The CSI 300 index future was launched by China Financial Future Exchange in April, 2010 after four years of mock trading. It has been traded for just more than two years by the time of writing. The underlying asset of CSI 300 index future is the CSI 300 index which is consist by the 300 selected companies list on either Shanghai or Shenzhen stock exchange. These companies covered more 60% of the market value and can be seen as the representatives of the market general performance. As the only practical tool to short in Chinese stock market after the last put option expired in 2008, the CSI index future plays a prominent role since its birth and develops quickly. Chinese stock market is different from most of the developed market in structure since most of its participants are individual investors.(Ba and Chu, 2008) The high entry standard of the index future market makes its participants distinguished from those in the underlying market. The asymmetrical structure caused an unbalanced problem between the future and spot markets. According to the report from Haitong Securities(2010), the annualized arbitraging return reached 120% in the first three months. The unbalance attracted massive arbitraging which signified the volatility of the market and made the CSI index experienced a sharp drop in that period. Such return dropped quickly to 15% in one year time and stabilized to about 5% percent recently. Such phenomenon makes the trading data from the first year unsuitable to study the market with purpose of studying the normal trading.

During recent years, as more and more mainland's companies being selected into Hang Seng Index and because of the growing capital flow between Hong Kong and mainland China, the interactions between the two markets is becoming more and more significant, which will surely affect the trading activity in the two index future markets. Although the market depth and the level of internationalization are quite different, such phenomenon provides a good chance to study the growth and characters of Chinese index future market based on the comparison with the Hangseng index future market. Hong Kong market is one of the most deeply traded markets in the world. The stock market in Hong Kong has a history of more than 100 years. The Hang Seng index future has been traded since 1992, and is one of the most influential index future markets in Asia. In the recent years, as more mainland companies becoming the constituent stocks and the surging of mainland economy, the relationship between the mainland market and Hong Kong market is much more significant than before. Such tendency is likely to be continued, which makes it meaningful to study the relationship between the two index future markets.

This study focuses on the characters of volatility in both markets from the view of different types of participants. In the modern financial market, the volatility is much more essential than the direction of the price. The hedgers build positions on future to get rid of the volatility; the speculators and arbitragers seek profit from volatility. The volatility is the most essential element in future market, the monthly clearing policy makes the buy-and-hold strategy impractical. Meanwhile, different traders eye on volatilities based on different time span. Most of the speculators and arbitragers put the intraday volatility as their first concern for daily trading. While volatility based on daily data are essential for the investor and also for speculators to make trading plan. Both types of volatilities are studied in the literature.

The Garman-Klass Volatility(1980) is used in order to study the intraday volatility. The literature compares the covariance between the volatility of the index future and underlying market, and investigates the interactions between the two markets' volatility. This can give a basic sense of the maturity of arbitraging and the effectiveness of hedging in the two markets since in a mature index future market, the intraday volatilities of the future market and the spot market should be highly correlated regard to speedy arbitraging. As stated above, the arbitraging in CSI 300 index future market has just stepped out of the infant stage in the recent year. The study explores the covariance between the volatility of future and spot markets and compares the results get from CSI and Hang Kong markets. VAR model is used twice. The first model aims at studying the causality between the intraday volatility with trading volume and market depth. The second model is used to study the lead-lag relationship of the intraday volatility in the two markets and then add volume and open interests as exogenous variables to study their influence on the daily movement. Impose response function is generated to study the path of information flow between the future market of mainland China and Hong Kong. The result suggests that higher margin should be left for the hedgers in Chinese stock market, and compared with the developed market in Hong Kong, the arbitraging return is still higher in China. The result from this study supports the opinion that the Chinese stock market can bring significant influence to the Hong Kong's market in recent years. The shock in the intraday volatility of Hang Seng index future will bring impact to the CSI 300 index future in the reverse direction. But the impact is not significant. Both markets can digest the shock from their own quickly. The overshot will come in the second period on both paths. The intraday volatility in the market is found to be granger caused by the log form of volume and open interest.

The Phillip-Perron(1988) test and ADF test are used to test the stationary of the closing price. Surprisingly, the results indicate there is no unit root in both series of data, but most of the financial data are not stationary. The main reason for this can be due to the short time span. The limited number of daily data cannot reflect such relationship significantly. However, the shortage in data won't influence the process to study the volatility prediction. The trading volume and open interest is separated into expected portion and unexpected portion. To do the volatility production, the ARMA(2,1)-GARCH(1,1) model and ARMA(2,1)-EGARCH(1,1) model are recognized as the most useful tools. The unexpected portions are set as exogenous variables to explore whether they can influence the trading activity. The expected volume and open interest are dropped since the series got in CSI 300 are showed to be un-stationary. The same procedure is used to process the data from both markets in order to make comparison. The result demonstrates that the impacts brought by unexpected open interest are in different directions in the two markets. For CSI 300 index future, the unexpected open interest can positively affect the volatility while such impact is negative in Hong Kong. Such difference is due to the fact that the Chinese stock market is relatively much more independent than the stock market in Hong Kong. The frequent jumps in opening price make the open interest of Hang Seng index future does not abbey the common rule since traders are less willing to hold positions overnight.

The literature is aimed at exploring the relationships between volatility, trading volume and open interest from aspects of different groups of traders. The following part of the literature is structured as follows: A review of the theoretical and empirical study on volatility of index future would be given in the beginning. The source and a basic analysis of the data would be stated in the section of data and descriptive statistics. In the section of methods and methodology, a preliminary description of the methods involved will be given and comes with an explanation and theoretical consideration of the econometric models. The intraday volatility study based on VAR model focuses on whether there are significant relationships with trading volume and open interest and its lagged terms, and how a given extent of shock can affect the path of the intraday volatility between CSI 300 index future and Hang Seng index future. The results are stated and interpreted in empirical result. The conclusion is based on a summary of findings and recommending procedures and will come in the end.

