The Greek Implied Volatility Index: Construction and Properties

Transcription

1 The Greek Implied Volailiy Index: Consrucion and Properies *, ** George Skiadopoulos Forhcoming in Applied Financial Economics * Universiy of Piraeus Deparmen of Banking and Financial Managemen Karaoli & Dimiriou 80, Piraeus 18534, Greece gskiado@unipi.gr ** Associae Research Fellow, Financial Opions Research Cenre, Warwick Business School, Universiy of Warwick Absrac There is a growing lieraure on implied volailiy indices in developed markes. However, no similar research has been conduced in he conex of emerging markes. In his paper, an implied volailiy index (GVIX) is consruced for he fas developing Greek derivaives marke. Nex, he properies of GVIX are explored. In line wih earlier resuls, GVIX can be inerpreed as a gauge of he invesor s senimen. In addiion, we find ha he underlying sock marke can forecas he fuure movemens of GVIX. However, he reverse relaionship does no hold. Finally, a conemporaneous spillover beween GVIX and he US volailiy indices VXO and VXN is deeced. The resuls have implicaions for porfolio managemen. JEL Classificaion: G10, G11, G13, G15. Keywords: Granger Causaliy Tess, Implied Volailiy Indices, Implied Volailiy Spillover, Volailiy Derivaives.

2 1. Inroducion There is a growing lieraure on he consrucion and he properies of implied volailiy indices in developed markes (Fleming e al., 1995, Moraux e al., 1999, Whaley, 1993, and 2000, Simon, 2003, and Wagner and Szimayer, 2004). However, no research has been conduced in he conex of emerging derivaives markes. The objecive of his paper is wofold. Firs, i consrucs an implied volailiy index for he fas growing Greek derivaives marke. Second, he properies of he consruced index are sudied. This allows examining for he firs ime some aggregae properies of he implied volailiies of his rapidly evolving marke. The sudy of he consrucion and of he properies of implied volailiy indices has been primarily moivaed by he increasing need o creae derivaives on volailiy (volailiy derivaives, see Brenner and Galai, 1989, 1993). These are insrumens whose payoffs depend explicily on some measure of volailiy. Hence, hey are he naural candidaes for speculaing and hedging agains changes in volailiy (volailiy risk). Volailiy risk has played a major role in several financial disasers in he pas 25 years (e.g., Barings Bank, Long-Term-Capial Managemen). Many raders also profi from he flucuaions in volailiy (see Carr and Madan, 1998, for a review on he volailiy rading echniques); Guo (2000), and Poon and Pope (2000) find ha profiable volailiy rades can be developed in he currency and index opion markes, respecively. In March 2004, he Chicago Board Opions Exchange (CBOE) inroduced volailiy fuures, and i announced he imminen inroducion of volailiy opions. A volailiy index can serve as he underlying asse o volailiy derivaives; i would play he same role as he marke index plays for opions and fuures on he index 1. The volailiy index can also be used for Value-a-Risk purposes (Gio, 2002b), o idenify buying/selling opporuniies in he sock marke (Sendahl, 1994, Whaley, 2000), and o 2

3 forecas he fuure marke volailiy (see Fleming e al., 1995, Moraux e al., 1999, Gio, 2002b, Simon, 2003). Gradually, he derivaives exchanges have sared consrucing implied volailiy indices. In 1993, CBOE inroduced an implied volailiy index, named VIX (currenly renamed o VXO; hereafer we will use he laer icker) ha is based on he S&P 100 index opions. In 1994, he German Fuures and Opions Exchange launched an implied volailiy index (VDAX) based on DAX index opions. In 1997, he French Exchange marke MONEP creaed wo volailiy indices (VX1, VX6) ha reflec he synheical a-he-money implied volailiies of he CAC-40 index opions. In 2000, CBOE inroduced he Nasdaq Volailiy Index (VXN) ha is derived from he implied volailiy of Nasdaq-100 Index (NDX) opions. The mehodology used o consruc he above menioned volailiy indices, is similar o his of VXO. However, he consrucion echnique of VXO is quie daa demanding. I requires wo opion series rading every day. Two pairs of opions are used from each series; each pair consiss of one call, and one pu wih he same srike. In oal, eigh opions mus be used. The implemenaion of he mehod assumes a very liquid marke. These consrains may no be me in emerging opion markes ha are less liquid han CBOE 2. In his paper, firs an implied volailiy index is consruced for he Greek opion marke (Ahens Derivaives Exchange, ADEX). The consrucion is based on an alernaive o he VXO mehod so as o respec he liquidiy consrains ypically encounered in emerging markes. Nex, he properies of he consruced Greek Volailiy Index (GVIX) are sudied. The focus is on he relaionship of GVIX wih he underlying sock index (FTSE/ASE-20) raher han on he power of GVIX o forecas he realized volailiy. Finally, he relaionship of he GVIX o VXO and VXN is sudied (implied volailiy spillovers). Despie he voluminous lieraure on he linkages and ineracions beween 3

