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INDEX FUTURES TRADING AND ASYMMETRIC VOLATILITY IN THE KOREAN STOCK MARKET Yeonjeong Lee Department of Economics, Pusan National University, Jangjeon2-Dong, Geumjeong-Gu, Busan, 609-735, Korea yeonjeong@pusan.ac.kr Sang Hoon Kang Department of Business Administration, Pusan National University, Jangjeon2-Dong, Geumjeong-Gu, Busan, 609-735, Korea sanghoonkang@pusan.ac.kr Hongbae Kim Division of Business Adminstration, Dongseo University, Jurye2-Dong, Sasang-Gu, Busan, 617-716, Korea rfctogether@gmail.com. Seong-Min Yoon1 Department of Economics, Pusan National University, Jangjeon2-Dong, Geumjeong-Gu, Busan, 609-735, Korea smyoon@pusan.ac.kr ABSTRACT This paper examines the impact of the introduction of index futures trading on the KOSDAQ market. We accounted for the asymmetric response and the long memory features of volatility using GJR-GARCH, FIGARCH, and FIAPARCH models. From our estimation results, we found an increase in asymmetric volatility after the introduction of index futures trading. Also, the degree of the long memory feature of volatility increased following the introduction of index futures trading. Consequently, these estimation results imply that the introduction of KOSDAQ Star Index futures trading is not related to the improvement of information efficiency in its underlying spot market. Keywords: Asymmetric volatility, Index futures trading, Information efficiency. INTRODUCTION Since KOSPI 200 index futures trading began in 1996, attention to the impact of index futures trading on the underlying spot market has greatly increased. In fact, since the stock market crisis of 1987, this issue has received attention from academic researchers and financial policy authorities. The main point of this issue 1 Corresponding author. 1 is to determine whether index futures trading is desirable or undesirable for underlying spot markets. It is generally accepted that a futures market is closely connected with its underlying spot market. However, the conclusion about the impact of index futures trading is not yet clear. According to the traditional point of view, expressed well by Friedman (1953), as futures trading encourages rational speculators, the introduction of derivative markets can move asset prices towards fundamentals and thus stabilize asset prices. Cox (1976) also argued that the introduction of futures trading increases the number of traders and the possible channels of information flow. However, some studies argue that increased volatility, following the introduction of futures trading, has been interpreted as the destabilization of spot markets. For example, Ross (1989) argued that increased information flow from a futures market leads to an increase in spot market volatility. Furthermore, there are some studies showing that the introduction of index futures trading can reduce the asymmetric volatility of its underlying markets (Antoniou, Holmes and Priestley, 1998). This paper examines whether the introduction of futures trading in the Korea Securities Dealers Automated Quotation (KOSDAQ) market improves information efficiency and reduces asymmetric volatility in its underlying spot market. Specifically, to fully understand the impact, we take account of the asymmetric response and long memory features of volatility before and after the introduction of index futures trading. The rest of this paper is organized as follows. The second section reviews previous literature with regard to the asymmetric and long memory features in the volatility of financial data. The third section presents the characteristics of volatility models. Data and empirical results are provided in the fourth section. The final section presents our conclusions. PREVIOUS STUDIES Previous empirical literature has presented mixed results on the impact of the introduction of futures trading. Several previous studies suggested that the market of derivatives such as index futures markets increases the volatility of the underlying spot market (Harris, 1989; Antoniou and Holmes, 1995; Chiang and Wang, 2002; Ryoo and Smith 2004). Harris (1989) observed an increase of volatility of the S&P 500 index after the introduction of future and options trading in 1983. Antoniou and Holmes (1995) suggested an increased volatility following the introduction of the FTSE 100 index futures contracts for the London Stock Exchange. Chiang and Wang (2002) also indicated that, in the Taiwan stock market, the introduction of index futures trading increases asymmetric