## Literature review

The literature mainly focus on exploring the relationship between volatility, volume and market depth in CSI index future market and compare the results getting from HSI index future market. The former studies have documented a positive relationship between volatility and volume. The recent studies on the causality relationships between trading volume and volatility can be dated back to the study done by Bessembinder and Seguin(1993), their result shows the relationship is a mixture of contribution, which supported the hypothesis made by Clark(1973). Massive studies have been published based on their study. Later studies put more indicators into model. Chartrath et al.(2003) studied the importance of open interest in commercial future market and stated that the open interest reflects the trading activities from large hedgers. For index future market, the open interest also indicates the behavior of large hedgers who have a significant position on underlying stocks. Bessembinder and Seguin suggested open interest is the best indicator for market depth. They separate the volume into two parts, the expected portion and the unexpected one. Using a method similar to GARCH, among the eight markets they studied, a strong positive relation between contemporaneous volume and volatility was found. They also find a negative relationship between volatility and both portions of open interests. Later on, more studies were done based on Bessembinder and Seguin's study. For example, Watanabe (2001) studied the same topic in Japanese market and indicated that a significance positive relationship lies between volatility and expected open interest. The study concluded that such difference is due to the different regulatory structure. Pati and Kumar (2007) found that the volume and open interest are much stronger determinants of future price volatility than the time-to-maturity effect in Indian index future market.

Two competing hypothesis can be found about the volume-volatility relationship. The first is the 'Mixture of Distribution Hypothesis'(MDH) (Clark, 1973). It suggests that a stochastic process can be found in return series. Such process is conditional on the information inflow and with changing second moment which can be judged as the intensity of information arrival. If such causality holds, new and unexpected information will bring contemporaneous and positive change to volatility and volume. Another hypothesis is raised by Copeland (1976), which is called 'Sequential Information Arrival Hypothesis' (SIAH). It suggests that the new information is not spread simultaneously to all the traders but with a sequential process. Both trading volume and price movements will be affected by such procedure, which will also leads to a contemporaneous and positive change to volatility and volume. However, such statement is criticized to be less sound by later studies. Tauchen and Pitts (1983) stated that returns volatility, trading volume and market depth are closely related regarding to their study. They argued that traders will revise their asset valuations after the arrival of new information. The disagreement among the traders is the causes for volume. Kyle (1985) gave a more widely accepted definition of market depth. By Kyle's study, market depth should be interpreted as the order flow required moving prices by one unit. The reason to use open interest as a representative is that the change in open interest is endogenous to the change in order flow. Kyle's study pushed the research on the relationship between futures price volatility and trading activity to a further step. Another theory developed in this area is one called the dispersion of beliefs which is first promoted by Harris and Raviv (1993). They demonstrated that the dispersion of beliefs is the driving force of the additional volatility and additional expected volume. Excess volatility and volume is because of the greater level of disagreement in the market. They suggested that such phenomenon is caused by the fact that although informed traders tends to trade in a small range of price; the herding behavior of the uninformed traders would push the volatility to a higher level.

Many later studies take liquidity into consideration. It's reasonable for the researchers to foucs on trading volume as a representative of liquidity and a signal of information flow when they study the financial market. Significant relationships between volume of transactions and the volatility of returns are found in many former studies. An early study done by Karpoff (1987) gave the following study a preliminary insight into such relationship and its importance. He suggested that the study on modern financial market should have an insight into the structure of the market and the speculative distribution should be paid attention to. It's of significant importance to study the bi-direction relationship between price and volume. Such information are accessible to all the traders and the traders in the markets believe that the understanding of the intrinsic causality would help to their success in the market. Karma (1993) suggested that the open interest could be considered as the representative of the market depth. The information about the daily activity can be drawn by monitoring the fluctuation of open interest after a whole day's trading. The study done by Gwilym et al (1999) examined the similar relationship in FTSE 100 index future using five minutes data. Evidence from the estimation of GMM suggests that a significant positive and contemporaneous correlation is existed between volume and volatility. Wang and Yau (2000) on S&P 500 index future for the period 1990-94 indicates that contemporaneous volume can bring a strong positive effect on price volatility, while the effect from past volume is negative and relatively small.

Jacoby, Fowler and Gottesman (2006) gave an theoretical argument on how the liquidity issue can effect financial asset pricing. They took the spread cost into consideration and build an adjusted CAPM model based on liquidity. When study Yen and Chen (2009) studied the relationship between volatility, volume and open interest of Taiwan index future market and find that significant relationship is existed among the daily volatility, the lagged total volume and the lagged open interest. Pati (2011) later studied the relationship between the future trading activity and volatility in price of the Indian stock future. Using the method introduced by Bessembinder and Seguin, the unexpected volume has a much more significant impact on volatility than the expected volume. The expected portion of open interest has a significant negative relationship with volatility while its unexpected part does not. Such result is bit different from Bessembinder and Seguin's study. Such difference is contributed to the characters of emerging market by the author. Li(2011) examines the secular relationship between the liquidity of cash market and the volatility of stock index futures in New York Stock Exchange (NYSE). The result suggests that the quarterly expected volume has a significant explanatory power for the daily volatility of main stock index futures based on the companies list on NYSE. The studies about causality between the indicators of the spot and future markets can also be found. Chang and Chou (2000) studied the relationship open interest of S&P 500 future market and the volatility of the underlying market, the result indicates that there is a positive relationship between the two variables. Such relationship can be interpreted as the increased volatility in the underlying market induces a higher need for hedging. Later on, Chartrath et al. (2003) further studied this issue, they separated the trader into four groups as CFTC does, which including commercial producer and consumers, spreaders, non-commercial reportable traders and other traders. Using the weekly report from CFTC, they concluded that the unexpected change in the commercial positions has a positive relationship with intraday volatility of the future and its underlying's market. Juan(2009) examines the lead-leg relationship in the S&P 500 index future market and suggested that a unidirectional directional relationship between future market volatility and the spot market volatility.