4 inernaional sock prices/volailiies (see for example, Malliaris and Uruia, 1992, Arshanapali and Doukas, 1993, and Koumos, 1996, among ohers), here has no been much aenion paid o he ransmission of implied volailiies across markes. Gemmill (1996) explored wheher he changes in he implied volailiy smile in England are correlaed wih hose of U.S. over he period Gemmill and Kamiyama (1997) examined wheher he implied volailiy ransmis across he Japanese, Briish, and American markes over he period Implied volailiy propagaion is of paricular imporance o opion porfolio managers; i affecs opion prices and hedge raios, and i may indicae changes in expeced volailiy. The consrucion of an implied volailiy index for he Greek marke and he sudy of is properies deserve aenion for a number of reasons. The Greek opion marke was founded in 2000, and i can be characerized as an emerging marke. Despie i s shor life, i has experienced a remendous growh; he volume has increased from 2,381,260 o 7,387,574 conracs from 2000 o 2002 (an increase of 210%!). The relaionship of he Greek volailiy index wih he spo marke may be of paricular imporance o invesors wih posiions in socks. This is because he Greek sock marke has experienced a remarkably coninuous crisis from mid 1999 o he beginning of 2003; i has declined abou 4,000 index poins. Finally, given he naure of he Greek marke, i is worh invesigaing he implied volailiy spillover beween an emerging and a developed marke. To he bes of our knowledge, his is he firs sudy ha examines he properies of a measure of implied volailiy in he Greek opion marke, and i s poenial use for porfolio managemen purposes. An inverse relaionship beween changes in GVIX and he FTSE/ASE-20 reurn is documened. Furhermore, in line wih Whaley (2000), Gio (2002a), and Simon (2003) who sudied he properies of VXO and VXN, his relaionship is asymmeric. This has an 4

5 imporan implicaion: he GVIX can be inerpreed as a gauge of he invesor s fear; an increase in GVIX affecs he sock reurn (negaively) more han a decrease does. On he oher hand, in conras o Malz (2000), we find ha he implied volailiies of he Greek marke canno provide an early warning of marke sress. However, he reverse relaionship does hold: he resuls indicae ha he FTSE/ASE-20 can be used o predic fuure movemens of GVIX. Finally, a spillover of implied volailiy beween he US implied volailiy indices VXO / VXN and GVIX is found. These resuls have imporan implicaions for porfolio managemen. The res of he paper is srucured as follows. In Secion 2, he consrucion of GVIX is explained; he daa se is described, as well as he calculaion of he implied volailiies. In Secion 3, he properies of he GVIX are examined. Secion 4 examines he ransmission of implied volailiy beween he Greek and he US markes. Secion 5 concludes and suggess some opics for fuure research. 2. The Greek Volailiy Index (GVIX): Consrucion and Daa Following he sandard pracice in consrucing implied volailiy indices, he Greek Volailiy Index (GVIX) represens he implied volailiy of a synheic a-he-money (ATM) opion wih weny-wo rading days o mauriy (or equivalenly, hiry calendar days o mauriy). ATM implied volailiies are used so as o minimize he measuremen errors in esimaing implied volailiies. This is because mos of he opions rading aciviy is concenraed close-o-he-money. A consan mauriy is used because i has been found ha implied volailiies change as he ime o mauriy changes (see e.g., Fleming e al., 1995). Mainaining a consan ime o expiraion minimizes he effec ha his consideraion may have on VXO. Nex, he consrucion mehod and he employed daa se are described. 5

6 2.1 Consrucion The suggesed consrucion mehod of GVIX requires four opion prices, for any day. More specifically, for any day, wo expiries are used: one is longer and he oher is shorer han he consan mauriy dae we aim o creae. In any expiry, he firs ou-of-he-money (OTM) call, and he firs OTM pu are idenified. Then, he implied volailiies are exraced. Nex, for any expiry, he ATM opion implied volailiy is calculaed by inerpolaing linearly beween he implied volailiies of he OTM call and pu. Finally, he consan mauriy implied volailiy is derived by inerpolaing linearly beween he ATM implied volailiy of he wo expiries. The proposed mehod differs from he VXO one. The laer uses boh in-he-money (ITM) and OTM opions. An addiional consrain is ha pairs of calls and pus wih he same srike need o be raded for he neares and second-neares series. In oal, eigh opions should be used (see also Whaley 1993, 2000, for more deails on he consrucion of VXO). In our case, applicaion of he VXO consrucion echnique is no possible due o liquidiy consideraions. However, here is no loss of informaion by excluding ITM opions. This is because an OTM (ITM) pu should have he same implied volailiy wih an ITM (OTM) call, provided ha he pu-call pariy relaionship holds (here is a simple arbirage if i does no hold). Moreover, using only OTM opions has he advanage ha i minimizes he effec of measuremen errors on he calculaion of implied volailiies (see Skiadopoulos e al., 1999, Bliss and Panigirzoglou, 2004, Panigirzoglou and Skiadopoulos, 2004) 3. GVIX is consruced separaely from he average of he bid-ask opion prices, and from he selemen opion prices. This allows us o invesigae which ype of opion price should be preferred in order o consruc he index wih as lile noise as possible (see Secion 3.1). In he implied volailiy lieraure boh ypes of opion prices have been used. 6

