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The intraday behaviors and relationships with its underlying assets: evidence on option market in Taiwan
International Review of Financial Analysis 14 (2005) 587 – 603
The intraday behaviors and relationships with its underlying assets: Evidence on option market in Taiwan Mingchih Lee*, Chun-Da Chen Department of Banking and Finance, Tamkang University, Tamsui, Taipei 251, Taiwan Available online 26 November 2004
Abstract In this paper, we use daily data to investigate the information asymmetric effects and the relationships between the trading volume of options and their underlying spot trading volume. Our results reveal that options with higher liquidity are near-the-money and expiration periods with 2 to 4 weeks have higher trading activity. We classify them into two parts with the ARIMA model: the expected trading activity impact and the unexpected trading activity impact. Using the bivariate generalized autoregressive conditional heteroscedasticity (GARCH) model, we investigate the trading activity effect and information asymmetric effect. In conclusion, the trading volume volatility of the spot and options markets move together, and a greater expected and unexpected trading volume volatility of the spot (options) market is associated with greater volatility in the options (spot) market. However, both markets generate higher trading volume volatility when people expect such an impact rather than when they do not. We also find that there are feedback effects within these two markets. Furthermore, when the spot (options) market has negative innovations, it generates a greater impact on the options (spot) market than do positive innovations. Finally, the conditional correlation coefficient between the spot and the option markets changes over time based on the bivariate GARCH model. D 2005 Elsevier Inc. All rights reserved. JEL classification: G14 Keywords: ARIMA model; GARCH model; Options market; Volatility transmission; Information asymmetric effect
* Corresponding author. Tel.: +886 2 26215656x2855; fax: +886 2 26214755. E-mail address: [email protected] (M. Lee). 1057-5219/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.irfa.2004.10.021
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1. Introduction Options on stocks were first traded on an organized exchange in 1973. Ever since then, there has been a dramatic growth in the options market, as options are now traded on many exchanges throughout the world. Huge volumes of options are also traded over the counter by banks and other financial institutions. The underlying assets include stocks, stock indices, foreign currencies, debt instruments, commodities, and futures contracts. In Taiwan the first option (call and put) was listed by the Taiwan Futures Exchange (TAIFEX) on the TSEC Capitalization Weighted Price Index (TAIEX) on December 24, 2001. The TAIEX option is a European-style bphysical deliveryQ option. In the beginning, investors unfamiliar with the new derivatives caused the trading volume to be very illiquid. However, following the options trading activities of South Korea and the United States, options with a better hedge performance have now become the most popular derivative in financial markets. Therefore, if investors can understand the applications and trading systems of options, then the options market in Taiwan has high growth potential. The Taiwan index future has the same underlying TAIEX listed on July 21, 1998. The investors hold the futures can utilize the option to hedge, and the option writers can also employ the index futures to hedge risk of the short position. Under these inter-applications, the futures market will become more perfect, and the option market will develop successfully. There are many uncertainties in the stock market that cause it to be unstable and this makes options very attractive. The main purpose of trading an option is for hedging. After the option lists, investors have more tools for hedging, and investment operations have more elasticity. The risks and costs of trading options are different from trading futures. Using an option not only reduces portfolio risks, but also lowers the investment cost. Applying options and futures at the same time will not cause crowding effects. However, the spot market will become more perfect, because of diverse hedging methods. There are many relationships between spot and option markets through speculating, arbitraging, and hedging by investors. In Taiwan the relationships and the volatility transmissions between the volume in the options and spot markets have never been examined. Therefore, the objectives of this paper are as follows: First, we analyze the relationships between the moneyness, expiration, and trading activities. We then consider the effects of the spot trading volumes after options became available in Taiwan. Finally, we investigate the information asymmetric effects and volatility transmissions on the trading volume between the spot and the options markets. Section 2 summarizes the previous literature. Section 3 describes the data and methodology. Section 4 explains the empirical results. Section 5 summarizes the results.