Among the most recent studies, the VAR, GARCH and VECM methods are widely involved. Bonilla and Sepulveda(2011) did a study across the stock markets in seven emerging economies, and try to compare the prediction power of the linear and nonlinear GARCH models. The result suggests that the basic GARCH model is preferable compared to the nonlinear EGARCH model. Yen and Chen use the lagged trading volume and lagged open interest as exogenous variables in the variance equation of the GARCH model. The reason for using lagged terms is that volume itself is partly determined by the volatility. They found significant relationship between the three variables. The similar method is used in this paper. LR test is used to select the best way of GARCH model specification. Wang(2011) used the GARCH methods to study the pricing behavior of FTSE Xinhua China A50 and H-Share Index Futures Markets. The result shows that the component GARCH model can help to improve the pricing performance of the Hemler-Longstaff model and the autocorrelation and regression results suggest high persistence in mispricing. Gulasekaran, Pattnayak and Samirana(2007) examines the lead-lag relationships between the spot index and futures index of the Hang Seng Stock Average using VAR and ECM method. ECM method is found to be the best. Yen and Chen use both the symmetric and asymmetric component GARCH models to study the effects that volume and open interest can take in the volatility predictions. They find that the augmented models are the best in forecasting the volatility in all three index future markets in Taiwan. Chang(2012) studied the volatility in crude oil future using EGARCH model. The result suggests that an asymmetric response to basis from covariance and conditional mean, while the response of transition probability is symmetric. Tokat and Tokat(2010) did a research on the Turkish index future market and investigated the effects of the future trading volume on spot market volatility. The literature used the FIGARCH model in order to assess the sensitiveness of market to the information flow. They found a long memory process in volatility, which is a common case in emerging market. The result indicated that the trading volume in the future market contribute to the volatility process of the underlying market. A unidirectional causality is also found which goes from future trading volume to spot market volatility. Fung, Liu and Tse(2010) examined the information flow and market efficiency the Chinese and American metallurgical futures markets over a ten-year span using VECM method. The results showed that the two markets are cointegrated and are comparably efficiency in incorporating information. Pati and Kumar put trading volume and open interest into the augmented GARCH(1,1) model as the exogenous variables in the covariance equation, the asymmetric problem is detected from the coefficient of open interest, they use the EGARCH(1,1) to accommodate the asymmetric bias. The splined-GARCH model is undertaken by Li in his research; a unit GARCH and a slow moving component are considered. The influence from the change in macroeconomics can be measured in this case.

The CSI 300 future market has just stepped into its third year. The study on this market is limited because of the short time span. The researchers in China began to focus on the volatility study since the introduction of the index future. Among those studies, the relative topic is done by Yang, Yang and Zhou(2012) who studied the intraday price discovery and volatility transmission in CSI future and underlying market. The ECM-GARCH method is used in the literature. The result from cointegration analysis shows that the index future market is not informational dominant in transmitting long-run information and price discovery. The shortcoming of the research is that the model used cannot take the dynamic short-run causality between the two markets into consideration. Wen, Wei and Huang(2011) examined the speculative efficiency and hedging effectiveness of CSI future market, their study compare the four ways of hedging; OLS, the symmetric bivariate GARCH, the asymmetric bivariate GARCH and time-varying copulas and find that CSI 300 index future price is cointegrated with the underlying index and is an unbiased estimator. The hedging effectiveness is nearly 91% which is enough to avoid the systematic risk. For the data collected from the first year's trading, the OLS is the best way of forming hedging strategy. Wu (2011) studied the characters of CSI 300 index future based on GARCH model. ARCH (4) effect is found in the data selected from the sample period. The basic GARCH model and the nonlinear GARCH models are used to detect the certain GARCH effect in volatility. The result suggests that obvious GARCH effect can be found in CSI 300 index future. The leverage effect is existed but not significant. The study also finds that the effect from large shock is dismissed very slowly and presents a high level of persistence in CSI 300 index future market.

In this study, following issues will be focused on:

The covariance between the intraday volatility of the future and spot would be detected and compared between the two markets. A basic image of the efficiency of price efficiency can be got through this.

The bi-directional causality between the intraday volatilities in CSI 300 index future and Hang Seng index future market. The impact from market depth and liquidity will be considered.

The GARCH and asymmetric EGARCH effect would be detected based on daily return. The market depth and liquidity would be considered as exogenous variables.

## Data and descriptive statistics

The data used in this literature is daily data collected from Wenhua Financial Database, including daily opening price, daily closing price, daily high, daily low, daily open interests and daily trading volume of the most commonly traded contracts in CSI 300 index future market and Hang Seng index future market. The similar data of the two underlying markets are collected except for the open interest which is specific data of future markets. The CSI 300 future market was launched in April, 2010. It's the first index future in mainland China. However, considering the shortages of the first year's trading stated in the introduction, only the data of the most recent year is selected, which starts from 9th, May, 2011 till 12th, May, 2012. The data includes the open price, close price, daily high and low, volume of both the future and spot markets in China and Hong Kong. After excluding the unmatched date between both markets, 238 observations are selected in the end. The data are collected from traded contract the most recent month.

A few adjustments are made in order to get rid of the disturbance caused by spillover. For CSI 300 future market, the expiration date is the third Friday of the current month. There are significant breaks in trading volume and open interest during the expiration weeks. The traders are rolling their positions from the contract of current month to the newly traded contract of next month. However, there's no change in participants and money involved during this procedure. For certain reason, the trading volumes and open interests of the two contracts are added together to match the data out of expiration week. The information of price is not changed since the difference between the two contracts is tiny. Hang seng index future contract is expired on the second last trading day of the contract month. The same adjustment is made to the data of the expiration week.

The daily return is generated by the following equation:

Rt=ln(Pt/Pt-1)

, where Pt is the closing price of the calculated date.

The same method is used to generate the daily return of all four series. The daily volatility is measured using Garman-Klass volatility. The Garman-Klass volatility is considered to be the best way to measure intraday price fluctuations since the methodology only considers those indicators which are accessible and meaningful to all investors. The Garman-Klass volatility is calculated as:

Where u is the normalized high, which is the difference between daily high and opening price,

d is the normalized low, which is difference between daily low and the closing price

c is the normalized close, which is the difference between the opening price and the closing price.