7 For example, he average of he bid-ask opion quoes is used o consruc he VXO since i reduces he bid-ask bounce (see e.g., Whaley, 1993). On he oher hand, using selemen prices ha are calculaed by some algorihm (usually as a weighed average) makes he derived index less prone o possible manipulaion. 2.2 The Daa Se and he Calculaion of Implied Volailiies Daily daa of index opions and fuures raded in he Ahens Derivaives Exchange (ADEX) from 10/10/2002 o 30/12/2002 are used (554 observaions). The raw daa se consiss of he las bid-ask quoes and selemen prices of opions on he FTSE/ASE-20 index, and he selemen prices of he FTSE/ASE-20 fuure 4. Opions and fuures wih ime-o-mauriy less han five working days, wih volume less han five conracs, and wih zero opion price were discarded from our daabase. The VXO and VXN implied volailiies are downloaded from he CBOE web sie ( The FTSE/ASE-20 index is a capializaion index comprising he weny mos liquid Greek socks rading in he elecronic sysem known as OASIS. The Greek sock marke operaes from 11:00-16:00. Trading in ADEX sared in Augus The FTSE/ASE-20 fuure was he firs conrac ha was launched. The FTSE/ASE-20 opion was launched in Sepember These are he wo mos liquid derivaive conracs: over he period , he volume in he fuure conrac increased from 968,486 o 4,170,146 conracs. In he opion conrac, he volume increased from 52,740 o 2,034,126 conracs. On every day, here are six series rading for boh he opion and he fuure conrac. The hree series correspond o he hree neares consecuive monhs, and he oher hree correspond o he hree monhs of he March-June-Sepember-December cycle. The expiraion day is he hird Friday of he conrac monh. Opions and fuures rade from 10:45-16:15. Their conrac size is 5 EUROS per index poin. The FTSE/ASE-20 opion is a 7

8 cash seled European opion 5. For every new opion series, here are iniially eleven srike prices; new srike prices are inroduced as he index moves. The srike prices differ by 50 index poins. The deph of he opions bid-ask quoes is five conracs. This volume consrain holds for he wo shores expiries and he hree opions ha are neares o-hemoney. Given ha he FTSE/ASE-20 pays dividends, a European opion-pricing model ha akes ino accoun he dividends paymen should be used in order o calculae he implied volailiies. We circumven he problem of esimaing a dividend yield by using Black s model (1976) ha prices European fuure opions. This is a sandard approach followed in he academic lieraure, provided ha he opion and he fuure have he same underlying asse and he same expiry dae (see for example, Pena e al., 1999). I is also in line wih he pracice of he Greek marke makers who hedge using he fuures raher han a porfolio of socks ha replicaes he index. In addiion, pricing opions off he fuures reduces any biases in he calculaed implied volailiies due o non-synchronous rading since he Greek derivaive marke does close a he same ime wih he spo marke. A ime, he Black s European call and pu prices c and p are given by rt, ( T ) c = e [ F N( d ) XN( d )],, T 1 2 (1) rt, ( T ) = [ ( 2 ), T ( d1) ] p e XN d F N (2) where d 1 2 ln( FT, / X) + ( v / 2)( T ), = d2 = d1 v T v T (3) and N(x) is he sandard cumulaive normal disribuion evaluaed a poin x, F,T is he price a ime of a fuure expiring a ime T ( T ), X is he srike price, r,t is he mauriy T riskfree ineres rae a ime, v is he volailiy, and T is he opion s expiry dae. 8

9 EURIBOR ineres raes obained from Daasream are used o proxy for he riskfree ineres rae. Daily ineres raes for one, wo, hree weeks, one, wo, and hree monhs were used, while hose for oher mauriies were calculaed by linear inerpolaion. The effec of any measuremen errors in he ineres rae is small since he rho of OTM opions is small. GVIX was no consruced for he days where here was only one series rading (39 such days were me) and/or here were no four opion prices available. Evenually, he GVIX could be consruced in he 303 ou of he 554 days. 3. Properies of he Greek Volailiy Index 3.1 Summary Saisics Figure 1 shows he evoluion of GVIX calculaed from he average bid-ask quoe and from he selemen opion prices. I also shows he evoluion of he FTSE/ASE-20 over he same period. We can see ha even hough mos of he ime he wo volailiy indices end o move ogeher, he GVIX calculaed from selemen prices seems o be more volaile. Furhermore, in cerain periods here seems o be a negaive correlaion beween he changes in he FTSE/ASE-20 and he changes of he wo volailiy indices. This has been ermed as leverage effec (see Figlewski and Wang, 2000, for a deailed review and an empirical sudy on he leverage effec). In order o sudy he ime series properies of he consruced indices formally, we proceed as follows. Table 1 shows he summary saisics (mean, median, maximum, minimum, sandard deviaion, skewness, kurosis, and he resuls from he Jarque-Bera es wih i s p-value in he brackes) of he FTSE/ASE-20 and he wo volailiy indices. We can see ha he hree series are disribued non-normally. Boh measures of GVIX reach heir highes value on 24/09/01. The consruced from bid-ask (selemen) quoes GVIX reaches 9