volatility. Some empirical studies have argued that the introduction of derivatives markets decreases the volatility of the underlying spot market (Subrahmanyam, 1991; Gorton and Pennacchi, 1993; Antoniou, Holmes and Priestley, 1998; Bologna and Cavallo, 2002; Byun, Jo and Cheong, 2003). In particular, Antoniou, Holmes, and Priestley (1998) found that, for Germany and Switzerland, the introduction of futures trading reduces the impact of positive feedback trading due to the movement of feedback traders from the spot to futures markets and attracts rational investors who make the market more efficient. The evidence of Byun, Jo, 2 and Cheong (2003) indicated that the introduction of index futures trading leads to the easing of asymmetries on volatility of the underlying spot prices. Unlike the abovementioned studies, several researchers have found that the introduction of a market of derivatives does not influence the underlying spot market (Freris, 1990; Antoniou and Foster, 1992; Darrat and Rahman, 1995; Kan, 1999). Freris (1990) investigated the Hang Seng Index Futures, finding that the introduction of stock index futures trading has no remarkable effect on the volatility of the stock price index. Antoniou and Foster (1992) examined the impact of the introduction of contracts on Brent Crude Oil and found no substantial change in volatility between the pre-futures period and post-futures period. In this study, we aim to provide evidence on the impact of the introduction of futures trading on spot market volatility in the KOSDAQ market. Our empirical study focuses on the impact of index futures trading in explaining the asymmetry and long memory of volatility. Through this analysis, the asymmetry and long memory of volatility to news can provide an insight into the role of market dynamics. METHODOLOGY Symmetric and Asymmetric Volatility Models We employ the GJR-GARCH (or threshold GARCH) model to analyze the impact of futures trading on its underlying market volatility. The standard ARCH model of Engle (1982) and the GARCH (generalized ARCH) model of Bollerslev (1986) are known to be able to capture the clustering and time-varying tendencies of volatility. However, the standard ARCH and the GARCH models forecast only a symmetric feature of volatility, while the GJR-GARCH model is able to measure the asymmetric response of volatility to news (Engle and Ng, 1993). A simple GARCH(1,1) model can be expressed as follows: t tt , (1) t ~ i.i.d . with E t 0 , var t 1 , (2) t2 1t21 1 t21 , (3) where 0 , 1 0 , 1 0 , and 1 1 1 . In the GARCH(1,1) model, current conditional variance t2 depends not only on the information about volatility during the previous period ( 1 t21 ) but also on the fitted variance from the model during the previous period ( 1 t21 ). Therefore, investors will increase the estimate of the next period’s variance if the return series is unexpectedly large in either the upward or the downward direction. However, the GARCH model cannot capture the asymmetric response of volatility to news despite its advantage in measuring volatility clustering. This is because the squared error term t21 in Equation (3) reflects only the symmetric impact on volatility, irrespective of good news or bad news. If a negative return shock tends to cause more volatility than a 3 positive return shock of the same magnitude, the GARCH model underestimates the amount of volatility responding to bad news and overestimates that of volatility responding to positive news (Engle and Ng, 1993). To overcome this limitation, Glosten, Jagannathan and Runkle (1993) proposed an asymmetric GARCH model, i.e., the GJR-GARCH model. The conditional variance function of a simple GJR-GARCH(1,1) model can be written as follows: t2 1t21 t21Dt 1 1ht 1 , (5) where Dt term equals one if t is less than zero, and Dt term equals zero otherwise. This GJR-GARCH model is similar to the simple GARCH model except for the presence of the Dt 1 dummy term in the lagged squared errors ( t21 ). The existence of the dummy term allows good news ( t 0 ) and bad news ( t 0 ) to have different impacts on the conditional variance. That is, an asymmetric volatility for financial data can be considered. For example, good news reflects only an 1 impact on volatility, while bad news reflects an (1 ) impact on volatility. Therefore, if is larger than zero, the GJR- GARCH model can capture an asymmetric effect of volatility. However, if is equal to zero, the GJR-GARCH model is the same as the simple GARCH model. Symmetric and Asymmetric Long Memory Volatility