Available online at ScienceDirect. Procedia Computer Science 55 (2015 )

Transcription

1 Available online a ScienceDirec Procedia Compuer Science 55 (215 ) Informaion Technology and Quaniaive Managemen (ITQM 215) Volailiy Spillovers in he CSI3 Fuures and Spo Markes in China: Empirical Sudy Based on Discree Wavele Transform and VAR-BEKK-bivariae GARCH Model Shiyun Li a * a China Universiy of Poliical Science and Law Beijing, 149, China Absrac China s inroducion of CSI3 fuures in 21 has aroused widespread aenion o wheher he sock index fuures marke has effecively sabilized price flucuaions of is spo marke in he pas four years. Since he prices of CSI3 fuures and CSI3 conain numerous noises and flucuae drasically over ime, his paper applies discree wavele ransform o denoise hese series by decomposing and reconsrucing heir reurn. Furher, a VAR-BEKK-bivariae GARCH model is esablished o sudy he volailiy spillover effecs. Empirical resuls show ha a bi-direcional volailiy spillover effec exiss beween CSI3 fuures and he spo marke, bu he former affecs he laer in a more obvious way. The inroducion of CSI3 fuures also conribues o he sabilizaion of he sock marke. 215 Published The Auhors. by Elsevier Published B.V. This by Elsevier is an open B.V. access aricle under he CC BY-NC-ND license (hp://creaivecommons.org/licenses/by-nc-nd/4./). Selecion and/or peer-review under responsibiliy of he organizers of ITQM 215 Peer-review under responsibiliy of he Organizing Commiee of ITQM 215 Keywords: CSI3 fuures; discree wavele ransform; volailiy spillovers; VAR-BEEK-bivariae GARCH model 1. Inroducion On April 16h, 21, China formally launched CSI3 fuures, which symbolizes he inroducion of a mechanism for shor sales of sock, providing an efficien vehicle o disclose marke informaion meanwhile. Theoreically, sock index fuures have imporan funcions including price discovery, volailiy sabilizaion, hedging, ec., and serve as a burgeoning bu efficien risk managemen ool. In pracice, however, a mass of irraional speculaive ransacions does exis in he fuures marke, increasing he risk of shor-erm flucuaions in he spo marke. Bad news magnified by he leverage effec also aggravaes he poenial jeopardy o he spo marke. Thus, i has already become a ho spo in Chinese academy wheher CSI3 sock index fuures marke, * Corresponding auhor. Tel.: address: @qq.com Published by Elsevier B.V. This is an open access aricle under he CC BY-NC-ND license (hp://creaivecommons.org/licenses/by-nc-nd/4./). Peer-review under responsibiliy of he Organizing Commiee of ITQM 215 doi:1.116/j.procs