10 i s minimum value on 18/05/01 (11/06/02). Finally, FTSE/ASE-20 reaches i s maximum value on 11/10/01, and i s minimum value on 30/12/02. Table 2 shows he summary saisics of he (coninuously compounded) reurns of he FTSE/ASE-20 and he changes GVIX=GVIX -GVIX -1 of he wo indices, as well as heir cross-correlaions. The sample mean for boh volailiy indices is zero indicaing ha here is no rend. The sandard deviaion for he volailiy index consruced from he bid-ask quoes is greaer. Boh volailiy indices are disribued non-normally; hence, exreme movemens in he volailiy changes are more probable han under he normal disribuion. The cross-correlaions confirm he exisence of he leverage effec, even hough his is raher weak. In he case ha bid-ask opion prices are used, he correlaion beween he FTSE/ASE-20 reurn and he changes in GVIX is found o be Using selemen prices yields a slighly higher correlaion of The correlaion beween he changes of he wo volailiy indices is Finally, regarding he auocorrelaion coefficiens, he sandard 5% significance bound is 2 / T = 2 / 302 = We can see ha he firs order auocorrelaion for boh measures of GVIX is saisically significan, and i is negaive. This can be inerpreed as evidence of mean reversion in he implied volailiy index. Alernaively, he negaive serial auocorrelaion can be inerpreed as a signal for he presence of measuremen errors in he calculaion of implied volailiies (Harvey and Whaley, 1991). This negaive auocorrelaion is much sronger in he case ha GVIX is consruced by he average of he bid-ask quoes ( compared o 0.167). Hence, his suggess ha he volailiy index consruced from bid-ask quoes is more prone o noise. Therefore, selemen prices should be preferred. For he res of he analysis we use he consruced from selemen prices GVIX. The presence of exra noise in he las bid-ask quoes can be explained by he fac ha i is very likely ha hese are no quoed simulaneously wih he spo index; in he 10

11 Greek opions marke, he marke makers are no obliged o provide quoes wihin he las fifeen minues of he daily rading session. In addiion, i is worh menioning ha he GVIX auocorrelaion resuls are lower han he ones found for oher European indices; for example, Moraux e al. (1999) found a value of 0.27 for he firs order auocorrelaion of he changes in VX1. This indicaes ha he presened here mehod may be a poenial candidae o consruc volailiy indices in less liquid han he U.S. markes. 3.2 Invesor s Gauge of Fear The capial asse pricing model heories (e.g., Sharpe, 1964) predic ha he expeced reurn depends on he expeced volailiy. In addiion, wihin he implied volailiy index lieraure, Whaley (2000), Gio (2002a) and Simon (2003) have found a negaive relaionship beween reurns and VXO/ VXN. A possible explanaion of his is ha he demand for pus increases when he marke declines. Increased demand means higher pu prices, and hence higher implied volailiies. Furhermore, his relaionship is asymmeric: an equal size posiive/negaive shock on implied volailiy does no have he same effec on he index reurn 6. Hence, hey inerpre he VXO as he invesor s fear gauge ; he furher VXO increases in value, he more panic here is in he marke. The furher VXO decreases in value, he more complacency here is in he marke 7. To invesigae wheher his inerpreaion can also be aribued o GVIX, we follow Whaley s (2000) mehodology in ha we regress he daily reurns R of he FTSE/ASE-20 on he daily changes GVIX of he GVIX, and he change GVIX + of GVIX when he change is posiive i.e. GVIX + = GVIX if GVIX>0, and GVIX + =0, oherwise 8 R = a GVIX + a GVIX + u (4) The regression resuls (-values in brackes) are 11

12 R GVIX GVIX R + 2 = , = 0.05 ( 3.302) ( 3.382) All regression coefficiens are significanly differen from zero a a 1% significance level. The inerpreaion of he coefficiens is he following: if GVIX falls by one percen, hen he FTSE/ASE-20 reurn will increase by ( 0.01) = unis. On he oher hand, if GVIX rises by one-percen, he FTSE/ASE-20 reurn will decrease by = unis. Therefore, he Greek sock marke is affeced (negaively) more by an increase in GVIX han i is affeced (posiively) by an equal size decrease in GVIX. Finally, we checked wheher he 11 h of Sepember aack affeced he risk-reurn relaionship. Towards his end, a muliplicaive dummy variable D was included in he regression model of equaion (4), i.e. R = a GVIX + a GVIX + b D GVIX + b D GVIX + u (5) where D=1 if >11/09/2001 and D=0, oherwise. We found ha R = GVIX GVIX 0.014D GVIX D GVIX + + ( 2.010) ( 2.920) ( 0.254) (0.851) where he -saisics are repored wihin brackes. We can see ha he coefficiens b 1 and b 2 are saisically insignifican. This implies ha he aack did no affec he risk-reurn relaionship in he Greek opions marke. Therefore, he risk-reurn relaionship remains sable during he period under scruiny. This is in accordance wih Gio (2002a) and Simon (2003) who found ha he risk-reurn relaionship is sable in he VXO (VXN) and he S&P 100 (Nasdaq-100) markes. 12