Models There have been numerous efforts to understand persistence dynamics in conditional variance. Robinson (1991) first adopted the fractional differencing model in the formulation of the conditional variance long memory GARCH (LMGARCH) model. Since then, many researchers have proposed various extended GARCH-type models that identify the long memory property in the conditional variance of financial data (Baillie, Bollerslev and Mikkelsen, 1996; Davidson, 2004; Giraitis et al., 2004; Teyssière, 1998). Baillie, Bollerslev, and Mikkelsen (1996) proposed the FIGARCH model with a fractionally differencing operator (1 L) d of fractionally integrated autoregressive moving average (ARFIMA) specification. A general FIGARCH ( p, d , q) model can be defined as follows: L 1 L t2 1 L t , d (6) where (L) 1L 2 L2 q Lq , ( L) 1L 2 L2 p Lp and vt t2 t2 . If 0 d 1 , all the roots of L and 1 L lie outside the unit root circle. The above equation (6) can be re-written as follows: 1 1 t2 1 L 1 1 L L 1 L d t 2 (7) 4 1 1 L ( L) t2 (8) . The FIGARCH model provides greater flexibility for modelling the conditional variance. That is, it admits the covariance stationary GARCH model when d 0 and the IGARCH model when d 1 as specific cases. For the FIGARCH model, the persistence of shocks to the conditional variance, or the degree of long memory is measured by the fractional differencing parameter d . Therefore, the attraction of the FIGARCH model is that for 0 d 1 , it is sufficiently flexible to allow for an intermediate range of persistence. The FIAPARCH model of Tse (1998) is one of the extended GARCH class of models that describe the idea of fractional differencing processes. The FIAPARCH model extends the APARCH model of Ding, Granger, and Engle (1993) with a fractionally integrated process in the conditional variance. 2 The general FIAPARCH ( p, d , q) model is specified as follows: 1 1 t 1 L 1 1 L L 1 L d t t , (9) where 0 , 1 1 , and 0 d 1 . The FIAPARCH model can accommodate the desired feature of asymmetric long memory in the conditional variances by t t term. If is larger than zero, negative shocks give rise to higher volatility than positive shocks, and vice versa. The FIAPARCH model comprises the FIGARCH model when 2 and 0 . Thus, the FIAPARCH model is superior to the FIGARCH model because the former model can capture asymmetric long memory features in conditional variances (Tse, 1998). Model Densities The parameters of the ARCH class models can be estimated by using non- linear optimization procedures to maximize a conditional likelihood function under the assumption of conditional Gaussian errors. This can be described as follows: 2 1 2 1 T ln( L) T log 2 2 t 1 log t2 t2 . t (10) Generally, subsequent inference is based on the Quasi Maximum Likelihood Estimation (QMLE) technique of Bollerslev and Wooldridge (1992). This is because most returns of financial data are not well described by the conditional 2 The APGARCH model of Ding, Granger, and Engle (1993) extends the GARCH model of Bollerslev (1986) with an optimal power transformation term in the lagged errors ( t i ). The general APARCH(1,1) model is as follows; t 1 ( t 1 1 t 1 ) 1 t1 . The parameter is a coefficient for the power term, whereas 1 accounts for asymmetric volatility on the positive or negative returns of the same magnitude. 5 normal distribution. The QMLE estimator T , based on T observations, is consistent and asymptotically normally distributed. T 1/2 T 0 N 0, A 0 B 0 A 0 , 1 1 (11) where 0 means the true parameter values and A and B represent the Hessian and outer product of the gradients, respectively. Bollerslev and Wooldridge (1992) confirmed that the normality assumption might be justified by the fact that the Gaussian QMLE estimator is consistent if the conditional mean and the conditional variance are correctly specified. EMPIRICAL RESULTS Data The data used in this paper are the KOSDAQ Star Index from the Korean Exchange (KRX).3 The data set consists of the daily closing prices covering the period from October 1, 2002, to October 31, 2008, for a total of 1,507 observations. The futures trading of the KOSDAQ Star Index was launched on November 7, 2005. In order to examine the impact of the introduction of futures trading on asymmetric volatility in KOSDAQ market, we divide the whole sample period into two sub-periods as follows: ● Pre-futures period: October 1, 2002, to November 6, 2005; ● Post-futures period: November 7, 2005, to October 31, 2008. The KOSDAQ Star Index prices and returns series constructed by logarithmic