2 Shiyun Li / Procedia Compuer Science 55 ( 215 ) he "shadow marke" of CSI3 sock index marke, sabilizes he sock price around is real value, and wha he dynamic relaion beween hem is. This paper chooses he CSI3 fuures marke and is spo marke as subjecs, rying o answer he following quesions via empirical analysis: wha is he volailiy spillover relaion beween CSI3 fuures and is spo marke? How does informaion flows beween hem? Does he inroducion of CSI3 fuures conribue o is spo marke s sabiliy? Should hese financial innovaions be encouraged in he presen Chinese financial marke? Exploring hese quesions allows us o unravel he relaionship beween CSI3 fuures and is sock marke for financial regulaory deparmens and invesors concerned, which also helps China s furher developmen of he financial marke. 2. Lieraure review Mos lieraure applied he GARCH family models o characerize price volailiy in he sock index fuures and is spo marke. These models are known for heir consideraion in modelling volailiy clusering and asymmery ha are ypical of sock index and is fuures prices. In sudying he volailiy spillover effec beween he sock index fuures and is spo marke, mos researchers agreed ha he relaion was generally bi-direcional, bu he direcion of volailiy spillover may vary wih differen counries, wih well-developed financial markes sock index fuures playing a leading role in spill. Koumos and Tucker (1996) [1] analysed daily S&P5 index fuures and spo prices. They found ha he fuures volailiy led he spo for one day, and he spillover effec was asymmeric. Tse (1999) [2] analyses DJIA index fuures and spo, suggesing bi-direcional spillover effec in he wo markes, wih he fuure markes spillover being more eviden. Bhar (21) [3] sudied daily Ausralian sock index fuures and spo daa and suggesed ha markes uilized volailiy spillover effec o ransfer informaion. In China s academia, Liu e al. (211) [4] analysed CSI3 and fuures wih a bivariae EGARCH model, finding ha he volailiy spillover effec is larger in he spo marke han he fuures marke, and suggesed ha boh good and bad news had leverage effec on marke reurns. Zhou Pu e al. (213) [5] applied boh linear and nonlinear Granger Causaliy Tes, co-inegraion es and buil a VECM model o analyse informaion spillover in he CSI3 fuures and spo marke, discovering only linear variance informaion spillover from he spo o fuures, bu remarkable nonlinear variance informaion spillover beween hem. The majoriy of exising research uilized bivariae ECM-EGARCH model, bu his model conains many parameers and may no guaranee he posiive definieness of is residual s variance-covariance marix, which quesioned he validiy of he model. To solve his problem, Engle and Kroner (1995) [6] proposed a parameric model wih posiive definieness resricions, namely he BEKK-GARCH model, and hus offered an effecive device for volailiy modelling. This new ype of GARCH is known for is ease in saisfying he posiive definieness of he variance-covariance marix as well as is efficiency in reducing parameers for esimaion. Compared o radiional GARCHs, he BEKK-GARCH has grea advanage in analysing he volailiy spillover effec of he sock index fuures marke. Thus in his paper, we uilize a VAR-BEEK-GARCH model o explore he volailiy spillover effec beween CSI3 sock index fuures marke and is spo marke in China. 3. Daa selecion and discree wavele ransform 3.1. Daa selecion We choose he 18 closing prices of CSI3 sock index and CSI3 sock index fuures from April 16h, 21 o Sepember 25h, 214 (Daa sources: Wind Daabase). To avoid drasic flucuaions of financial prices series, we ransform he prices ino daily reurns using logarihmic difference, namely R 1 log(p / P ), 1 and obain 179 reurn raes since CSI3 fuures inroducion in China. Figure 1 plos he reurn raes of CSI3 and CSI3 fuures ogeher. As he picure shows, CSI3 and is fuures share much in common in boh rend and volailiy, and he volailiy clusers in cerain periods.

3 382 Shiyun Li / Procedia Compuer Science 55 ( 215 ) II III IV I II III IV I II III IV I II III IV I II III HS 3_S POT HS 3_ F UTUR E Fig1 reurns of CSI3 Spo and CSI3 Fuures 3.2. Discree wavele ransform Because high-frequency CSI3 and is fuures reurns include inerfering informaion such as shor-erm supply and demand flucuaions, innovaion shocks, speculaion behaviour, ec., daa may deviae from heir rue value and conain grea noises. The exisence of Calendar effecs and oher cyclical behaviours also makes quaniaive analysis based on original daa lacks robusness. Thus, his paper applies wavele analysis o preprocess he reurns series. 1. The raionale and superioriy of wavele ransform The raionale of he wavele ransform can be summarized as below: by decomposing he signal ino differen levels, we obain he low frequency par of he signal ha corresponds o is main characerisics and he high frequency par of he signal ha corresponds o is deails. Wih he increase of decomposiion layers, we can observe he signal from coarse o fine. The essence of wavele ransform is o decompose signals ino low and high frequency pars by using high-pass and low-pass filers. Wavele ransform provides fine localiy for he series in boh ime and frequency spaces. I can subdivide high-frequency signal in ime space and low-frequency signal in frequency space hrough flexing and ranslaing operaions so ha we can focus on any deail of he signal. Thus, wavele ransform are widely applied in ime-frequency analysis, noise separaion, weak signal exracion and signal idenificaion, ec.. Since high-frequency fuures and spo reurns conain srong noises in high frequency, wavele ransform can effecively remove hese noises while reain he low-frequency and sable characerisics of he original signal. Above all, wavele ransform shows enormous superioriy in dealing wih he high-frequency and noisy fuures and spo daa. 2. The decomposiion and reconsrucion of reurns series of CSI3 fuures and spo Since Daubechies wavele (Db wavele) has superioriy in decomposing and rebuilding signals, his paper chooses DbN wavele funcion as he wavele base. Considering boh decomposiion accuracy and signal smoohness, we choose Db4 wavele o decompose and rebuild CSI3 fuures and spo reurn series o ge he acual rend of he original reurns. More precisely, seps are aken as follows:

4 Shiyun Li / Procedia Compuer Science 55 ( 215 ) (1) Decompose he sock index and fuures reurns. Resuls are shown in Figure 2 and 3. We denoe lowfrequency signal wih a4 and high-frequency signal wih d1, d2, d3, d4. d1 d2 d3 d4 a a4 d4 d3 d2 d Fig2 decomposed reurns of sock index Fig3 decomposed reurns of sock index fuures (2) Reain he low-frequency wavele coefficiens bu se he high-frequency wavele coefficiens o. Then use he above wavele coefficiens o rebuild he sock index and fuures reurns. Resuls are shown in Figure 4 and Figure 5. We denoe a4 as he sock index and fuures reurns afer rebuilding, and furher named hem as Rs and Rf, respecively. Compared wih heir original reurns series before wavele ransform, he srong noises of he sock index and fuures reurns have already been removed and heir rend becomes more obvious. Original reurns Original reurns a4 a4-2 Fig4 rebuil sock index reurns -2 Fig5 rebuil sock index fuures reurns 4. Empirical analysis 4.1. Saionary es and VAR model esablishmen ADF uni roo es examines he saionariy of he sock index fuures and spo reurns series afer wavele decomposiion and reconsrucion. Afer aking he ADF es, boh CSI3 sock index fuures and spo reurn series prove o be saionary, so a VAR (p) model can be esablished for empirical analysis. According o Akaike Informaion Crieria, we choose lag 6 as he order of he VAR model (i.e. building a VAR(6) model). The Granger Causaliy Tes (able 1) shows ha sock index fuures and heir spo are Granger reasons for each oher, indicaing a bi-direcional price guidance beween he sock index fuures and sock marke. Table1 Granger Causaliy Tes of CSI3 fuures and spo

5 384 Shiyun Li / Procedia Compuer Science 55 ( 215 ) Pairwise Granger Causaliy Tess Null Hypohesis: Obs F-Saisic Prob. HS3_SPOT does no Granger Cause HS3_FUTURE HS3_FUTURE does no Granger Cause HS3_SPOT BEKK-Bivariae GARCH (1, 1) Model Furher examinaion on he VAR model reveals srong serial correlaion beween he squared residuals, and his ARCH effec conribues o volailiy clusering. A GARCH model can hus be esablished o furher explore he volailiy spillover effec beween CSI3 and is fuures marke. Because he BEKK model shows advanages in reducing he number of parameers esimaed compared wih ordinary GARCHs and can guaranee he posiive definieness of he variance-covariance marix under weak condiions, his paper selecs a BEKK-GARCH (1,1) model (whose ARCH and GARCH erms orders are widely considered adequae in describing financial marke volailiy, while mulivariae GARCH model can fully porray he correlaion of marke flucuaion in a dynamic way), and build he VAR-BEKK-bivariae GARCH (1,1) model as follows: We firs inroduce he mean equaion defined by he VAR model: p Rs a a Rs a Rf 1 11, i i 12, i i 1 i1 i1 p p Rf a a Rf a Rs 2 21, i i, i i 2 i1 i1 h11, h12, Here 1 2 are condiional residuals. We define H as he residual s condiional h21, h, variance-covariance marix wih informaion known a ime -1 and before, and furher srucure a variance equaion as follows: H BH B A A Here 21 is a lower riangular consan marix, and is seing guaranees he posiive definieness of H. A 21 measures he ARCH effec while B 21 measures he GARCH effec. The formula is equivalen o: 2 h11, h12, h11, 1 h12, , 1 1, 1 2, h21, h, h21, 1 h, , 11, 1 2, 1 Equivalenly, we ge h h 2 h h 2 2 h 11, , , 1 21, , , 1 2, , , 1 h h 2 h h , , , 1, , , 1 2, 1 2, 1 h h ( ) h h ( ) , , , 1 21, , , 1 2, , 1 Here 11, h denoes he condiional variance of he sock index reurns; h denoes he condiional variance of, h he sock index fuures reurns; 12, denoes he condiional covariance of spo and fuures reurns. Examining he volailiy spillover effec ha he fuures marke has on he spo marke is equivalen o examining wheher p