Descriptive statistics for return series are reported in Table 1 and for volatility series are reported in Table 2.

## Table 1

## Future Contract

## CSI 300 Future(ifr)

## Hang Seng Index Future (hsir)

## Sample Size

238

238

## Mean (%)

-.07334

-.06208

## Max (%)

5.63168

5.4778

## Min (%)

-3.51382

-5.82703

## StD (%)

1.36183

1.56378

## Skewness

.446049

-.32872

## Excess Kurtosis

1.380664

1.761591

## Table 2

## Future Contract

## CSI 300 (gkvif)

## Hang Seng Index (gkvhsi)

## Sample Size

238

238

## Mean (%)

.01341

.00883

## Max (%)

.09837

.2173

## Min (%)

6.19e-04

3.43e-04

## StD (%)

.01348

.01643

## Skewness

2.578952

9.305583

## Excess Kurtosis

9.37267

119.3573

D'Agostino test(1990) is used to test normality for both the return and volatility series, the results showed in Table 3 showed that for all these for series, the null hypothesis has been rejected which means that they are not normally distributed. The skewness and excess Kurtosis are significant.

In Table 1, the mean daily returns of both CSI 300 future(-0.073%) and Hang Seng index future(-0.062%) are close to zero which is typical for financial data. The slightly negative number may be attributed to the asymmetric bias in market due to human behavior. The standard deviation is slightly larger for Hang Seng Index Future(1.56%) compared to CSI 300 Future(1.36%). Both markets' return exhibits excess kurtosis which is commonly seen in financial data series. The fat tail is appeared to be more obvious in Hong Kong's market with an excess kurtosis of 119.3573 compared with 9.37267 in China's index future market. The data stated in Table 2 indicates that the intraday volatility is higher in CSI 300 Future market (0.013%) compared to Hang Seng Index future market (0.009%). The standard deviations of the two markets are nearly the same, which brings a basic sense that the daily fluctuations of the two markets may be correlated. The index future market in Hong Kong reflects a much higher kurtosis (119.36) than the same market in mainland China (9.37). Such phenomenon can be caused by the reason that in most cases, the opening price of Hang Seng Index is highly e correlated with the former day's performance of American stock markets which are closed 4 hours before the Hang Seng index future begins to be traded. However, according to Hwang(2012), China's stock market is the only marketin Asia which doesn't have a significant linkage with the American stock market. The jumps in opening price induce a much higher kurtosis for data from Hang Seng Index Future.

## Table 3

## Variables

## Pr(Skewness)

## Pr(Kurtosis)

## chi2(2)

## Prob>chi2

## Ifr

0.006

0.002

17.15

0.002

## Hsir

0.037

0.000

16.92

0.0002

## Gkvif

0.000

0.000

154.18

0.0000

## Gkvhsi

0.000

0.000

416.94

0.0000

Before moving to the future steps, the stationary needs to be checked for all the variables that would be used as exogenous variables in regression later. The Phillip-Perron test and Augmented Dickey-Fuller test are both used to assess the stationary of volume and open interest across the both markets. The volume and open interest data are processed into logged form. The results are stated in Table 4.

## Table 4

## ADF test

## Phillip-Perron test

## Volume

## OI

## Volume

## OI

## CSI 300

-6.186***

-1.717

-56.049***

-5.792***

-5.071

-1.273

## Hang Seng Index

-6.935***

-5.047***

-80.710***

-6.960***

-50.819***

-5.292***

Superscript ***, **, *, represent 1%, 5%, 10% significance level.

The results from both tests show that the total volume is significant at 1% level for both markets. However, the open interest data from CSI 300 future market is not significant at any level while the open interest data from Hong Kong market is significant at 1% significant level. Since the null hypothesis of unit root cannot be rejected for the open interest data of CSI 300 future, this series cannot be used as an exogenous variable in the later model. The unit root effect in CSI 300 market is caused by the significance growth in open interest during last year. The Figure 1 exhibits this rapid growth.

The reason for the growth can be due to two main reasons. One is that the index future market has just stepped out its infant stage, the rapid growth in the number of participants and the increasing use of hedging strategy both contribute to the growth in open interest. Secondly, the People's Bank of China increased the reserve requirement ratio six times from 19% to 21.5% percent in the first half of 2011, which significantly decrease the market liquidity. The interbank offered rate (SHIBOR) reached its peak at an average of 4.56% in June 2011. The reverse case happened since the end of the same year. Till May, 2012, the RRR has come back to 20%. (from the database of Eastmoney.com) Mostly, the open interest is more sensitive to the fluctuation in liquidity than volume. This effect may also bring the unit root effect to the data.

Methods and methodology

## Garman-Klass Volatility

There are various way to measure volatility. Among those methods, Parkinson's High-Low Volatility Estimator (PHLE) and Garman-Klass Volatility (GKV) are used specially to measure the intraday volatility. The PHLE is calculated as:

Comparing with this, the GKV which is calculated using opening price, closing price, daily high and daily low tends to contain more information into consideration. The GKV is based on Parkinson's (1976) model, which is stated as:

Where u is the normalized high, which is the difference between daily high and opening price,

d is the normalized low, which is difference between daily low and the closing price

The original model is criticized as it failed to consider the joint effect of daily high, daily low and closing price. Using the method of analytic scale-invariant estimators, after adjust the optimal value, the formula of GKV comes as:

Where c is the normalized close, which is the difference between the opening price and the closing price.

The GKV as calculated for all the four markets contained in the sample, and use as the representative for intraday volatility.