transformation are shown in Figure 1. A vertical line represents the introduction of the futures market. It divides the whole period into the two sub- periods: the pre-futures and post-futures periods. Descriptive statistics for the entire sample period as well as the sub-periods for the KOSDAQ Star Index returns are summarized in Table 1. The sample mean of returns is very small and hard to distinguish from zero. Both skewness and excess kurtosis statistics in the table show that the returns distribution is not normally distributed. The KOSDAQ Star Index return series reveals that it does not correspond with the normal distribution assumption, especially for the post- futures period. Likewise, the Jarque-Bera test statistics (J-B) reject the null hypothesis of normality at the 1% significance level. According to the Box-Pierce test statistic of the standardized residuals to the th 12 order, Q(12) , the null hypothesis of no serial correlation is rejected for all periods. It means that there is significant evidence of serial dependence in returns for all periods. Additionally, the Box-Pierce test statistic of the squared 3 The KOSDAQ Star Index is comprised of 30 gilt-edged constituents selected from all listed stocks on the KOSDAQ market and are chosen based on factors such as liquidity, financial requirements, and how well they represent their markets. The Index is calculated using market capitalization weighted on the number of free-floats. 6 standardized residuals to the 12th order, Qs (12) , shows that there is significant evidence of serial correlation in the variance for all periods, which indicates the volatility clustering. Therefore, these statistics show non-normality, serial correlation, and volatility clustering characters in the KOSDAQ Star Index. Figure 1 Dynamics of KOSDAQ Star Index Prices (a) and Returns (b) Table 1 Descriptive Statistics for Daily KOSDAQ STAR Index Returns Whole Period Pre-futures Period Post-futures Period No. of Obs. 1,506 767 739 Mean (%) -0.019 0.012 -0.053 Std. Dev. (%) 1.999 1.911 2.076 Skew. -0.553 -0.259 -0.783 Excess Kurt. 4.798 1.755 6.943 J-B 1521*** 107*** 1559*** Q(12) 35.5*** 21.0* 22.2** Qs (12 ) 741.6*** 213.8*** 442.9*** Notes: Under the null hypothesis for normality, the J-B (Jarque-Bera) statistic is distributed as 2 2 . Q(12) and Qs 12 are the Box-Pierce test statistics for the return series and for the squared return series at lag up to 12. *, **, and *** indicate the rejection of the null hypothesis of independence at the 10%, 5%, and 1% significance levels, respectively. 7 To account for serial dependence, we consider a standard autoregressive moving average (ARMA) model for the conditional mean, assuming the standard GARCH(1,1) model. We determine the orders n and s of the ARMA (n, s) model to build parsimonious models for the return series of all periods. Based on the Schwarz Bayesian Information Criteria (SIC), this study considers all the possible combinations for the ARMA (n, s) with n = 0, 1, 2 and s = 0, 1, 2. Table 2 shows the order selection of ARMA (n, s) -GARCH(1,1) models based on the values of the SIC. The certain specification is selected as the best one, which has a minimum SIC value. The whole and pre-futures periods require an AR(1) specification while the ARMA(1,1) specification is selected for the post-futures period. Table 2 Order Selection of the ARMA n, s -GARCH(1,1) Model ARMA n, s - Whole Pre-futures Post-futures GARCH(1,1) Period Period Period n 0, s 0 -5.2650 -5.1785 -5.3607 n 0, s 1 -5.2679 -5.1814 -5.3629 n 0, s 2 -5.2631 -5.1738 -5.3614 n 1, s 0 -5.2680 -5.1804 -5.3627 n 1, s 1 -5.2635 -5.1729 -5.3630 n 1, s 2 -5.2595 -5.1666 -5.3606 n 2, s 0 -5.2637 -5.1730 -5.3607 n 2, s 1 -5.2597 -5.1656 -5.3603 n 2, s 2 -5.2549 -5.1580 -5.3583 Note: This table includes the values of the Schwarz Bayesian Information Criterion (SIC) across the various ARMA specifications using a GARCH(1,1) specification. Estimation Results of the GJR-GARCH(1,1) Model We investigate the impact of introduction of futures trading on the asymmetric volatility on the KOSDAQ market for the GJR-GARCH(1,1) model. Table 3 shows the estimation results and diagnostic tests from the ARMA n, s - GJR-GARCH(1,1) models for the sub-periods of the KOSDAQ Star Index returns. The estimated results suggest several interesting findings. First, the Box-Pierce test statistics, Q(12) and Qs (12) , are insignificant, except for the value of Qs (12) of the post-futures period. These indicate that the standardized and squared standardized residuals for up to 12th order follow identically and independently distributed (i.i.d) processes. Thus, the estimated GJR-GARCH(1,1) models are accurately specified to capture time-varying volatility. Second, the asymmetry coefficients ( ) for all periods are positive and statistically significantly different from zero. That is, unexpected negative returns (bad news) result in more volatility than unexpected positive returns (good news) of the same magnitude. 