REVISITING THE FINANCIAL VOLATILITY DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS

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1 BRUSSELS ECONOMIC REVIEW-CAHIERS ECONOMIQUES DE BRUXELLES VOL. 56(3/4) AUTUMN-WINTER 2013 REVISITING THE FINANCIAL VOLATILITY DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS CLAUDIU TIBERIU ALBULESCU (POLITEHNICA UNIVERSITY OF TIMISOARA), DANIEL GOYEAU ** (UNIVERSITY OF POITIERS) AND AVIRAL KUMAR TIWARI *** (ICFAI UNIVERSITY TRIPURA) ABSTRACT: The presen paper analyses he relaionship beween he volume of ransacions wih fuures equiy index producs and he reurn volailiy of heir underlying asses. The sudy addresses he case of five sock markes, members of he Euronex.liffe. We employ a frequency domain analysis o idenify he direcion of he causaliy. In addiion, we es he relaionship beween he volume of fuures conracs and boh negaive and posiive shocks in erms of he hisorical volailiy of index reurns. Our resuls indicae he frequency causaliy only in he case of Brussels financial marke. For Lisbon, he causaliy is presen, bu i is no validaed by he confidence level ess, while for London, Paris and Amserdam, no causaliy can be observed. In he case of Brussels, he causaliy is bidirecional, boh in he shor and long run frequencies. The fuures equiy index volume Granger-causes he posiive shocks in erms of volailiy in he long run and he negaive shocks in he shor run. JEL CODES: C32, F37, G12, G15. KEYWORDS: Volailiy, fuures index producs, frequency domain Granger causaliy, Euronex. Corresponding auhor. address: claudiu.albulescu@ up.ro, claudiual@yahoo.com. Managemen Deparmen, Poliehnica Universiy of Timisoara, 2, P-a. Vicoriei, , Timisoara, Romania. ** CRIEF, Universiy of Poiiers, 2, Rue Jean Carbonnier, Bâ. A1 (BP 623), 86022, Poiiers, France. *** Faculy of Managemen, ICFAI Universiy Tripura, Kamalgha, Sadar, Wes Tripura, Pin , India. 349

2 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS INTRODUCTION The impac of derivaive producs on he volailiy of heir underlying asses was inensively assessed during las decades and i sill sands for a subjec of ineres nowadays. However, only few sudies approached he bidirecional relaionship which may exis beween he volume of derivaives and he financial volailiy. The heoreical lieraure on he opic developed in a single direcion and is endeavour was o emphasize he impac of derivaive producs on he volailiy of heir underlying asses. Neverheless, wo anagonising approaches were developed. The firs approach, which is he dominan one, suppors he idea ha he ransacions wih derivaives lead o an increase of he volailiy on he spo markes, hrough he leverage effec. This effec is suscepible o arac an increasing number of invesors on he derivaives markes, siuaion which may generae an augmenaion of he volailiy on he spo markes. The second approach shows ha he inroducion of derivaives diminishes he price volailiy of heir underlying asses (Skinner, 1989). This siuaion can be explained by he condiions which mus be accomplished by he underlying asses, in order o allow he derivaives ransacions, condiions which ameliorae he confidence of invesors on he spo marke, favouring hus a smaller volailiy. Moreover, he addiional informaion obained on he derivaives markes acs as a break for he financial volailiy (Chan e al., 2002). From he empirical poin of view, he influence of derivaive producs on he volailiy of he underlying asses was also analysed in wo differen ways. The firs approach compares financial volailiy before and afer he inroducion of derivaive producs and a large par of hese sudies discovered ha he inroducion of derivaives amplified he underlying asses volailiy (Robinson, 1994; Anoniou and Holmes, 1995; Reyes, 1996; Anoniou e al., 1998). The second approach invesigaes he impac of derivaives on he behaviour of heir underlying asses, including heir volailiy and has been inensively developed, reaching wo differen ses of resuls, depending on he heoreical background. A series of sudies showed ha he inroducion of derivaive producs have led o an increased volailiy on he spo markes, desabilising hus hese markes (see e.g., Figlewski, 1981; Sein, 1987). Oher sudies susained he opposie and demonsraed ha he inroducion of derivaive producs conribued o reducing he volailiy (see e.g., Powers, 1970; Schwarz and Laasch, 1991; Fedenia and Grammaikos, 1992). In he same line, more recenly, Kasman and Kasman (2008) reached he conclusion ha he fuures inroducion lowered he condiional volailiy of he ISE 30 index. Neverheless, a considerable number of papers eiher did no find a significan effec of derivaives on he marke volailiy (Edwards, 1988; Darra and Rahman, 1995) or repored a reduced effec (Dennisa and Sim, 1999; Jeanneau and Micu, 2003). Consequenly, he empirical lieraure provides mixed resuls (Charupa, 2006). These conradicory resuls are influenced by he analysed marke and reained periods, by he considered asses, by he volailiy calculaion and by he employed empirical mehodology. However, despie he well-defined heoreical framework and despie he empirical developmens, he analysis of he bidirecional causaliy beween he sock marke volailiy and derivaives is of recen ineres in he lieraure. If a sronger volailiy 350