13 3.3 Granger Causaliy Tes We perform a Granger causaliy es in order o check wheher GVIX (R) helps o predic R ( GVIX). The Granger causaliy es consiss of running bivariae regressions of he form K GVIX = c + a GVIX + b R + u l l l l l= 1 l= 1 K (6) K R = c+ a R + b GVIX + u l l l l l= 1 l= 1 K (7) The null hypohesis is H0 : b1 =... = bk = 0. The inerpreaion of he null is ha R does no Granger-cause GVIX in he firs regression and ha GVIX does no Granger-cause R in he second regression 9. Table 3 shows he resuls from he Granger causaliy es using wo lags (K=2). We can see ha R Granger-causes GVIX (i.e., rejecion of he null) while he reverse does no hold. This resul is robus o he choice of K. Moreover, i is in conras o Malz (2000). He also ran similar Granger causaliy ess, and he found ha several measures of volailiy (consan mauriy implied, hisorical, exponenially weighed moving average) could predic he fuure (squared) reurns of various asses 10. Our findings are of paricular imporance o an invesor who has a posiion in FTSE/ASE-20 opions. They sugges ha he can use he reurns of he underlying asse in order o forecas he fuure movemen of he implied volailiy, and hence of he opion price. On he oher hand, he Greek implied volailiy index does no conain informaion regarding he direcion of fuure reurns. Towards idenifying he power of lagged values of GVIX and of R o forecas he fuure movemens of GVIX, we run he following regression 2 2 GVIX = a GVIX + b R + u l l l l l= 1 l= 1 (8) 13

14 The R 2 of he regression is 10%. Table 3 also shows he coefficien esimaes, and heir - values (in brackes) and p-values. We can see ha he α l, b l (l=1,2) coefficiens are saisically significan and negaive. The negaive sign in he coefficiens of he lagged values of GVIX confirms ha GVIX follows a mean-revering process. Following a general-o-specific approach, we have also run similar regressions wih higher order lags and by including an inercep. We found ha hese do no have any addiional forecasing power. Therefore, he invesor can use he informaion conained in he values of GVIX and R of he pas wo periods in order o develop he appropriae opion sraegy. 4. Spillover Effecs In his secion, we examine wheher here is a ransmission of implied volailiy across he CBOE and he ADEX markes. Towards his end, he relaionship beween VXO, VXN, and GVIX is sudied. Figure 2 shows he evoluion of VXO, VXN, and GVIX over he period Applicaion of he augmened Dickey-Fuller es reveals ha he series are nonsaionary. Table 4 shows he cross-correlaions beween VXO, VXN, and GVIX in heir firs differences. We can see ha he correlaion beween he changes of VXO and GVIX, and VXN and GVIX is almos zero (0.06, and 0.02, respecively). The small correlaion values indicae ha he correlaions beween emerging and developed derivaive markes are low; so far, here was evidence on low cross-correlaions beween emerging and developed sock markes (see Howell, 1998). The correlaion beween he changes of VXO and VXN is 0.7. Nex, we es wheher here is a Granger causaliy relaionship beween changes in GVIX and each one of he US volailiy indices; four lags are used (see also Malliaris and Uruia, 1992, for an applicaion of Granger causaliy ess in he conex of lead-lag 14

15 relaionships for sock marke indices). Table 5 shows ha in general, here is no such Granger causaliy relaionship; here is some weak evidence for he case where lagged values of VXN are used o forecas he changes in GVIX. This implies ha he changes in he US indices canno forecas he changes in GVIX (and vice-versa). Finally, in line wih Gemmill and Kamiyama (1997), he following unidirecional regressions are performed in order o sudy furher he presence of any spillover effecs: GVIX = c + a VXO + a VXN + u (9) GVIX = c2 + b1 VXO 1+ b2 VXN + 1 u (10) GVIX = c3+ a1 VXO + a2 VXN + b1 VXO 1+ b2 VXN 1+ u (11) Equaion (9) ess wheher here is a conemporaneous relaionship beween GVIX and he changes in he US volailiy indices. Equaion (10) checks wheher he US indices lead he Greek volailiy index. Equaion (11) examines wheher here is boh a conemporaneous and lead relaionship beween he Greek and he US indices. In order o undersand he meaning of conemporaneous and lead effec, he ime zones wihin which he indices are repored, need o be idenified. The US indices rade from 8:30-15:15 (Chicago ime), or 16:30-23:15 Greek ime. Given ha closing prices are used o consruc he volailiy indices, conemporaneous refers o he same calendar dae, even hough he ime a which he US and Greek indices are measured differs. Table 5 shows he esimaed coefficiens, he -saisics in brackes and he p-values. The R 2 for equaions (9) and (10) is 1% and for equaion (11) is slighly greaer (3%). We can see ha here is a conemporaneous spillover effec beween he changes in VXO and GVIX (significan α 1 in equaion (9)). In addiion, here is a conemporaneous spillover 15