2. Literature review Because Taiwan’s options market is an emerging market, few attempts by researchers have been made at investigating options. Prior empirical research can be classified into three parts: First, there are some previous studies about the impact of an expiration on the trading volume of options (warrants can be call options). Chen and Wu (2001) showed that the expiration of warrants causes a positive price effect on the expiration day, a negative
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price effect after expiration for in-the-money warrants, and a negative price effect prior to the expiration for out-of-the-money warrants. In their study there also appears to be a strong relationship between price and trading volumes of warrants. Corredor, Lechon, and Santamaria (2001) found that the expiration of Ibex-35 index derivatives (Spanish Equity Derivatives Exchange) has no significant effect on either the underlying asset prices or the level of volatility on the expiration day. However, the expiration of stock options does have a significant impact on their underlying assets. They showed a downward pressure on prices, a reduction of the volatility level in the week before the expiration date, and a significant increase in trading volume on the expiration day. Chamberlain, Cheung, and Kwan (1993) by contrast analyzed the effect of the listing of options on the price behavior, trading volume, and liquidity of underlying stocks on Canadian stock exchanges. The results indicate that return volatility declines, trading volume increases, and liquidity is enhanced, though the findings are not statistically significant. They also tested whether the impact of listing on volume depends on the pre-listing liquidity of a stock. However, they failed to detect any statistically significant relationship. The second part of the literature investigates the nature of the relationship between moneyness and three liquidity proxies for options. Etling and Miller (2000) conducted their study on the Standard & Poor’s (S&P) 100 and S&P 500 indexes. They used bid-ask spreads, volume, and time between quotes as liquidity proxies. Their statistical analysis rejected the hypothesis of a simple quadratic relationship between moneyness and liquidity in these markets. Although liquidity was maximized near the money, liquidity did not decrease symmetrically when option strikes moved deeper into the money or deeper out of the money. Kamara and Miller (1995) avoided the early exercise problem by testing putcall parity using S&P 500 European options. The result shows that most of the trading volume of put and call options during 1986 to 1989 was concentrated in near-the-money options (0.98bS/Xb1.02, where X is the exercise price and S represents the S&P index price) and somewhat out-of-the-money options (calls with 0.96bS/Xb0.98 and puts with 1.02bS/Xb1.04). Moreover, the trading volume fell monotonically as the options moved away from at-the-money options. The third part in the literature (and the most important argument of this paper) examines the cross-sectional relationship of volatility transmissions of trading volume between stock and option markets. Darper, Mak, and Tang (2001) examined the impact of warrant introductions on price, volatility, and volume of trading in the underlying security. An increase in trading volume is found as a result of the introduction, but has little impact on volatility. Price effects are also identified, although these effects appear to be temporary and do not persist much beyond the listing of the warrants. On delisting, however, a large negative price effect is observed. Hagelin (2000) investigated the relationship between options market activity and spot market volatility on Sweden’s OMX index. The findings show that for the complete sample period there is unidirectional causality from spot market volatility to options market activity for calls and puts jointly, as well as for calls and puts, respectively. While unidirectional causality from spot market volatility to call options market activity is documented for both subperiods, bilateral causality between put option market activity and spot market volatility was found for one of the subperiods. The interesting findings are that both the lagged expected and unexpected put options market activities were found to be positive and significant for the first period. For the second
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period, the lagged expected put options market activity was found to be negative and significant, while the unexpected component was reported to be negative, but insignificant. Overall, the evidence suggests that calls and puts may affect spot market volatility differently and that this potential impact can vary under different market conditions. Park, Switzer, and Bedrossian (1999) wrote that unexpected options trading activity contributes to enhanced volatility in the underlying equity returns. Moreover, the analysis indicates that expected options trading activity significantly affects equity volatility in only a minority of firms. This is consistent with the contention that trading in the equity options market does not systematically lead to price destabilization in the underlying equity market. Boluch and Chamberlain (1997) indicated that the option volume/stock price relationship is largely characterized by feedback, with the option volume causing the stock price to change and vice versa. Fase (1994) demonstrated the feedback hypothesis for trading volume on the Amsterdam stock and options markets. The most important finding is that very often causality runs from options to the stock market, which seems to support the feeling of the business profession and the main hypothesis of his analysis. Stephan and Whaley (1990) used intraday data to examine the lead/lag relation between price changes in the option market and stock market. The results indicate that price changes in a stock lead the options market by as much as 15 min. The analysis of trading volume indicates that the stock market lead may be even longer.