3 CLAUDIU TIBERIU ALBULESCU, DANIEL GOYEAU AND AVIRAL KUMAR TIWARI is anicipaed, boh risk managers and speculaors decide o hedge or o srenghen heir posiions by means of derivaive producs. Therefore, a bidirecional relaionship has o be analysed and several heoreical argumens suppor his demarche. Firs, assuming a one-way causaliy beween derivaives and financial volailiy supposes he exisence of perfec markes wih homogeneous informaion, being also required ha he volume of ransacions does no provide informaion o he operaors in respec of he fuure volailiy of he underlying asses. Neverheless, some raders are beer informed han ohers and lead he marke. If hese markemakers are no able o accuraely anicipae he underlying asses reurn volailiy, he causaliy beween he volume of ransacions wih derivaive producs and he financial volailiy is no longer necessarily a unidirecional relaion, bu a bidirecional one. Anoher argumen supporing he bidirecional causaliy is relaed o lower coss associaed wih derivaive producs ransacions and hus, higher leverage effecs of hese insrumens. If he raders who are beer informed are suscepible of being more araced by derivaives, he volume of ransacions wih derivaive producs has o forego he price volailiy of heir underlying asses. Kim e al. (2004) sudied for he bidirecional causaliy and discovered a posiive conemporaneous relaionship beween he sock marke volailiy and he derivaives volume, while Sarwar (2005) esed he double poenial causaliy beween he volume of ransacions wih opions producs and he volailiy of he S&P 500 index. More recenly Albulescu and Tiwari (2013) have analysed he double causaliy beween derivaive producs and he price reurn of heir underlying asses on Eurnonex.liffe, using he hidden coinegraion echnique. All he above menioned sudies developed heir researches in he ime domain. The presen paper differs from he previous ones in several ways. Firs, i is based on he shor and long run Granger causaliy using he frequency domain approach of Breiung and Candelon (2006). This mehodology is heoreically appealing because he bidirecional causaliy can be observed for differen frequencies (i.e., period of cycles). The radiional approach acily ignores he possibiliy ha he srengh and he direcion of he Granger-causaliy can vary (Lemmens e al., 2008). Second, we idenify posiive and negaive shocks in erms of volailiy, employing he Hamilon s (2003) mehodology. This way, we are able o see if he bidirecional causaliy manifess differenly in he case of ne increases or decreases of he volailiy. Finally, we focus on he hisorical volailiy and he value of he derivaives volume. The value of he volume is more appropriae han he number of conracs in order o esimae he ampliude of ransacions involving derivaives. We also wan o see if an increasing volume of derivaives causes posiive or negaive shocks in erms of volailiy 1. If he derivaives volume Granger-causes posiive volailiy shocks, hen, he speculaive operaions prevail on he marke. Speculaors induce a higher volailiy on he sock markes hrough derivaives ransacion, in order o benefi aferwards from his increased volailiy. Reversely, 1 Posiive volailiy shocks are associaed wih an increased volailiy, above he average of he las observaions, while negaive shocks reveal a reducion of he volailiy below he average (see Secion 2 for a descripion of shocks compuaion). 351