## VAR model

Following the studies of Yen and Chen (2009), VAR model is applied to study the characters of intraday volatility and the causality relationship with market depth and liquidity. The order of the VAR model should be checked in this case. The study uses the Akaike (1974) information criterion (AIC) to detect the best order. The purpose to use the information criteria is due to the common competing factors in VAR model, which is that although adding more lags will reduce the RSS, there would also be a loss of freedom. A balance needs to be found in order to justify the optimal model. Compared with Schwarz-Bayesian Information Criteria (SBIC), the AIC is more efficient. The multivariate version of the AIC is used here. The VAR model with the optimal lags would be generated to check the bi-directional relationships between volatility, volume and open interest in both markets. The specified result will be checked using Granger causality test.

In the second stage, the relationships between the daily presences of the two markets will be examined using VAR model. Intraday volatilities of the two markets are used as dependent variables to test the bi-directional relationships. The other daily characters would be used as exogenous variables. AIC would be used in the very beginning in order to get the optimal lags.

The generated formula would be:

Where gkvif is the Garman-Klass volatility of the data from CSI 300 index future,

gkvhsi is the Garman-Klass volatility of the data from Hang Seng index future,

lifvol is the logged form of the trading volume of CSI 300 index future,

lifoi is the logged form of the open interest of CSI 300 index future,

lhsivol is the logged form of the trading volume of Hang Seng index future,

lhsioi is the logged form of the open interest of Hang Seng index future.

Impose response function is generated from the original VAR model. The bi-directional causality between the two markets as the impact brought by the liquidity and market depth would be studied through the statistic result generated from the impose response function.

## Augmented GARCH Model

## Symmetric GARCH model

The Generalized Autoregressive Conditional Heteroskedasticity (GARCH) model is widely accepted as a useful tool in forecasting the volatility of financial time series. To be mentioned, the volatility here is different the one in the former steps. The volatility generated by GARCH model is based on the movement across a certain period. Compared to VAR model, it has a certain advantage that the heteroskedasticity of volatility is allowed. Basically, the general form of GARCH (p,q) model can be stated as:

In this case, the value of the variance scaling parameter ht is based on both the past values of shocks and the past value of itself.

Based on the study done by Pati (2011), the trading volume and open interest are separated into the expected part and unexpected part through a proper ARMA procedure. Such procedure can be constructed as:

Similar procedure is also processed on the Hang Seng index future's data. For open interest, since mostly the expected open interest is the open interest at the beginning of each trading day, the unexpected part in just the change in open interest after one day's trading. However, in this case, because it has been detected that the unit root is existed in the open interest data of CSI 300 index future, the unexpected part should be interpreted as the positions added out of the normal growth trend, which can give a more clear sense about the unexpected elements appeared in the market.

In order to generate the proper form of the mean equation in GARCH model, LR test is used to select the best form from different orders of autoregressive, moving average and ARMA models. The expected form and unexpected form of the volume and open interest obtained from the former procedure would be used as exogenous variables in the variance equation. Through the result got from LR test, the is presented to be the best form for mean equation. So the GARCH model is built as:

## Asymmetric GARCH model

## EGARCH model

The study of behaviour finance shows that because of irrational behaviour in the financial market, the feeling of fear tends to make the market reflect more fierce fluctuation when the trend is going down.(see Tvede, 2003) The asymmetric movement is commonly accepted by the researchers. EAGRCH model is one of the most commonly used asymmetric GARCH models. It can be presented as:

## Empirical results

## Covariance between the intraday volatility

The covariance between the intraday volatility between the index future and underlying market about the two markets are presented in table 5:

## Table 5

## CSI 300 index

## CSI 300 index future

## Hang Seng index

## Hang Seng index future

## CSI 300 index

1.0000

## CSI 300 index future

0.9121

1.0000

## Hang Seng index

0.3987

0.2943

1.0000

## Hang Seng index future

0.4239

0.3086

0.9795

1.0000

As showed in the table 5, the covariance between the intraday volatility of CSI 300 index and CSI 300 index future is 0.9121 compared with 0.9795 of the market in Hong Kong. The smaller number indicates that the daily movement of CSI 300 index future does not match the underlying asset quite well compared with Hong Kong's market. Such result reflects that compared with developed index future market, the arbitraging activity is still under development and an abnormal return can be got through arbitraging during the sample period in China's index future market. There is no significant correlation between the daily movements of the two markets. The covariance between the intraday volatility of CSI 300 index and Hang Seng index is only 0.3987, while the covariance between the two index futures' intraday volatilities is even smaller. Such result is mostly due to the data collected. Although same component companies are existed in both indices, the opening price of Hang Seng index is highly affected by the performance of US stock market in the former trading day while china's stock market does not. (Hwang, 2012) Such result demonstrates that for hedgers, the Hang Seng index future has better hedging power than the CSI 300 index. The relatively low covariance of CSI 300 index future suggests that the hedgers in China's stock market should leave more margins in order to absorb the unexpected book loses when the index future does not match the underlying well.

## VAR Model

## Interrelationship between volatility, open interest and volume

Using AIC, the optimal lag is suggested to be 5 in the model for CSI 300 index future and 3 for Hang Seng index future. By this way, VAR(5) model is built for the three variables of CSI 300 index future market and VAR(3) is built for the variables of Hang Seng index future. The result got from the relevant Granger test results are presented in table 6 for CSI 300 index future and in table 7 for Hang Seng index future.

## Table 6

## Contract type

## Variable explained: gkvif

## Variable explained: lifvol

## Variable explained: lifoi

All

Ex-lifvol1

Ex-lifoi

All

Ex-gkvif

Ex-lifoi

All

Ex-gkvif

Ex-lifvol

CSI 300 index future

1.90571

1.546

.44529

21.688***

10.342**

8.7289**

26.775***

19.164***

10.197**

## Table 7

## Contract type

## Variable explained: gkvhsi

## Variable explained: lhsivol

## Variable explained: lhsioi

All

Ex-lhsivol1

Ex-lhsioi

All

Ex-gkvhsi

Ex-lhsioi

All

Ex-gkvhsi

Ex-lhsivol

HSI future

14.2221**

14.137***

7.6268*

11.493*

.88106

10.205**

22.102***

2.9948

21.582***

For table 6 and table 7:

*1. Exclude is used as 'Ex' for short.