16 effec beween GVIX and boh US indices in he case ha he previous period values of boh indices are also aken ino accoun (equaion (11)). The coefficiens of he lagged values are insignifican hough; his is consisen wih he earlier rejecion of he Granger causaliy hypohesis beween he indices. On he oher hand, he change in he U.S. implied volailiy indices does no lead he nex day s change in GVIX [equaion (10)]. The empirical evidence on he implied volailiy spillovers lieraure is mixed. Gemmill (1996) found ha conemporaneous changes in he shape of he English and U.S. smiles are uncorrelaed over he period Gemmill and Kamiyama (1997) found ha he S&P 500 implied volailiies lead he FTSE and Nikkei ones over he period Our resuls on he lead/lag relaionship may be aribued o he anecdoal evidence ha Greek opion raders end o be affeced by he previous day movemens of he European raher han hose of he US opion markes (Gemmill, 1996, explains his findings as a resul of he differen kinds of paricipans in he various markes). 5. Conclusions We have consruced an implied volailiy index for he rapidly evolving Greek derivaives marke using he FTSE/ASE-20 fuure and opion conracs. The consrucion mehod may be used in emerging markes ha are less liquid han he U.S. opion markes. To consruc he Greek implied volailiy index (GVIX), selemen opion prices are found o be preferred from he average bid-ask opion price. Nex, he properies of GVIX have been sudied. They shed ligh on he behavior of an aggregae measure of implied volailiies in an emerging marke and hey have imporan implicaions for porfolio managemen. In line wih Whaley (2000), Gio (2002a) and Simon (2003), we found ha he index can be used as a gauge of he invesor s fear. This measure 16

17 is sable over ime and i is no affeced by he 11 h of Sepember crash. Moreover, he resuls from Granger causaliy ess imply ha he invesor can use he informaion conained in he values of GVIX and he FTSE/ASE-20 of he pas wo periods in order o develop a profiable opion sraegy. On he oher hand, GVIX canno forecas he fuure FTSE/ASE-20 reurns. Therefore, i canno be reaed as a leading indicaor for he sock marke. This finding is in conras o he resuls found in he lieraure, so far. Finally, a conemporaneous spillover of change in he implied volailiy beween he GVIX and he U.S. volailiy indices was deeced. However, no lead-lag effecs are presen. This paper creaes a leas hree srands for fuure research. Firs, he abiliy of GVIX o forecas he fuure marke volailiy should be invesigaed. This can be done by means of a saisical analysis, or under a more pracical meric such as Value-a-Risk by performing he appropriae backesing. Second, i may be worh examining he presence of common facors in GVIX and US indices using alernaive mehodologies. Towards his end, a nonlinear vecor auoregression approach may be used (see, e.g., Lekkos and Milas, 2004, for an applicaion on he ineres rae swap markes). Finally, he GVIX mehodology could be applied o US daa and compared agains he VXO echnique. These issues are beyond he scope of his paper, bu hey deserve o become opics for fuure research. Acknowledgmens I am paricularly graeful o Nikos Porfiris who kindly provided he daa se for his sudy, and o Carol Alexander, Chris Brooks, Harris Linaras, Sewar Mayhew, Nikolaos Panigirzoglou, Peer Pope, Mark Shackleon, and Rober Whaley for many helpful discussions. I would also like o hank Chrisos Dadamis, Ahanasios Episkopos, Dimiris Flamouris, Gikas Hardouvelis, Iakovos Iliadis, Kaerina Panopoulou, Dimiris Papas, Cosas Pesas, and he paricipans a he 2003 Universiy of Piraeus-ADEX Research Seminar 17

18 Series, and a he 2003 Hellenic Finance and Accouning Associaion Meeing for useful discussions and commens. This paper was par of he projec Volailiy Derivaives funded by he Ahens Derivaives Exchange (ADEX). Financial suppor from he Research Cenre of he Universiy of Piraeus is also graefully acknowledged. The views expressed herein are hose of he auhor and do no necessarily reflec hose of ADEX. Any remaining errors are my responsibiliy alone. References Arshanapali, B. and Doukas, J. (1993) Inernaional Sock Marke Linkages: Evidence from he Pre- and Pos-Ocober 1987 period, Journal of Banking and Finance, 17, Black, F. (1976) The Pricing of Commodiy Conracs, Journal of Financial Economics, 3, Bliss, R.R. and Panigirzoglou, N. (2004) Opion-Implied Risk Aversion Esimaes, Journal of Finance, 59, Brenner, M. and Galai, D. (1989) New Financial Insrumens for Hedging Changes in Volailiy, Financial Analyss Journal, July-Augus, Brenner, M. and Galai, D. (1993) Hedging Volailiy in Foreign Currencies, Journal of Derivaives, 1, Brenner, M., Ou, E. and Zhang, J. (2002) Hedging Volailiy Risk, Working Paper, New York Universiy, Sern School of Business. Carr, P. and Madan, D. (1998) Towards a Theory of Volailiy Trading, in R. Jarrow (Edior), Volailiy, Risk Publicaions, Figlewski, S. and Wang, X. (2000) Is he Leverage Effec a Leverage Effec?, Working Paper S-00-37, New York Universiy, Sern School of Business. 18