6 Shiyun Li / Procedia Compuer Science 55 ( 215 ) and 21 are significanly zero, so we can se he null hypohesis as H: Similarly, we can examine he volailiy spillover effec ha spo has on fuures reurns, and se he null hypohesis as H: If here is no direc relaionship beween spo and fuure marke, he condiional variance of fuures and spo reurns will only be deermined by heir own pas values, and hus he non-diagonal elemens H of he marix are all. The associae null hypohesis will be : Based on he discussion above, we solve he BEKK-bivariae GARCH (1,1) model by applying Marquard T algorihm in esimaion, and choose 1 l( ) Tlog(2 ) (ln H ) H as he likelihood funcion. 2 1 According o AIC, lag 2 is chosen as he order of he VAR model, and his indicaes ha an VAR(2) model is used as he mean equaion of he GARCH model. Table2 he variance equaion and Wald resricion ess on volailiy spillover effec (.1) Coefficien marix Coefficien marix A Coefficien marix B (.1152) (.1) (.) (.1198) H: no volailiy spillover from he fuures marke o he spo marke 2 (2) (.11) (.125) (.332) (.314) (.318).666 (.31) H : no volailiy spillover from he spo * marke o he fuures marke (2) ** * H : no volailiy spillover beween he wo markes (4) Noe: +, P<.1; *, P<.5; **, P<.1;, P<.1. In brackes are S.E. of he esimaed parameers. 2 ** ** Table 2 shows he esimaed resul of he variance equaion. We find ha,, 11 are significanly differen from zero a 1% level, which means ha he ime-varying variance characerisic of he sock index and he ime-varying variance as well as volailiy persisence characerisics of sock index fuures are well described. This implies ha he volailiy of he sock index can be explained by innovaions in is marke, while he volailiy of he sock index fuures can be explained by boh innovaions in he fuures marke and he fuures previous volailiy, and boh of hem sugges posiive correlaions. Meanwhile, he esimaed parameers , , , shows obvious bi-direcional volailiy spillover effec beween sock index fuures and spo marke. However, he former coefficiens are much larger han he laer for boh alpha and bea, which means ha he effec he fuures marke has on he spo marke is much larger han he spo marke does on he fuures marke, confirming he leading posiion of fuures marke relaive o he spo marke. Invesigaing he hree hypoheses using Wald resricion es, we can also confirms his volailiy spillover effec beween he sock index and is fuures marke. Resuls show ha all hese hypoheses are refused a 1% level, subsaniaing he bi-direcional volailiy spillover effec beween he wo markes. Addiional examinaion shows no ARCH effec in residuals, proving he validiy of applying BEKK-GARCH models o furher delineae he VAR model. Based on he above model, figure 1 shows a synergic rend of sock index fuures and spo marke volailiy in a more inuiive way. We observe ha since he inroducion of CSI3 fuures in April, 21, he volailiy of boh he sock index and is fuures markes plunged dramaically, and he flucuaion became mild a a low level afer only a monh, characerized by a synergic flucuaion rend in he wo markes. This furher illusraes he