2. The value stated in the value is the chi-square statistic

3. Superscript ***, **, *, represent 1%, 5%, 10% significance level.

The result shows that in CSI 300 index future market, the intraday volatility and open interest have a bi-directional relationship with the current trading volume. However, in Hong Kong's market, such relationship is now as significant. When taken the intraday volatility out of the model, the relationship becomes invalid. For the intraday volatility, the result get from data of Hang Seng index future shows that the intraday volatility in the market is granger caused by the log form of volume and open interest at 5% significant level. While no exact relationship is found in the CSI 300 index future market by any extent when using the intraday volatility as dependent variable. Turning to open interest, both markets reflect the fact that the open interest is granger caused by the intraday volatility and trading volume in the past few days.

Such result can be interpreted as that in future market, the open interest is the sign of the level of the disagreement between long and short and the level of the participants' enthusiasm. For example, the high intraday volatility and trading volume is always a sign of herding behaviour. The open interest shows the participants' outlook towards the market after a whole day's movement. High volatility and volume will make some traders want to follow the trend while some others want take profit from the call-back. The result get here shows that the herding behaviour is commonly existed in both markets. In most cases, the intraday volatility should be related with the volume and open interest in the past few days since the open interest is the fuel for the later volatility. Such relationship is showed to be significant in Hang Kong. However, no significant relationship is found in CSI 300 future market. This should be partly due to the fact that the CSI 300 index future is still under its growing stage during the last year which can be judged by the resistant growth in open interest. Such phenomenon twists the theoretical relationship. In both markets, volume is showed to be granger caused by the past open interest and intraday volatility. However, for the Hang Seng index future, the relationship is mainly caused by the intraday volatility. As showed in the table 7, after excluding the intraday volatility, the causality becomes insignificant.

## The bi-directional causality between CSI 300 index future and Hang Seng index future market

Another VAR model is built to study the bidirectional causality between the volatilities of the two markets. As stated in the section of methods and methodology. The model is constructed as:

(1)

(2)

Following the procedure used in the former section, the optimal lag is first to be selected using AIC. The result indicates that the optimal lag is 1 (k=1) in this case. The result from Granger causality test is showed in table 8, which indicates that the intraday volatility of Hang Seng index future is granger caused by the intraday volatility of the intraday volatility of CSI 300 index future when taking the trading volume and open interest as exogenous variables. The critical value doesn't suggest the existence of the reverse relationship.

## Table 8

## Equation

## order

## Prob > chi(2)

## gkvhsi

1

0.000***

## gkvif

1

0.271

Superscript ***, **, *, represent 1%, 5%, 10% significance level.

The coefficients and test statistics get from the VAR model are stated in table 9 below:

## Table 9

## Dependent variable

## Independent variable

## coefficient

## P value

## gkvhsi

gkvhsi(-1)

0.0301

0.618

gkvif(-1)

0.2760

0.000***

lifvol

0.0001

0.114

lhsivol

0.0002

0.000***

lifoi

0.0001

0.192

lhsioi

0.0003

0.003***

constant

0.0014

0.174

## gkvif

gkvif(-1)

-0.0508

0.271

gkvhsi(-1)

0.0294

0.617

lifvol

0.0002

0.000***

lhsivol

0.0002

0.000***

lifoi

-0.0001

0.003***

lhsioi

-0.0005

0.000***

constant

0.0020

0.008***

Superscript ***, **, *, represent 1%, 5%, 10% significance level.

Judged by the critical value, the coefficients on the lagged intraday volatility in CSI 300 index future market and the log form of the trading volume and open interest in the Hang Seng index future market are significant. The intraday volatility of the CSI 300 index future in the former day has a significant influence to the current day's volatility in Hong Kong's market. It's a direct sign that the Chinese stock market can bring significant influence to the Hong Kong's market in recent years. Commonly, the trading volume and open interest would have direct relationship with current day's volatility. It's because of the reason that the trading volume is the most direct force that can induce volatility, while high volatility will cause the herding effect which will make more traders want hold their positions overnight. The small values of the coefficients are due to the difference in order of the data. Although the causality from the intraday volatility of Hong Kong's market to Chinese market is not significant, all the critical values on the coefficients of the exogenous variables are significant. It should be noticed that the trading volume and open interest of Hong Kong's index future market has significant impact on the current day's volatility of CSI 300 index future. This also indicates the strong correlations between the two markets in the current year.

Impose response functions are generated on the original model in order to get the general path. The time span is set to be 10 which is the number of trading days in two weeks. The path is showed in figure 2 and the numerical results are stated in table 10.

## Table 10

step

gkvhsi on gkvhsi

gkvhsi on gkvif

gkvif on gkvhsi

gkvif on gkvif

IRF

1

.029377

-.050833

.275971

.030069

2

-.013165

-.003022

.016405

-.013124

3

-.001221

.000578

-.00314

-.001229

4

.000124

.000079

-.000431

.000123

5

.000026

-3.9e-06

.000021

.000026

6

-3.3e-07

-1.4e-06

7.7e-06

-3.1e-07

7

-4.0e-07

-2.6e-08

1.4e-07

-4.0e-07

8

-1.9e-08

2.0e-08

-1.1e-07

-1.9e-08

9

4.8e-09

1.6e-09

-8.4e-09

4.8e-09

10

5.7e-10

-2.0e-10

1.1e-09

5.7e-10

From table 10, the results suggest that among all the four paths, a unit shock will die out quickly in the following trading days. After one trading week, the impact would be tiny. The most significant effect comes from the intraday volatility of CSI 300 index future to Hang Seng index future. In the next trading day, nearly 27% of the shock is remained. Such impact would be drop sharply in later periods and became negative for two days after going through the second period. The shock in the intraday volatility of Hang Seng index future will bring impact to the CSI 300 index future in the reverse direction. But the impact is not significant. Both markets can digest the shock from their own quickly. The result shows that nearly 99% of the shock will die out in the next period. And the over shoot happened in the second and third steps.