19 Fleming, J., Osdiek, B. and Whaley, R.E. (1995) Predicing Sock Marke Volailiy: A New Measure, Journal of Fuures Markes, 15, Gemmill, G. (1996) Did Opion Traders Anicipae he Crash? Evidence from Volailiy Smiles in he U.K. wih U.S. Comparisons, Journal of Fuures Markes, 16, Gemmill, G. and Kamiyama, N. (1997) Inernaional Transmission of Opion Volailiy and Skewness: When you re smiling, does he whole world smile?, Working Paper, Ciy Universiy Business School. Gio, P. (2002a) Implied Volailiy Indices as Leading Indicaors of Sock Index Reurns?, Working Paper, CORE, Universiy of Leuvain. Gio, P. (2002b) The Informaion Conen of Implied Volailiy Indexes for forecasing Volailiy and Marke Risk, Working Paper, CORE, Universiy of Leuvain. Guo, D. (2000) Dynamic Volailiy Trading Sraegies in he Currency Opion Marke, Review of Derivaives Research, 4, Hamilon, J.D. (1994) Time Series Analysis, Princeon Universiy Press, Princeon, N. J. Harvey, C.R. and Whaley, R.E. (1991) S&P 100 Index Opion Volailiy, Journal of Finance, 46, Howell, M.J. (1998) Emerging Markes I., in Alexander C. (Edior) Risk Managemen and Analysis: New Markes and Producs, Vol. 2, Wiley Series in Financial Engineering. Koumos, G. (1996) Modeling he Dynamic Inerdependence of Major European Sock Markes, Journal of Business, Finance, and Accouning, 23, Lekkos, I. and Milas, C. (2004) Common Risk Facors in he US and UK Ineres Rae Swap Markes: Evidence from a Non-Linear Vecor Auoregression Approach, Journal of Fuures Markes, 24, Malliaris, A.G. and Urruia, J.L. (1992) The Inernaional Crash of Ocober 1987: Causaliy Tess, Journal of Financial and Quaniaive Analysis, 27,

20 Malz, A.M. (2000) Do Implied Volailiies Provide Early Warning of Marke Sress?, Working Paper, The RiskMerics Group. Moraux, F., Navae, P. and Villa, C. (1999) The Predicive Power of he French Marke Volailiy Index: A Muli Horizons Sudy, European Finance Review, 2, Panigirzoglou, N. and Skiadopoulos, G. (2004) A New Approach o Modeling he Dynamics of Implied Disribuions: Theory and Evidence from he S&P 500 Opions, Journal of Banking and Finance, 28, Pena, I., Rubio, G. and Serna, G. (1999) Why do we Smile? On he Deerminans of he Implied Volailiy funcion, Journal of Banking and Finance, 23, Poon, S.H. and Pope, P.F. (2000) Trading Volailiy Spreads: A Tes of Index Opion Marke Efficiency, European Financial Managemen Journal, 6, Sharpe, W.F. (1964) Capial Asse Prices: A Theory of Marke Equilibrium Under Condiions of Risk, Journal of Finance, 19, Simon, D.P. (2003) The Nasdaq Volailiy Index During and Afer he Bubble, Journal of Derivaives, Winer, Skiadopoulos, G., Hodges, S.D. and Clewlow, L. (1999) The Dynamics of he S&P 500 Implied Volailiy Surface, Review of Derivaives Research, 3, Sendahl, D. (1994) The Volailiy Index, Technical Analysis of Socks and Commodiies 12, Also available a Wagner, N. and Szimayer, A. (2004) Local and Spillover Shocks in Implied Marke Volailiy: Evidence for he U.S. and Germany, Research in Inernaional Business and Finance, forhcoming. Whaley, R.E. (1993) Derivaives on Marke Volailiy: Hedging Tools Long Overdue, Journal of Derivaives, 1, Whaley, R.E. (2000) The Invesor Fear Gauge, Journal of Porfolio Managemen 26,

21 Greek Volailiy Indices and FTSE/ASE-20 am implied volailiy /10/00 21/12/00 7/02/01 10/04/01 28/05/01 11/07/01 6/09/01 25/10/01 12/12/01 4/02/02 2/04/02 24/05/02 10/07/02 13/09/02 18/10/02 20/12/ FTSE/ASE-20 Vol index (Bid-ask) Vol index (closing prices) FTSE/ASE-20 Figure 1: The Greek implied volailiy index (GVIX) and he FTSE/ASE-20 over he period 10/10/ /12/2002. The GVIX is calculaed from he average bid-ask opion quoe and from he selemen opion prices, separaely. VXO, VXN, and GVIX Evoluion Implied Volailiy Index /10/00 10/12/00 10/2/01 10/4/01 10/6/01 10/8/01 10/10/01 10/12/01 10/2/02 10/4/02 10/6/02 10/8/02 10/10/02 10/12/02 dae VXO GVIX VXN Figure 2: Evoluion of VXO, VXN, and GVIX implied volailiy indices over he period 10/10/ /12/