8 Table 3 Estimation Results for ARMA n, s -GJR-GARCH(1,1) Mean equation: yt 1 yt 1 t 1 t 1 , t | t 1 ~ N 0, 1 Variance equation: t2 1t21 t21Dt 1 1ht 1 Whole Period Pre-futures Period Post-futures Period AR(1) - AR(1) - ARMA(1,1) - Model GJR-GARCH(1,1) GJR-GARCH(1,1) GJR-GARCH(1,1) 0.000 0.000 0.000 (0.000) (0.000) (1.554) 0.119 0.117 -0.357 1 (0.027)*** (0.036)** (-1.957)* 0.480 1 - - (2.917)*** 0.279 0.197 0.303 (0.072)*** (0.135) (3.351)*** 0.040 0.033 0.035 1 (0.022)* (0.022) (0.863) 0.771 0.850 0.687 1 (0.037)*** (0.064)*** (10.72)*** 0.214 0.114 0.371 (0.051)*** (0.060)* (3.598)*** ln L 4006 2009 2055 SIC -5.281 -5.171 -5.339 0.5 1 0.918 0.940 0.907 Skewness -0.335*** -0.233*** -0.392*** Excess Kurtosis 0.936*** 0.518*** 1.327*** Jarque-Bera 83.32*** 15.55*** 75.32*** Q(12) 10.0 12.4 12.1 Qs (12) 18.0 10.6 34.7** ARCH(5) 1.083 1.340 0.262 Note: *, **, and *** indicate the rejection of the null hypothesis at the 10%, 5%, and 1% significance levels, respectively. Third, the degree of asymmetries in the post-futures period is higher than that in the pre-futures period. This means that the introduction of futures trading affects the increase of asymmetric volatility in the KOSDAQ market. In fact, Harris (1989) and Antoniou and Holmes (1995) pointed out that futures trading can lead to the excessive increase of volatility of stock markets because of disturbance factors such as the speculation and program trading by noise traders. Therefore, the increase in asymmetric volatility after the introduction of futures trading is indirectly related to the traditional explanation. Fourth, the sum of the coefficients 1 and 1 for the whole period is 0.811 and highly statistically significant. It means that the volatility is persistent to some degree. In particular, the value of the pre-futures period is higher than that of the post-futures period. Additionally, the stationary condition ( 0.5 1 ) of Ling and McAleer (2002) is valid for both periods. These indicate that the volatility is more persistent in the pre-futures period than in the post-futures 9 period. However, the values of 1 for both periods are statistically insignificant at 10%. Table 4 Estimation Results for ARMA n, s -FIGARCH (1, d ,1) Model Mean equation: yt 1 yt 1 t 1 t 1 , t | t 1 ~ N 0, 1 Variance equation: t2 1 t21 1 1L 1 1L1 Ld t2 Whole Period Pre-futures Period Post-futures Period AR(1) - AR(1) - ARMA(1,1) - Model FIGARCH (1, d ,1) FIGARCH (1, d ,1) FIGARCH (1, d ,1) 0.000 0.000 0.000 (0.000) (0.000) (0.608) 0.089 0.098 -0.503 1 (0.025)*** (0.035)*** (-3.079)*** 0.576 1 - - (3.782)*** 0.250 0.143 0.418 (0.096)*** (0.103) (2.354)** 0.283 0.396 0.249 1 (0.158)* (0.128)** (0.920) 0.431 0.375 0.608 d (0.098)*** (0.099)*** (2.596)*** -0.056 0.043 -0.186 1 (0.100) (0.106) (-1.323) ln L 3997 2009 1996 SIC -5.269 -5.171 -5.321 Skewness -0.422*** -0.208** -0.615*** Excess Kurtosis 1.256*** 0.489*** 1.888*** Jarque-Bera 143.84*** 13.20*** 156.49*** Q(12) 14.5 14.8 14.6 Q s (12 ) 12.7 4.9 21.7** ARCH(5) 0.184 0.354 0.224 Note: See Table 3. Estimation Results of FIGARCH and FIAPARCH Models The estimated parameters of the GJR-GARCH model in the previous section cannot describe the persistence of conditional variances. For this reason, we employed the FIGARCH and FIAPARCH models in this section. Tables 4 and 5 provide the estimated results from the FIGARCH and FIAPARCH models in the whole sample and sub-periods, respectively. Through these approaches, we can detect some remarkable features of the symmetric and asymmetric long memory in the volatility of the KOSDAQ market. In Table 4, the ARMA n, s -FIGARCH (1, d ,1) models for all periods capture the long memory volatility for the KOSDAQ Star Index returns. That is, the long memory parameter d for all periods is statistically significant at the 1% level as the null hypothesis ( d 0 ) is rejected. Therefore, the volatility of KOSDAQ Star Index returns seems to be a long memory process. 