Markes, 21. 1119-1149. hp://dx.doi.org/10.1002/fu.2202 Konsaninidi, E., & Skiadopoulos, G. (2011). Are VIX Fuures Prices Predicable? An Empirical Invesigaion. Inernaional Journal of Forecasing, 27(2). 543-560. hp://dx.doi.org/10.1016/j.ijforecas.2009.11.004 Konsaninidi, E., Skiadopoulos, G., &Tzagkaraki, E. (2008). Can he Evoluion of Implied Volailiy Be Forecased? Evidence from European and US Implied Volailiy Indices. Journal of Banking and Finance, 32. 2401-2411. hp://dx.doi.org/10.1016/j.jbankfin.2008.02.003 Lin, Y. N., & Chang, C. H. (2009). VIX Opion Pricing. Journal of Fuures Markes, 29. 523-543. hp://dx.doi.org/10.1002/fu.20387 Majmudar, U., & Banerjee, A. (2004). VIX Forecasing. The 40 h Annual Conference of he Indian Economerics Sociey. Mark, H. (2003). The 'New' VIX and Wha I May Mean. [Online] Available: hp://www.markewach.com/sory/ (December 20, 2009). Mayhew, S., & Sivers, C. (2003). Sock Reurn Dynamics, Opion Volume, and he Informaion Conen of Implied Volailiy. Journal of Fuures Markes, 23(7). 615-646. hp://dx.doi.org/10.1002/fu.10084 Ni, S. X., Pan, N., & Poeshman, A. M. (2008). Volailiy Informaion Trading in he Opion marke. Journal of Finance, 63(3). 1059-1091. hp://dx.doi.org/10.1111/j.1540-6261.2008.01352.x Pan, J., & Poeshman, A. M. (2006). The Informaion in Opion Volume for Fuure Sock Prices. Review of Financial Sudies, 19. 871-908. hp://dx.doi.org/10.1093/rfs/hhj024 Poon, S. H., & Granger, C. (2003). Forecasing Volailiy in Financial Markes: A Review. Journal of Economic Lieraure, 41(2). 478-539. hp://dx.doi.org/10.1257/002205103765762743 Poon, S. H., & Granger, C. (2005). Pracical Issues in Forecasing Volailiy. Financial Analyss Journal, 61( 1). 45-56. hp://dx.doi.org/10.2469/faj.v61.n1.2683 Seep, A. (2008). VIX Opion Pricing in Jump-Diffusion Model. Risk, April. 84-89. Shu, J., & Zhang, J. E., (2011). Causaliy in he VIX Fuures Marke. Journal of Fuures Markes, 32. 24-46. hp://dx.doi.org/10.1002/fu.20506 Szado, E. (2009). VIX Fuures and Opions - A Case Sudy of Porfolio Diversificaion During he 2008 Financial Crisis (Working paper). Amhers, MA: Universiy of Massachuses. hp://dx.doi.org/10.3905/jai.2009.12.2.068 Szakmary, A., Ors, E., Kim, J. k., & Davidson Ⅲ, W. N. (2003). The Predicive Power of Implied Volailiy: Evidence from 35 Fuures Markes. Journal of Banking and Finance, 27. 2151-2175. hp://dx.doi.org/10.1016/s0378-4266(02)00323-0 Wang, Z. C., & Daigler, R. T. (2011). The Performance of VIX Opion Pricing Models: Empirical Evidence beyond Simulaion. Journal of Fuures Markes, 31(3). 251-281. hp://dx.doi.org/10.1002/fu.20466 Whaley, R. E. (2000). The Invesor Fear Gauge. Journal of Porfolio Managemen, 26. 12-17. hp://dx.doi.org/10.3905/jpm.2000.319728 Whaley, R. E. (2009). Undersanding VIX. The Journal of Porfolio Managemen, 35(3). 