22 FTSE/ASE-20 GVIX (Bid-Ask) GVIX (Selemen) Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Jarque-Bera (0.00) (0.00) (0.00) Table 1: Summary Saisics of he FTSE/ASE-20 and of GVIX. The GVIX has been consruced separaely from he average bid-ask opion quoes and from he selemen opion quoes. Reurn FTSE/ASE-20 GVIX (Bid-Ask) GVIX (Close) Mean Median Maximum Minimum Sd. Dev Skewness Kurosis Jarque-Bera (0.00) (0.00) (0.00) Cross-Correlaions Reurn FTSE/ASE GVIX (Bid-Ask) GVIX (Close) ! Auocorrelaions! ρ (1) * *! ρ (2) ρ (3) Table 2: Summary Saisics of he reurns of FTSE/ASE-20 and he changes of GVIX consruced separaely from he average bid-ask opion quoes and he closing opion quoes. Cross-Correlaions and he auocorrelaions up o hree lags are repored. The aserisk indicaes significance of he auocorrelaion coefficien a 5% level of significance. 22

23 Null Hypohesis F-Saisic Probabiliy R does no Granger Cause GVIX 8.42* GVIX does no Granger Cause R Regression Resuls Coefficien Esimae (-value) Probabiliy α * (-4.04) α ** (-2.54) b ** (-2.07) b * (-3.29) Table 3: Granger Causaliy Tes beween GVIX and R using wo lags (K=2). Resuls from he regression 2 2 l l l are also repored. One aserisk denoes l= 1 l= 1 GVIX = a GVIX + b R l significance a a 1% significance level, and wo aserisks denoe significance a 5% significance level. GVIX VXO VXN GVIX VXO VXN Table 4: Cross-Correlaions beween VXO, VXN, GVIX in he firs differences over he period 10/10/ /12/

24 Null Hypohesis F-Saisic Probabiliy VIX does no Granger cause GVIX GVIX does no Granger cause VXO VXN does no Granger cause GVIX 2.45*** 0.05 GVIX does no Granger cause VXN Regression Resuls: Equaions (9) and (10), R 2 =0.01 Coefficien Esimae (-value) Probabiliy c (-0.16) 0.87 α *** (1.88) 0.06 α (-1.66) 0.10 c (-0.06) 0.95 b (-0.06) 0.95 b (1.34) 0.18 Regression Resuls: Equaion (11), R 2 =0.03 c (-0.12) 0.91 α ** (2.30) 0.02 α *** (-1.76) 0.08 b (0.31) 0.75 b (1.32) 0.19 Table 5: Granger Causaliy Tes beween GVIX and VIX ( VXN) using four lags (K=4). The resuls from he regressions GVIX = c1+ a1 VXO + a2 VXN + u, GVIX = c + b VXO + b VXN + u, and GVIX = c + a VXO + a VXN + b VXO b VXN + u are also repored. One aserisk denoes significance a a 1% significance level, wo aserisks denoe significance a a 5% significance level, and hree aserisks significance a a 10% significance level. 24

25 Foonoes 1 A volailiy derivaive can also be wrien on an asse ha has a payoff closely relaed o he volailiy swings, e.g., a sraddle. See Brenner e al. (2002) who propose an opion on a sraddle. 2 For example, MONEP consrucs i s volailiy indices using only call prices ha rade more frequenly. However, his may inroduce severe biases in he consrucion of he implied volailiy index since i is well documened ha he implied volailiies of calls and pus may differ significanly (see for example, Gemmill, 1996). See also Moraux e al. (1999) for a discussion of he measuremen errors in he consrucion of he French volailiy indices. 3 In Sepember 2003, CBOE inroduced wo new volailiy indices, ermed VIX and VXN, respecively. These are based on an alernaive o he old VIX and VXN consrucion mehod. Among oher differences, he new mehod also uses only OTM opions. 4 The opion prices quoed as closing in ADEX are no he las-raded prices. They are selemen prices in he sense ha ADEX uses an algorihm o calculae hem. For he shores expiry, he hree neares-o-he-money call and pus are used. For he second expiry series only he closes-o-he-money call and pu is required. Then, Black s (1976) model is used o back ou he implied volailiy using he las raded fuure price and a consan ineres rae of 3%. In he nex sep, he arihmeic average of he implied volailiy is obained. Finally, he selemen opion price is calculaed using he average implied volailiy and he fuure selemen price. 5 A disinguishing characerisic of he Greek derivaives marke is ha he selemen and margining are performed a an end-clien level allowing a ransparen monioring of he ransacions ha faciliaes risk managemen. This is in conras o he omnibus pracice followed by oher exchanges. 6 Figlewski and Wang (2000) confirm his asymmeric relaionship by reaing he changes (of he logarihm) of implied volailiy as he dependen variable, and he index reurns as he independen variable, in a linear regression seup. 7 As such a measure of fear, VXO can help o deermine wheher OEX opions are undervalued or overvalued (see Sendahl, 1994, for a discussion on using VXO for volailiy rading purposes). 8 Whaley (2000) uses also an inercep in his regression formulaion. We found ha he inercep componen was insignifican and hus we omied i. 9 Y is said o be Granger-caused by X if X helps in he predicion of Y, or equivalenly if he coefficiens on he lagged X s are saisically significan. I is imporan o noe ha he saemen X Granger causes Y does no imply ha Y is he effec or he resul of X. Granger causaliy measures precedence and informaion conen bu does no by iself indicae causaliy in he more common use of he erm (see Hamilon, 1994, for a deailed descripion of he Granger causaliy es). 25

26 10 We applied he Granger-causaliy es o squared reurns, as well. However, he resuls did no change. 26