4 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS if he derivaives volume Granger-causes negaive volailiy shocks, he hedging operaions are predominan. The reminder of he paper is srucured as follows. Secion 1 presens he frequency domain mehodology. Secion 2 describes he daa. Secion 3 depics he empirical resuls and he conclusion. 1. METHODOLOGY The key idea of his approach, which considers ha a saionary process can be described as a weighed sum of sinusoidal componens wih a cerain frequency, is relaed o he possibiliy of analysing separaely he slowly flucuaing componens and he quickly flucuaing componens of he variables (Croux and Reusens, 2013). Consequenly, he Granger-causaliy is calculaed for each individual frequency componen, and, o he bes of our knowledge, he financial volailiy derivaive producs relaionship has no ye been explored in he frequency domain. This approach complemens a convenional ime domain framework (McCullough, 1995). The causaliy beween wo variables x and y is usually analysed based on he Granger (1969) approach, which is mean o show how much of he curren y can be explained by he pas values of y, and hen o see wheher adding lagged values of x can improve he explanaion regarding he presen values of y. Consequenly, y is said o Granger-cause x if, x helps in he predicion of y, or if he coefficiens of he lagged x are saisically significan (and vice-versa). However, i is imporan o know ha he convenional Granger causaliy ess measure precedence and informaion conen, bu do no indicae he causaliy in is convenional sense. As Granger and Lin (1995) showed, he exen and he direcion of he causaliy differ beween frequency bands and he convenional Granger causaliy ess are unable o assess hem. Ye, i was Granger (1969) iself who advanced he idea of furher disenangling of he causaliy relaionship beween wo ime series and suggesed ha a specral-densiy approach would give a beer-off and more complee picure han an one-sho Granger causaliy measure 2. To overcome his limiaion, Breiung and Candelon (2006) proposed a new approach where he causal relaionship beween variables is decomposed by frequencies. However, he approach of Breiung and Candelon (2006) is based on he work of Granger (1969). This approach provides an elegan inerpreaion of he frequency domain Granger causaliy, as i decomposes he oal specral inerdependence beween he wo series ino a sum of insananeous, feedforward and feed-back causaliy erms (Tiwari, 2012). This new measure of he Granger causaliy can be applied across all frequencies and allows knowing exacly for which frequency one variable Granger-causes he oher. 2 The causaliy is supposed o apply across all periodiciies (e.g., in he shor run, over he business-cycle frequencies, and in he long run). 352

5 CLAUDIU TIBERIU ALBULESCU, DANIEL GOYEAU AND AVIRAL KUMAR TIWARI Therefore, in he presen sudy we employ he Breiung and Candelon (2006) approach o assess he Granger causaliy in he frequency domain 3. This approach has been used in quie a few sudies, limied o he moneary policy and sock markes analyses (Assenmacher-Wesche and Gerlach, 2007; Assenmacher-Wesche and Gerlach, 2008a; Assenmacher-Wesche and Gerlach, 2008b; Assenmacher- Wesche e al., 2008; Lemmens e al., 2008; Gronwald, 2009). The Breiung and Candelon (2006) approach can be described as follows: Le z be observed a form: 1,..., T and have a finie-order VAR represenaion of he z ( L) z (1) where... p ( L) I 1 L is a 2 pl 2 lag polynomial wih k L z z. k We assume ha he error vecor is a whie noise wih E( ) 0 and ' E( ), where is posiive. In order o simplify he descripion, any deerminisic erms in (1) are negleced. 1 Le G be he lower riangular marix of he Cholesky decomposiion G ' G, ' such ha E( ) I and G. If he sysem is assumed o be saionary, he Moving Average (MA) represenaion of he sysem is: z ( L) ( L) ( L) 1 ( L) (2) 21( L) 22 11( L) ( L) 21( L) 12( L) 1 L 22( ) 2 (3) where ( ) ( ) 1 L L and 1 ( L) ( L) G. Using his represenaion, he specral densiy of x can be expressed as: 1 i 2 i 2 f x ( ) { 11( e ) 12( e ) } (4) 2 3 In saisics, frequency domain describes he domain for analysis of mahemaical funcions or signals wih respec o frequency, raher han ime. 353