## GARCH Model

GARCH type model is to be good fit to the prediction of financial volatility. The first step to build a proper GARCH model is to detect the optimal form of the mean equation. Sufficient numbers of lagged terms should be added in order to remove any predictability. As stated in the section of methods and methodology, the Wald test is generated to detect the most appropriate form. In this study, different forms of ARMA models are tested to get the proper one for the mean equation. The result is showed in table 11:

## Table 11

## ifr

## hsir

## ARMA type

## P value

## ARMA type

## P value

AR1

0.2225

AR1

0.4330

AR2

0.4715

AR2

0.4668

AR3

0.599

AR3

0.6066

ARMA(1,1)

0.1935

ARMA(1,1)

0.5221

ARMA(2,1)

0***

ARMA(2,1)

0.0529*

ARMA(2,2)

0.634

ARMA(2,2)

0.7202

MA2

0.442

MA1

0.4785

MA1

0.2103

MA2

0.4341

MA3

0.3875

MA3

0.5693

Superscript ***, **, *, represent 1%, 5%, 10% significance level.

From table 11, the p value got from Wald test suggests that for both market, the ARMA (2,1) form are the best structure in forecasting the volatility. Regards to the order for the GARCH type model, the GARCH (1,1) form is lost commonly used, which is set as the basic specification of p=1 and q=1. No significant improvement in goodness of fit is showed when higher orders are adjusted. For this reason, the GARCH (1,1) is used for both markets in the following study. In order to study the impact brought by the expected and unexpected part of volume and open interest to the volatility, the original data of volume and volatility are processed by the following process as stated in the former section:

The error terms are collected which are the representatives of unexpected part of the four variables. The predicted series of the dependent variables are considered to be the expected portion. Both the expected variables and unexpected variables would be put into the conditional covariance function. However, before certain steps, such variables should be checked for stationary since they are considered to be the exogenous variables in the conditional variance function. Augmented Dickey-Fuller test (ADF test) is used to achieve such purpose. The result from the ADF test is listed in table 12:

## Table 12

## Contract type

## Volume

## Open interest

## Expected

## Unexpected

## Expected

## Unexpected

## CSI 300 index future

-1.747

-14.266***

-0.751

-15.401***

## Hang Seng Index future

-7.970***

-15.235***

-6.219***

-14.580***

As showed in the section of data and descriptive statistics, the open interest of the CSI 300 index future is not appeared to be stationary, the predicted form shows the same property. It's also found that when transformed into predicted form, the unit root problem also exists in the volume data from CSI 300 index future. Since for the exogenous variables must meet the condition of stationary, these two variables cannot be put into the conditional variance equation in the later stage. Because this study is aimed at investigating the relationships and making comparisons between the index future markets in China with the same market in Hong Kong, the variables with the same definitions from Hang Seng index future are dropped from the condition covariance equation in the same way in order to make comparisons. In this case, the GARCH model is built as:

For CSI 300index future,

The similar model is used to process the data of Hang Seng index future.

The regression results are stated in table 13:

## Table 13

## CSI 300 index

## Hang Seng Index

## Estimators

## Estimation

## P value

## Estimation

## P value

0.0015**

0.044

-0.0011

0.148

-0.7245

0.162

-0.8294**

0.037

-0.0880*

0.091

-0.0841

0.249

-0.6661

0.195

0.7712*

0.052

-8.9295***

0.000

-8.6458***

0.000

-0.0611**

0.013

0.0627

0.155

0.0899

0.363

-0.0663

0.633

0.00001***

0.000

0.00001***

0.003

0.00007*

0.100

4.56e-6

0.726

## Wald test

0.2084

0.1156

Superscript ***, **, *, represent 1%, 5%, 10% significance level.

The short-run dynamics of the resulting volatility time series can be judged by the value of the ARCH and GARCH parameters. The small parameters we get here indicate that in both market, the persistence of the volatility is quite weak. The ARCH parameter of the CSI 300 index's model is significant judged by the P value. In both markets, the sum of the ARCH and GARCH parameters leads to a percentage less than 15%, which indicates that the current volatility can only affect the volatility of the coming days to a small extent. More than 85% of the shock would die out in next period. Both of the models have negative parameters on the lagged terms of return in the mean equation. The parameter of the one-lagged term in Hong Kong's model is significant at 5% level of significance while the two-lagged term in CSI 300 index's model is significant at 10% level of significance. The parameters of the lagged term in the mean equations indicate the persistence in the daily return. In this model, the sums of the two parameters in both markets give values more than negative 80%. The parameters on the last day's return shows that the current day's return could be different from the return in last trading day at a level of more than 70%, which means that in most cases, a significant portion of the movement of the market in the current day will be reversed soon. The consistency of the direction is quite weak in the short-run. The Wald test is used to check the goodness of fit. It shows that the specifications of both models are not specified well. The Model on Hang Seng Index future is better specified compared to the model on CSI 300 index future with P value of 0.1156, but both above 10% significance level.

## EGARCH Model

ARMA(2,1)-EGARCH model is processed on the series from both markets in order to detect the asymmetric effects in the market. The regression is specified as:

For CSI300 index future:

The result is stated in table 14:

## Table 14

## CSI 300 index

## Hang Seng Index

## Estimators

## Estimation

## P value

## Estimation

## P value

-0.0748

0.612

0.8634***

0.000

0.00007

0.128

0.00001***

0.003

0.00001***

0.000

-0.00003**

0.048

## Wald test

0.0597*

0.0000***

Superscript ***, **, *, represent 1%, 5%, 10% significance level.

Both models are significantly improved by using EGARCH model regarding to the p value got from Wald test. The specification of CSI 300's model is significant at 10% level while the significance of the specification on Hang Seng Index is at 1% significant level. The EGARCH term is significant in Hang Seng index future's model but not in CSI 300 index's. The EGARCH term of Hang Seng index future is even significant at 1% significant level. This indicates that the asymmetric effect is prominent in Hong Kong. Although, the EGARCH term is not tested to be significant in CSI 300 index future, the conspicuous improvement in the goodness-of-fit suggests that the EGARCH has a relatively strong explanatory power compared with the GARCH model.