10 Table 5 Estimation Results for ARMA n, s -FIAPARCH (1, d ,1) Model Mean equation: yt 1 yt 1 t 1t 1 , t | t 1 ~ N 0, 1 Variance equation: t 1 1 1L1 1 1L1 Ld t t Whole Period Pre-futures Period Post-futures Period AR(1) - AR(1) - ARMA(1,1) - Model FIAPARCH (1, d ,1) FIAPARCH (1, d ,1) FIAPARCH (1, d ,1) 0.000 0.000 0.000 (0.000) (0.000) (-0.085) 1 0.107 0.108 -3.375 (0.018)*** (0.036)*** (-1.312) 1 - - 0.470 (1.770)* 13.789 2.177 31.154 (11.969) (4.813) (0.962) 1 0.359 0.317 0.336 (0.093)*** (0.142) (2.412)** d 0.441 0.336 0.501 (0.079)*** (0.112)*** (3.779)*** 1 0.000 0.014 -0.001 (0.059) (0.094) (-0.009) 0.538 0.416 0.645 (0.120)*** (0.166)** (3.137)*** 1.176 1.543 1.007 (0.183)*** (0.402)*** (4.502)*** ln L 4014 2014 2007 SIC -5.283 -5.166 -5.335 Skewness -0.313*** -0.198** -0.382*** Excess Kurtosis 0.941*** 0.432** 1.352*** Jarque-Bera 80.38*** 11.01*** 74.31*** Q(12) 11.6 14.0 14.0 Q s (12 ) 17.1 7.6 25.1** ARCH(5) 0.605 0.713 0.452 Note: See Table 3. However, similar to the general GARCH model, the FIGARCH model does not describe the asymmetric volatility in the KOSDAQ market. To overcome this limitation, the ARMA n, s -FIAPARCH (1, d ,1) model is employed. The asymmetric coefficient of volatility ( ) is positive and statistically significant, at least at the 5% significant level. Thus, we conclude that the unexpected negative returns (bad news) resulted in more volatility than the unexpected positive returns (good news). Additionally, the value of the estimated asymmetry coefficient in the post- futures period is higher than that in the pre-futures period. This indicates that some factors such as the introduction of futures trading and the disturbance of 11 noise traders with the development of the financial trading system might have the effect of increasing the asymmetric volatility in the KOSDAQ market. Lastly, the values of the fractionally differencing parameter ( d ) for all periods are statistically highly significant at 1% for both the FIGARCH (1, d ,1) and FIAPARCH (1, d ,1) models. This suggests that the return series has the long memory volatility process. In particular, the values of the long memory parameters in the post-futures period are higher than those in the pre-futures period. This indicates that the KOSDAQ market has become inefficient after the introduction of its futures trading. CONCLUSIONS Although the impact of index futures instruments affected the entire Korean financial market, there is no practical agreement concerning the role of the futures market with regard to stabilizing or destabilizing its underlying spot market. It is hard to find empirical results on the impact of index futures trading, especially for the KOSDAQ Star Index. This paper examined the impact of KOSDAQ Star Index futures trading, accounting for long memory and asymmetric volatility. Empirical analysis in this paper suggests three main conclusions. First, using GJR-GARCH and FIAPARCH models, this paper investigated the asymmetric volatility of the KOSDAQ market before and after the introduction of index futures trading. The results indicate that the KOSDAQ market for all periods shows the asymmetric response of volatility to positive and negative news. Second, asymmetric volatility has increased in the post-futures period. This indicates that the introduction of KOSDAQ Star Index futures trading does not contribute to the improvement of information transmission in the underlying spot market. Lastly, we captured the asymmetric long memory feature in the volatility of KOSDAQ Star Index returns. Comparing the FIGARCH and FIAPARCH models, we found that both of the models can fully present the lone memory volatility. The values of long memory parameter d increase from the pre-futures period to the post-futures period. This result implies that the introduction of futures trading might make the KOSDAQ market less efficient. In summary, in the case of the KOSDAQ market in Korea, it seems to be hard to accept the traditional theoretical explanation that the introduction of index futures trading can improve the mechanism of information transmission in financial markets. ACKNOWLEDGEMENTS This work was supported by the National Research Foundation of Korea Grant funded by the Korean Government (NRF-2010-371-B00008). REFERENCES Antoniou, A. & Foster, A. J. 1992. The effect of futures trading on spot price volatility: evidence for Brent crude oil using GARCH. Journal of Business Finance & Accounting, 19, 473-484. 12 Antoniou, A., Holmes, P., & Priestley, R. 1998. The effect of stock index futures trading on stock index volatility. Journal of Futures Markets, 18, 151-166. Antoniou, A. & Holmes, P. 1995. 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