6 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS The measure of he causaliy suggesed by Geweke (1982) and Hosoya (1991) is defined as: 2f x ( ) M yx ( ) log (5) i 2 11 ( e ) 12( e log1 ( e 11 i i ) ) (6) 2 i If 12 ( e ) 0, hen he Geweke (1982) s measure will be zero and he y will no Granger-cause he x a frequency. If he elemens of z are I(1) and coinegraed, in he frequency domain, he measure of he causaliy can be defined by using he orhogonalized MA represenaion: ~ z ( L) ~ ( L) ~ ~ 1 where ( L) ( L) G, G, and G is a lower riangular marix, such ' ha E( ) I. Noe ha, in a bivariae coinegraed sysem, ' ~ (1) 0, where is a coinegraion vecor, such ha ' z is saionary (Engle and Granger, 1987). As in he saionary case, he resuling causaliy measure is: (7) M yx ~ i 12( e ) ( ) log1 (8) ~ i ( e ) 11 To es he hypohesis ha he y does no cause he x a frequency, we consider he null hypohesis: M y x ( ) 0 (9) wihin a bivariae framework. Following Breiung and Candelon (2006), we can presen his es by reformulaing he relaionship beween x and y in he VAR (p) equaion: x a1 x 1... a px p 1y 1... p y p 1 (10) 354

7 CLAUDIU TIBERIU ALBULESCU, DANIEL GOYEAU AND AVIRAL KUMAR TIWARI The null hypohesis esed by Geweke (1982), M ( ) 0, corresponds o he null hypohesis of: yx H0 : R( ) 0 (11) where is he vecor of he coefficiens of y and cos( ) cos(2)...cos( p) R( ) sin( )sin(2)...sin( p) (12) The ordinary F saisic for (13) is approximaely disribued as F( 2, T 2p) for ( 0, ). In order o perform he frequency domain Granger causaliy ess wihin a coinegraing framework, Breiung and Candelon (2006) sugges o replace x in he regression (10) by x, while he righ-hand side of he equaion remains he same 4. In coinegraed sysems he definiion of he causaliy a a frequency equal o zero is equivalen o he concep of long run causaliy and, in a saionary framework, here is no long run relaionship beween he ime series. A series may neverheless explain fuure low frequency variaion of anoher ime series. Hence, in a saionary sysem, he causaliy a low frequencies implies ha he addiional variable is able o forecas he low frequency componen of he variable of ineres, one period ahead. 2. DATA The derivaives daa were exraced from Euronex.liffe daabase and cover he period 2001: :06 (monhly daa). This imeframe is large enough o presen significan evoluions of he derivaives volume and of he index reurns volailiy, which proves o be high during crisis periods. The volume of fuures equiy index producs for each sock marke is described in Fig See Breiung and Candelon (2006) for a deailed discussion in he case when one variable is I(1) and oher is I(0). 355

8 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS FIGURE 1. FUTURES EQUITY INDEX PRODUCTS TRADED ON EURONEXT.LIFFE (BILL. EUR) Source: Euronex.liffe. We can observe ha in he analysed period, London, Paris and Amserdam represen he main sock markes for ransacions wih fuures equiy index producs, while Brussels and Lisbon lag far behind. We can also see ha he derivaives volume is higher around he financial markes urbulences and decreases laer. Fig. 2 illusraes he rend of he sock indexes which are represenaive for he Euronex.liffe sock markes. We observe heir correlaion and also an increased volailiy afer he crisis ouburs. FIGURE 2. STOCK INDEXES (CLOSE VALUES) Source: Yahoo.finance. In order o proceed wih he daa analysis and o ensure he saionariy of he series, a number of ransformaions were necessary. Firs, we have derended boh he derivaives volume and he sock indexes series, using X-12-ARIMA mehodology for monhly daa (3x5 filers) 5. Second, we have compued he naural logarihm of 5 Kim e al. (2004) proceeded in a similar way in heir research, using an ARIMA (10, 0, 10) model. 356