After taking the asymmetric effect into consideration, in CSI 300 index future market, the regression result shows that the parameter of unexpected open is significant while the parameter of unexpected open interest does not. The parameter of the unexpected open interest is significant at 1% level. This suggests that the shock in open interest is very likely to bring impact on volatility. The positive values got on both parameters demonstrate that the shock in trading volume and open interest will influence the market in the same direction as itself. The higher value on the coefficient of unexpected trading volume suggests that the unexpected trading volume can bring stronger impact to the volatility.

Such relationships are more significant in CSI 300 index future market. Both of the coefficients on the unexpected variables in the Hang Seng index's model are showed to be significant, which means that the unexpected changes in both volume and open interest have a significant relationship with the volatility. The positive value on trading volume indicates that the unexpected fluctuation happened in trading volume will induce the change in volatility in the same direction. An unexpected increase in the trading volume will come with a higher volatility and vice versa. The coefficient on unexpected open interest is negative, which demonstrates that in Hang Seng index future market, the shock in open interest would bring fluctuation to the volatility in the reverse direction. The negative relations between open interest and volatility are seldom seen in the future market. Such difference is due to the fact that compared to the stock market in Hong Kong, the Chinese stock market is relatively independent. Because the movement of the US stock market can significantly influence the opening price of Hang Seng index, the speculators in Hong Kong seldom leave positions overnight. This causes the fact that most of the open interest is consisted by the positions hold by investors and hedgers. The significant different structure of open interest in Hong Kong should be a reason for the unusual relationship. Such result also indicates that traders do not need to use specific strategy to react to the unexpected open interest. The bigger absolute value on the unexpected open interest demonstrates that the unexpected change on open interest brings more information compared to unexpected change on trading volume. All of the parameter values got on unexpected terms is relatively small. This is due to the difference in the numerical order among variables. The value of trading volume and open interest are significantly larger than daily return, which is different from the market in China's market. The result indicates that the unexpected change in trading volume conveys more information and brings larger effect to the market.

## Conclusion

China launched the CSI 300 index future in April, 2010. Compared to the index future in some developed markets, the Chinese index future is still immature but growing in a fast pace during the last two years. The study examines the characters in the volatility of the CSI 300 index future's trading in the recent year. The Hang Seng index future market is chose to be the sample of developed market. The trading volatility of Hang Seng index future during the same period is studied in the same way in order to make comparisons. The study on volatility is mainly focused on the interrelationships between the volatility and the trading volume and open interest since it's widely accepted that the latter two parameters can be judged as signs of the movement in volatility. There are mainly three types of participants in the index future market, which are arbitrager, hedger and trader. The needs and concerns of different groups of participants are considered separately. Traders can be further separated into speculators and investors. Speculators care more about the intraday volatility since the intraday volatility is where the risk and volatility come from, while the latter concerns more about the volatility between a certain periods because they need to take the volatility into consideration to protect their margin.

The covariance between the index future and underlying is studied based on the point that for hedgers, the matching efficiency is their first consideration. The same is for arbitragers; the arbitraging profit comes from the asymmetric movement between the index future and underlying index. The Garman-Klass Volatility is instrumented as the measurement of intraday volatility. The results shows that the covariance of the intraday volatilities between CSI 300 index future and its underlying index is relatively small compared to the result got on Hang Seng index future. It indicates that compared to the hedgers in Hong Kong's market, the hedgers in China should leave more margins in order to absorb the unexpected book loses when the index future does not match the underlying well. It also suggests that the arbitraging return on CSI 300 index future is still relatively high compared to the Hang Seng index future after one year's development.

Two VAR models are constructed in this study. A simple VAR is first applied to study the characters of intraday volatility and the causality relationship with market depth and liquidity. The result get from data of Hang Seng index future shows that the intraday volatility in the market is granger caused by the log form of volume and open interest at 5% significant level. While no exact relationship is found in the CSI 300 index future market by any extent when using the intraday volatility as dependent variable. The result from Hang Seng index future is reasonable since it reflects the herding behaviour which is commonly seen in financial markets. However, since a unit root problem has been detected in the open interest data of CSI 300 index future, it indicates that the fast growing pace of this market twist such relationship. The effect should be temporary. Another VAR model with logged form of trading volume and open interest as exogenous variables is used to study the bi-directional causality between intraday volatilities of CSI 300 index future market and Hang Seng index future market. Impose response function is generated to get the path of the information flow. The intraday volatility of the CSI 300 index future in the former day has a significant influence to the current day's volatility in Hong Kong's market. It's a direct sign that the Chinese stock market can bring significant influence to the Hong Kong's market in recent years. The shock in the intraday volatility of Hang Seng index future will bring impact to the CSI 300 index future in the reverse direction. But the impact is not significant. Both markets can digest the shock from their own quickly. The overshot will come in the second period on both paths.

GARCH and EGARCH model are used in the third stage. The volatility produced by GARCH and EGARCH is based on the fluctuations in daily returns which represent the volatility that can happen in a certain periods of time later. Investors always care about this volatility since it can affect the safety of the account directly. Trading volume and open interest are separated into expected portion and unexpected portion. The expected portions are dropped because expected trading volume and expected open interest of CSI 300 index future have unit root problem. Only unexpected portions are studied. ARMA (2,1) model is chose as the form for the mean equation. The asymmetric effect is found to be significant in Hong Kong's market but not in the Chinese market. However, both models show improvement in specification using EAGRCH model. The study finds that in Hong Kong's index future market, both the unexpected volume and unexpected open interest can significantly affect volatility. However, only unexpected open interest can influence the volatility of CSI 300 index future. The impacts brought by unexpected open interest are in different directions in the two markets. For CSI 300 index future, the unexpected open interest can positively affect the volatility while such impact is negative in Hong Kong. Such difference is due to the fact that as proved by Hwang(2012), the Chinese stock market is more independent compared wi