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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   tt ,                               (1)
                      t ~ i.i.d . with E t   0 , var t   1 ,               (2)
                                t2    1t21  1 t21 ,                      (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 t21 ) but also on the fitted variance from
the model during the previous period (  1 t21 ). 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  t21  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    1t21  t21Dt 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
(  t21 ). 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 t1 . 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    1t21  t21Dt 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 t21  1  1L  1  1L1  Ld  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  1t 1 , t | t 1 ~ N  0, 1
Variance equation:  t     1  1  1L1 1  1L1  Ld   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).

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