9 CLAUDIU TIBERIU ALBULESCU, DANIEL GOYEAU AND AVIRAL KUMAR TIWARI boh series. Third, we have calculaed he firs difference for boh he derivaives volume and he sock indexes 6. Finally, we have assessed he financial volailiy based on he sandard deviaion of he obained index reurns, using a 12 monhs rolling window (-12:). Afer he idenificaion of he hisorical volailiy, we have compued he posiive and negaives shocks, employing he Hamilon s (2003) mehodology, relaive o ne increases and decreases in he oil price. Adoping he same approach, we ransform each volailiy series ino wo differen series characerising he posiive and negaive shocks, respecively. If he volailiy in monh is higher ha is level over he pas 6 monhs, hen a posiive shock occurs. I is equal o he difference beween he level of he volailiy in he monh and is maximum values over he previous 6 monhs.. If he volailiy in monh is lower ha is level over he pas 6 monhs, he absence of he shock is recorded. The same reasoning applies for he negaive shocks, according o he following wo formulae: vol IF vol MAX( vol : vol ), vol MAX( vol : vol ),0) (13) ( vol IF vol MIN( vol : vol ), vol MIN( vol : vol ),0) (14) ( where vol + and vol - represen posiive and negaive volailiy shocks 3. RESULTS The ransformaion of daa described in he previous secion allows o obain saionary series. For each sock marke we firs compue a VAR and we reain he Schwarz informaion crierion for he lag lengh selecion. In wha follows, we presen he Granger causaliy resuls in frequency domain, for he Brussels sock exchange (Fig. 3), for he Lisbon sock exchange (Fig. 4) and for hose of London, Paris and Amserdam (Fig. 5). These figures repor he es saisics, along wih heir criical values (5% grey broken lines; 10% black broken lines) for all frequencies (which are expressed as fracion of ) in he inerval (0, ). On he horizonal axis, he frequency is ranslaed ino a cycle or periodiciy of T monhs by T 2 /, where T is he period. Thus, he frequency of a cycle is relaed o is period T, assessed by he number of observaions, and akes is usual value. Consequenly, a frequency of / 4 corresponds o a period of 8 observaions (monhs) 7. The variable x 1 represens he derivaives volume while x 2 sands for he underlying asse volailiy/shocks in erms of volailiy. 6 The firs difference of he naural log of he sock index is associaed in his case wih he index reurn. 7 Noe ha, since high frequencies are having shor periods and vice versa, he figures of he Granger causaliy in he frequency domain sand reversed, wih shor erm flucuaions/cycles a he righ end and long erm movemens/cycles a he lef side. 357

10 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS FIGURE 3. GRANGER BIDIRECTIONAL CAUSALITY IN THE FREQUENCY DOMAIN FOR BRUSSELS Noe: The firs char from Figure 3 analyses he bidirecional causaliy in erms of general volailiy, while he second and he hird char analyse he bidirecional causaliy in erms of posiive and negaive volailiy chocks respecively. Based on Fig. 3, we can firs analyse if he fuures conracs volume Granger-causes he index reurn volailiy (he grey coninuous line) 8. I is obvious ha, a 95% confidence level, he derivaives volume is able o predic he volailiy of heir underlying asses, boh a low frequencies, in he range (0,1 ), and high frequencies, wih (2.5,3.2 ). Furhermore, if we look o he posiive shocks in erms of volailiy (Figure 3b), we can see ha in he long erm (low frequencies), hey are prediced by he derivaives volume. A he same ime, in he shor run (high frequencies), he volume of derivaives Granger-causes he negaives shocks in erms of volailiy, in he range (2.2,3.2 ) Fig. 3c. These findings show ha, in he shor run, he hedging operaions prevail, while in he long run, he speculaive operaions are dominan, as he derivaives cause an exreme volailiy. These oucomes highligh he sraegy behind he decisions made by speculaors wih he purpose of aking advanage of he increased volailiy induced on he marke. The second sep is o see if he index reurns volailiy Granger-causes he fuures conracs volume on he Brussels sock exchange, analysing hus he black coninuous line. Figure 3a shows ha boh in he shor and long runs he null hypohesis of no causaliy is rejeced a 5% level of significance. Consequenly, he pas values of he index reurns volailiy predic he derivaives volume 9. No causaliy can be observed in he case of posiive shocks (Figure 3a). Neverheless, in he case of negaive shocks a 90% confidence level, i seems ha, in he shor run, he volailiy Granger-causes he derivaives volume in he range (0.3,0.6). 8 We associae his causaliy wih speculaive aciviies (see he Secion 1). 9 We associae his wih hedging aciviies (a higher volailiy implies an increase of derivaives conracs). However, i is no very clear if hese new conracs are designaed o cover risks on he spo marke or o speculae an increased volailiy. If we make a comparison wih he Granger causaliy, going from derivaives o volailiy, we observe ha he las one is sronger. In his case, we can asser a dominance of he speculaive aciviies wih derivaives, on he Brussels sock exchange. 358