7 386 Shiyun Li / Procedia Compuer Science 55 ( 215 ) synergy of wo markes flucuaion, and shows he abiliy of he markes o reac concurrenly o common informaion. A he same ime, he resul highlighs he advanage of he fuures marke in sabilizing he flucuaion of he sock index s price, suggesing diversified financial insrumen s funcion in he developmen and perfecion of financial markes II III IV I II III IV I II III IV I II III IV I II III VAR_Y1 VAR_Y2 COV_Y1Y2 5. Conclusion Fig 6 synergic volailiy of sock index and fuures marke This paper uilizes four years CSI3 and is fuures reurns daa since April 16h, 21 o dae. We firs apply discree wavele ransform o denoise, decompose and reconsruc he reurns for furher analysis. Then we esablish a VAR- BEKK-bivariae GARCH model o sudy volailiy Spillovers. Empirical resuls are as follows: Firs, here is a bi-direcional bu asymmeric volailiy spillover effec beween CSI3 fuures and is spo marke, wih he influence of he fuures volailiy o he spo s volailiy sronger han ha of he spo s o he fuures s. This conclusion subsaniaes he leading role played by he fuures marke o he spo marke in China. By comparing he volailiy spillover effec beween he wo markes, we can have a beer undersanding abou how informaion flows and amplifies in he process, and effecively conrol risks in advance. Financial regulaion agencies should pay aenion o he linkage beween he spo and fuures markes and keep aler o volailiy ransmission beween hem especially when prices flucuae violenly, so ha hey can beer regulae and ensure he balance and sabiliy of CSI3 fuures marke and is spo marke. Second, he inroducion of CSI3 fuures can lead o an immediae and significan volailiy decrease in he sock marke, and can also succeed in keeping he volailiy a a low level hereafer. This underline he imporance of diversified financial insrumen for he sabilizaion and perfecion of Chinese exising financial markes, poining ou he necessiy for China o embrace powerful financial ools for fuure developmen. The inroducion of CSI3 sock index fuures represens a milesone of China's financial marke reform in achieving muli-level developmen of China's capial markes. I provides diversified invesmen sraegies for invesors, improves he capial leverage of he financial insiuion, promoes he financial marke s liquidiy and efficiency, and expands he breadh and deph of he financial marke. Wih he opening of China s financial markes, ogeher wih a beer regulaion sysem and a macro environmen, complemenary fuures and spo will arac more capial ino he sock marke, and his promoe is prosperiy and liquidiy. Wih he gradual mauriy of he fuures marke, is leading posiion o he spo will become more significan, and is hedging, risk managemen funcion will also be brough ino full play, hus effecively reducing he volailiy of he sock marke and furher promoing he developmen of China's financial marke.

8 Shiyun Li / Procedia Compuer Science 55 ( 215 ) References: 1Koumos G, Tucker M. Temporal relaionships and dynamic ineracions beween spo and fuures sock markes.journal of Fuures Markes 1996(16): Tse, Y. Price Discovery and Volailiy Spillovers in he DJIA Index and Fuures Markes. Journal of Fuures Markes 1999;19(8): Bhar R. Reurn and volailiy dynamics in he spo and fuures markes in Ausralia: An inervenion analysis in a bivariae EGARCH-X framework. Journal of Fuures Markes 21; 21(9): Liu QF, Hua RH. Risk Transmission beween Sock Index Fuures and Sock Index Spo Markes in China. Saisical Research 211(11): Zhou Pu, Lu Fengbin, Wang Shouyang. A Sudy on he Nonlinear Informaion Spillover and Price Discovery of CSI3 Fuures Marke and CSI3 Marke. Accouning and Finance 213 (3):1-7. 6Engle RF, Kroner KR. Simulaneous generalized ARCH. Economeric Theory 1995(11):1-15.