98-105. hp://dx.doi.org/10.3905/jpm.2009.35.3.098 Yu, W. W., Lui, E. C. K., & Wang, J. W. (2010). The Predicive Power of he Implied Volailiy of Opions Traded OTC and on Exchanges. Journal of Banking and Finance, 34. 1-11. hp://dx.doi.org/10.1016/j.jbankfin.2009.06.017 Zhang, J. E., Shu, J. H., & Brenner, M. (2010). The New Marke for Volailiy Trading. Journal of Fuures Markes, 30(9). 809-833. hp://dx.doi.org/10.1002/fu.20448 Zhang, J. E., & Zhu, Y. Z. (2006). VIX Fuures. Journal of Fuures Markes, 26(6). 521-531. hp://dx.doi.org/10.1002/fu.20209 226 ISSN 1916-971X E-ISSN 1916-9728
Noes Noe 1. See he World Federaion of Exchanges, 2008 IOMA Derivaives Marke Survey. [Online] Available: hp://www.world-exchanges.org (March 2, 2010). Noe 2. Whaley (2009) poined ou ha he OEX rading volume accouned for 75% of he rading volume of index opions in 1992. Noe 3. Yu e al. (2010), Szakmary e al. (2003), Covrig and Low (2003), and Ederingon and Guan (2002) also adoped he implied volailiies of boh call opions and pu opions in heir sudies. Noe 4. The formulas can be found in The CBOE volailiy index VIX, [Online] Available: hp://www.cboe.com/micro/vix/vixwhie.pdf. Noe 5. The realized volailiies of he pas five days are seleced as he conrol variables by he Akaike Informaion Crierion, as suggesed by Wang e al. (2006). Noe 6. We would like o hank he Taiwan Fuures Exchange for providing he valuable daa, which grealy conribue o our research. As he daa sem from December 1, 2006 o Ocober 31, 2008, he research period for he equaion (15) is se accordingly beween December 1, 2006 and Ocober 31, 2008. Noe 7. Due o space consrains, only he resuls for he lag lengh equal o 1 are repored in Tables 3~6, and only he resuls for he unransformed daa are repored in Tables 4~6. The resuls for oher lag lengh (i=5, 10, 20) and for he log-ransformed daa are available upon reques. Table 1. Summary Saisics for he Realized Volailiy, Implied Volailiy, Volailiy Index, GARCH Forecas Volailiy, Opion Marke Trading Volume, and Opion Marke Open Ineres. Var. IV_A IV_C IV_P TVIX GFV VOL OI Mean 0.2541 0.2870 0.2586 0.3155 0.2883 0.2462 348693.00 702585.20 Median 0.2190 0.2767 0.2472 0.2999 0.2829 0.2382 324712.00 696440.00 Maximum 1.1349 0.8615 0.8697 1.3816 0.6041 0.5577 955561.00 1313587.00 Minimum 0.0526 0.1121 0.0862 0.0956 0.1174 0.0632 78893.00 230219.00 Sd. Dev. 0.1502 0.1115 0.0967 0.1456 0.0914 0.0979 139332.00 214602.70 Skewness 1.6552 1.0741 1.1182 1.8835 0.5548 0.4690 1.08 0.20 Kurosis 7.1422 4.7566 5.9973 9.9594 3.1461 2.2904 4.63 2.63 N 825 825 825 825 825 825 825 825 Table 2. The Correlaion Coefficiens beween Six Types of Volailiy Indicaors and Two Types of Opion Marke Informaion Variables. Var. IV_A IV_C IV_P TVIX GFV VOL OI 1.00 IV_A 0.56 1.00 IV_C 0.54 0.88 1.00 IV_P 0.50 0.95 0.68 1.00 TVIX 0.56 0.95 0.88 0.87 1.00 GFV 0.54 0.83 0.75 0.78 0.84 1.00 VOL 0.30-0.09-0.09-0.08-0.14-0.08 1.00 OI -0.17-0.35-0.36-0.30-0.38-0.31 0.62 1.00 Published by Canadian Cener of Science and Educaion 227