11 CLAUDIU TIBERIU ALBULESCU, DANIEL GOYEAU AND AVIRAL KUMAR TIWARI All in all, in he case of he Brussels sock exchange we observe a bivariae causaliy beween he derivaives volume and he volailiy of heir underlying asses, boh in he shor and long runs 10. The fuures equiy index volume predics posiive shocks in erms of volailiy in he long run and negaive shocks in he shor run. For he Lisbon sock exchange, he null hypohesis on no causaliy is no rejeced a 5% level of significance for all frequencies (Fig. 4). This implies ha he derivaives volume does no Granger-cause he index reurn volailiy (he gray line Fig. 4a). A he same ime, he volailiy does no Granger-cause he derivaives volume (he black coninuous line). Regarding he shocks in erms of volailiy (Figs. 4b and 4c), he siuaion looks similar. To conclude, we observe a bidirecional Granger causaliy relaionship which is no however validaed by he confidence level ess. Similar resuls were repored by Albulescu and Tiwari (2013) in a hidden coinegraion framework. FIGURE4. GRANGER BIDIRECTIONAL CAUSALITY IN THE FREQUENCY DOMAIN FOR LISBON Noe: The firs char from Figure 4 analyses he bidirecional causaliy in erms of general volailiy, while he second and he hird char analyse he bidirecional causaliy in erms of posiive and negaive volailiy chocks respecively. In he Fig. 5 we have grouped he resuls of he causaliy analysis for he Amserdam, London and Paris sock exchanges, as he siuaion is similar for hese markes. The findings show ha he derivaives volume does no Granger-cause he volailiy of he underlying asses, as he null hypohesis of no predicabiliy is no rejeced a 5% level of significance for all frequencies in he inerval ( 0, ) 11. This implies ha he fuures producs volume is unable o forecas he low and high frequency componens of he volailiy (or of he posiive and negaive shocks in erms of volailiy), one period ahead. The findings prove ha in he large sock exchange markes he predominance of speculaive or hedging operaions canno be 10 A bidirecional causaliy beween he derivaives volume and he index reurn volailiy was repored in he ime domain by Sarwar (2005). 11 Darra and Rahman (1995) showed in heir urn he absence of he relaionship beween he derivaives and financial volailiy in a ime domain analysis. 359

12 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS observed. Furhermore, on hese sock markes, invesors are eiher specialised on derivaives or spo markes ransacions and do no inerfere on he wo markes in he same ime. This is also due o he difficuly o influence individually a large marke in comparison o a small one. FIGURE 5. GRANGER BIDIRECTIONAL CAUSALITY IN THE FREQUENCY DOMAIN FOR AMSTERDAM, LONDON AND PARIS Noe: The rows of chars represen he Amserdam, London and Paris sock exchange. The firs char from each row analyses he bidirecional causaliy in erms of general volailiy, while he second and he hird char analyse he bidirecional causaliy in erms of posiive and negaive volailiy chocks respecively. Subsequenly, we also analyse he shor and long run Granger causaliy, going from he financial volailiy owards he derivaives volume. We discover he same siuaion as in he previous case for Amserdam, London and Paris sock exchanges. We conclude ha here is no evidence of bidirecional causaliy beween he financial volailiy and he derivaive producs on hese markes. 360

13 CLAUDIU TIBERIU ALBULESCU, DANIEL GOYEAU AND AVIRAL KUMAR TIWARI These mixed resuls deermine us o check for he robusness of our findings. Consequenly, we perform a resampling of he iniial daa-series, and we es for he presence of he same characerisics in daa, afer 2003, in order o avoid he influence of he sock marke crash from 2000 o The resuls are similar, excep for he London sock exchange, where a bidirecional bu non-significan causaliy appears (Appendix A). However, alogeher our resuls are robus and are similar o hose obained using ime domain approaches for a similar period. Albulescu and Tiwari (2013) showed in heir urn ha Brussels and Lisbon sock exchanges presen a higher number of hidden coinegraion siuaions, as compared o more developed markes. All in all, our findings shows ha on he small marke, he bivariae relaionship beween derivaives and financial volailiy is more inense, as he financial shocks are much more easily perceived by he marke players. CONCLUSION In his paper, we used he frequency domain approach of Breiung and Candelon (2006) o invesigae he shor and long run bidirecional Granger causaliy beween he volume of he fuures equiy index producs and he volailiy of heir underlying asses. We analysed he case of five sock exchange markes, members of he Euronex.liffe, for he period Firs, we have ransformed he daa in order o obain heir saionariy and we have chosen he VAR lag lengh based on he Schwarz crierion. Second, we have compued he bivariae causaliy for each financial marke. Our resuls can be summarized as follows. In he case of he Brussels sock exchange, we found bidirecional causaliy beween derivaives and he volailiy of heir underlying asses, boh in he shor and long runs. Afer compuing he posiive and negaive shocks in erms of volailiy, we also have discovered ha he derivaives volume predics posiive shocks in erms of volailiy in he long run and predics negaive shocks in he shor run. In he case of he Lisbon sock exchange, he bidirecional causaliy is no validaed by he significance or by he confidence level, while for Amserdam, London and Paris, his relaionship does no exis in a frequency domain analysis. Consequenly, he causaliy can be observed for he small sock exchange markes members of Euronex.liffe, while for he large markes, i is absen. The resuls are robus when using he resampling approach. Due o he fac ha small markes as Brussels or Lisbon can be influenced by individual players, being hus more vulnerable, our resuls are no surprising. I is easy o observe on hese markes he predominance of he speculaive or of he hedging operaions. However, for Amserdam, Paris and London, he bidirecional relaionship is absen because individual invesors can hardly influence by hemselves a large marke. Moreover, on large markes, invesors are eiher specialized on fuures or spo markes ransacions and are rarely involved in boh markes in he same ime, in order o ake advanage from volailiy increases 361

14 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS REFERENCES Albulescu, C.T. and K.A., Tiwari, Asymmeric causaliy beween fuures conracs and he reurn volailiy of heir underlying asses on Euronex.liffe, Journal of Economic and Financial Modelling, 1, pp Anoniou, A. and P., Holmes, Fuures Trading, Informaion and Spo Price Volailiy: Evidence for he FTSE-100 Sock Index Fuures Conrac Using GARCH, Journal of Banking & Finance, 19, Anoniou, A., O. Holmes and R. Priesley, The effecs of sock index fuures on sock volailiy: An analysis of he asymmeric response of volailiy o news, Journal of Fuures Markes, 18, pp Assenmacher-Wesche, K. and S. Gerlach, Money a Low Frequencies, Journal of he European Economic Associaion, 5, pp Assenmacher-Wesche, K. and S. Gerlach, 2008a. Inerpreing Euro Area Inflaion a High and Low Frequencies, European Economic Review, 52, pp Assenmacher-Wesche, K. and S. Gerlach, 2008b. Money Growh, Oupu Gaps and Inflaion a Low and High Frequency: Specral Esimaes for Swizerland, Journal of Economic Dynamics and Conrol, 32, pp Assenmacher-Wesche, K., S. Gerlach and T. Sekine, Moneary Facors and Inflaion in Japan, Journal of he Japanese and Inernaional Economies, 22, pp Breiung, J. and B. Candelon, Tesing for Shor and Long-Run Causaliy: A Frequency Domain Approach, Journal of Economerics, 132, pp Charupa, N., The effec of derivaive rading on he underlying markes: Evidence from Canadian insalmen receips rading, Inernaional Review of Economics and Finance, 15, pp Chan, K., Y.P. Chug and W-M. Fong, The Informaional Role of Sock and Opion Volume, The Review of Financial Sudies, 15, pp Croux, C. and P. Reusens, Do sock prices conain predicive power for he fuure economic aciviy? A Granger causaliy analysis in he frequency domain, Journal of Macroeconomics, 35, pp Darra, A.F. and S. Rahman, Has fuures rading aciviy causes sock price volailiy?, Journal of Fuures Markes, 15, pp Dennisa, S.A. and A.B. Sim, Share price volailiy wih he inroducion of individual share fuures on he Sydney Fuures Exchange, Inernaional Review of Financial Analysis, 8, pp Edwards, F.R., Fuures rading and cash marke volailiy: Sock index and ineres rae fuures, Journal of Fuures Markes, 8, pp Engle, R.F. and C.W.J. Granger, Co-Inegraion and Error Correcion: Represenaion, Esimaion, and Tesing, Economerica, 55, pp Fedenia, M. and T. Grammaikos, Opions Trading and he Bid-Ask Spread of he Underlying Socks, Journal of Business, 65, pp Figlewski, S., Fuures Trading and Volailiy in he GNMA Marke, Journal of Finance, 36, pp Geweke, J., Measuremen of linear dependence and feedback beween muliple ime series, Journal of American Saisical Associaion, 77, pp Granger, C.W.J., Invesigaion causal relaions by economeric models and cross-specral mehods, Economerica, 37, pp