Table 3. The Informaion Conen of he Hisorical Volailiy versus he Implied Volailiy, he Volailiy Index, and he GARCH Forecas Volailiy. Inercep HV -i IV_A -i Implied Volailiy IV_C -i IV_P -i TVIX -i GFV -i R 2 Adj-R 2 F Panel A Unransformed Daa 0.1442 *** 0.4326 *** (15.5315) (13.7547) 0.1871 0.1861 189.1920 0.0378 *** 0.7536 *** (3.1536) (19.3545) 0.3130 0.3122 374.5952 0.0581 *** 0.7581 *** (4.4515) (16.0348) 0.2383 0.2373 257.1153 0.0807 *** 0.5498 *** (7.6256) (18.0553) 0.2840 0.2831 325.9968 0.0073 0.8560 *** (0.4946) (17.4826) 0.2710 0.2702 305.6404 0.0647 *** 0.7696 *** (5.2731) (16.6274) 0.2517 0.2508 276.4694 0.0313 *** 0.1735 *** 0.6227 *** (2.6329) (5.0446) (13.4404) 0.3337 0.3321 205.5919 0.0489 *** 0.2396 *** 0.5584 *** (3.8237) (6.8198) (10.2363) 0.2791 0.2773 158.9301 0.0606 *** 0.2208 *** 0.4355 *** (5.6406) (6.6361) (12.6913) 0.3204 0.3188 193.5516 0.0094 0.2064 *** 0.6668 *** (0.6500) (5.8664) (11.5293) 0.3004 0.2987 176.2397 0.0531 *** 0.2285 *** 0.5807 *** (4.3909) (6.5388) (10.8309) 0.2887 0.2870 166.6349 Panel B Log-ransformed Daa -0.7454 *** 0.5105 *** (-15.3379) (17.0118) 0.2604 0.2595 289.4011-0.3559 *** 0.8848 *** (-6.3718) (21.7287) 0.3648 0.3641 472.1376-0.3633 *** 0.8171 *** (-5.6328) (18.5683) 0.2955 0.2946 344.7831-0.5738 *** 0.7624 *** (-11.8319) (20.6674) 0.3419 0.3411 427.1396-0.2412 *** 0.9904 *** (-3.7014) (20.2658) 0.3332 0.3324 410.7009-0.3945 *** 0.7610 *** (-6.5704) (19.4874) 0.3160 0.3152 379.7578-0.2805 *** 0.2239 *** 0.6835 *** (-5.0340) (6.5123) (13.5784) 0.3960 0.3946 269.1664-0.2776 *** 0.2947 *** 0.5613 *** (-4.4318) (8.5662) (10.8604) 0.3533 0.3517 224.2614-0.4288 *** 0.2547 *** 0.5673 *** (-8.4507) (7.5223) (12.8587) 0.3844 0.3828 256.3038-0.1939 *** 0.2553 *** 0.7266 *** (-3.0544) (7.3782) (12.2468) 0.3746 0.3731 245.9186-0.2942 *** 0.2781 *** 0.5431 *** (-4.9797) (8.1639) (11.7820) 0.3674 0.3658 238.3686 This able repors he regression coefficiens and -saisics (in parenheses). The number of lag periods is se o be 1 (i=1). *, ** and *** denoe significance a he 10%, 5% and 1% levels, respecively. 228 ISSN 1916-971X E-ISSN 1916-9728
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Noe: SI is he TAIEX. is he annualized realized volailiy. IV_A is he average of he implied volailiies of pu and call opions. IV_P is he implied volailiy of pu opions. IV_C is he implied volailiy of call opions. VIX is he TVIX. GFV is he GARCH forecas volailiy. Figure 1. The Trends of Differen Types of Volailiy Indicaors versus TAIEX Published by Canadian Cener of Science and Educaion 231