15 CLAUDIU TIBERIU ALBULESCU, DANIEL GOYEAU AND AVIRAL KUMAR TIWARI Granger, C.W.J. and J-L. Lin, Causaliy in he long run, Economeric Theory, 11, pp Gronwald, M., Reconsidering he macroeconomics of he oil price in Germany: Tesing for causaliy in he frequency domain, Empirical Economics, 36, Hamilon, J.D., Wha is an oil shock?, Journal of Economerics, 113, pp Hosoya, Y., The decomposiion and measuremen of he inerdependence beween second-order saionary process, Probabiliy Theory and Relaed Fields, 88, pp Jeanneau, S. and M. Micu, Volailiy and derivaives urnover: a enuous relaionship, BIS Quarerly Review, March, pp Kasman, A. and S. Kasman, The impac of fuures rading on volailiy of he underlying asse in he Turkish sock marke, Physica A, 387, pp Kim, M., G.R. Kim and M. Kim, Sock marke volailiy and rading aciviies in he KOSPI 200 derivaives markes, Applied Economics Leers, 11, pp Lemmens, A., C. Croux and M.G. Dekimpe, Measuring and Tesing Granger Causaliy Over he Specrum: An Applicaion o European Producion Expecaion Surveys, Inernaional Journal of Forecasing, 24, pp McCullough, B.D., A specral Analysis of Transacions Sock Marke Daa, The Financial Review, 30, pp Powers, M.J., Does Fuures Trading Reduce Price Flucuaions in he Cash Markes?, American Economic Review, 60, pp Reyes, M.G., Index fuures rading and sock price volailiy: Evidence from Denmark and France, Journal of Economics and Finance, 20, pp Robinson, G., The effec of fuures rading on cash marke volailiy: Evidence from he London sock exchange, Review of Fuures Markes, 14, pp Sarwar, G., The Informaional Role of Opion Trading Volume in Equiy Index Opions Markes, Review of Quaniaive Finance and Accouning, 24, pp Schwarz, T.V. and F. Laasch, Dynamic Efficiency and Price Leadership in Sock Index Cash and Fuures Markes, Journal of Fuures Markes, 11, pp Skinner, D., Opions markes and sock reurn volailiy, Journal of Financial Economics, 23, pp Sein, J.C., Informaion Exernaliies and Welfare Reducing Speculaion, Journal of Poliical Economy, 95, pp Tiwari, A.K., Tax burden and GDP: Evidence from Frequency Domain Approach for he USA, Economics Bullein, 32, pp

16 REVISITING THE FINANCIAL VOLATILITY-DERIVATIVE PRODUCTS RELATIONSHIP ON EURONEXT.LIFFE USING A FREQUENCY DOMAIN ANALYSIS APPENDIX A. ROBUSTNESS CHECK FOR THE SUB-PERIOD 2003: :06 Noe: The rows of chars represen he Amserdam, Brussels, Lisbon, London and Paris sock exchange. The firs char from each row analyses he bidirecional causaliy in erms of general volailiy, while he second and he hird char analyse he bidirecional causaliy in erms of posiive and negaive volailiy chocks respecively. 364