3. Data and methodology 3.1. Data Among the many stock indices of the TSEC (Taiwan Stock Exchange) that have listed derivatives, the most frequently quoted one is the TSEC Capitalization Weighted Price Index (TAIEX). The TAIEX has been used since 1971 and is based on the average capitalization in 1966. Other weighted indices include non-finance, non-electronics, and 22 sector indices by individual industries. Index options on the TAIEX were introduced by TAIFEX (Taiwan Futures Exchanges) on December 24, 2001. At present, there are only European options. During the beginning of their listing, there was little activity within the trading volumes, because investors at that time did not understand how to use an index option to hedge their investment risk. Currently, the trading activities of call options are still higher than put options. In this paper, we use the daily and intradaily data for the trading volume of the TAIEX and TAIEX options. Taiwan Stock Exchange (TSE) transaction data together with contemporaneous options trading volume were obtained from the Taiwan Economic Journal (TEJ), which is a local data vendor, and from the Taiwan Futures Exchanges (TAIFEX). The investigated period in this study for the 92 days is from September 25, 2002 to December 27, 2002. The period before September 25, 2002 was omitted due to low trading activities in the options market.1 After eliminating non-transaction days, the 1
The standard deviation of the trading volume volatility of options is 0.3055 during the investigated period, but is 0.4004 from when the options began in December 24, 2001 up until September 24, 2002.
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estimated period is 65 days. The data was filtered in a series so as to satisfy various criteria. All transactions after 1:30 p.m. Taiwan Time were eliminated since the TSEC closes its market at that time. New information that comes to the options market between 1:30 and 2:00 p.m., when the TAIFEX is closed, can be acted upon immediately, whereas the corresponding change in the TSEC may not occur until the next trading day. We therefore chose the intraday sampling interval. The interval has to be large enough so that trading is sufficiently heavy in each interval to provide useful information, but small enough to capture a short-term causal relationship. After inspecting the data, an interval of 15 min was set up. The data was then aggregated for the trading volumes of the TAIEX market and TAIEX options based on this 15-min time interval in order to give the total number of put and call contracts traded, as well as the total number of put and call transactions in each interval. In those cases, the total amount of the intraday sampling interval data at 15-min intervals was 1170 observations per series. In order to capture the volatility transmissions between the TAIEX spot market and TAIEX options on the trading volumes, we have to derive the ordinary series data with the rate of volume changes. Two points need to be considered. The first point is that the intraday data from the database come in 1-min intervals. Before an analysis with the empirical model, we need to sum the trading volumes in 15-min intervals per series. We next process first-order difference to become stationary-I(0) series. We define the change rate of trading volume as a logarithm of the ratio of the daily trading volume as: VS;t ¼ log ms;t =ms;t1 100
ð1Þ
VO;t ¼ log mo;t =mo;t1 100;
ð2Þ
where m s,t represents the 15-min interval trading volume of the TAIEX spot market at time t; and m o,t represents the 15-min interval trading volume of TAIEX options at time t. Time t1 is the last 15-min interval trading volume, while V S and V O are the rate change of volume in the TAIEX and TAIEX options, respectively. 3.2. Methodology In this study the main point falls on demonstrating the feedback relationship of trading volumes and information asymmetric effects between the TAIEX and TAIEX options. We first employ the autoregressive integrated moving average ARIMA (p,0,q) model to classify the rate change of TAIEX and TAIEX option volumes into expected and unexpected activity variables (terms). Investors may follow their expectations from the trading volumes in this market to adjust their investment strategies. We thus conclude that using the intraday data with 15-min intervals to consider volatility transmissions and their influences between these two securities can obtain better expectations. The residual term that is derived from the ARIMA model is separated into positive and negative threshold effects; specifically, separating the unexpected volatility into positive and negative volatility effects. Finally, these two threshold dummy variables are added into the bivariate generalized autoregressive conditional heteroscedasticity (GARCH) (1,1) model. The models of this study are given below.
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3.2.1. ARIMA model In order to use the ARIMA methodology, it is first necessary to identify whether each series is stationary. The ARIMA model can only be used on a stationary series, and if it is determined that a series is non-stationary, then it could be repeated until a stationary series results. Most of the spot and options volume series require first-order differencing. We take a first difference that produces a stationary series and apply the ADF and PP tests. The result shows that the spot and options volume series become stationary after being firstorder differenced, as denoted by I(0). We then employ the general ARIMA (p,0,q) model to divide the expected and unexpected variables from the change in the volume. The ARIMA (p,0,q) model can be written as follows: Vi;t ¼ a0 þ
p X
aj Vtj þ
j¼1
q X
bj etj
i ¼ TAIEX; TAIEX OPTION;
ð3Þ
j¼0
where V is composed of a logarithm of the ratio of the trading volume, and ! ! p q X X EV i;t ¼ a0 þ E aj Vtj þ E bj etj i¼1
UEV i;t ¼ Vi;t EV i;t ;
ð4Þ
j¼0
ð5Þ
where EVi,t represents the expected volatility of volumes and UEVi,t shows the unexpected volatility of volumes. One thing worth mentioning now is how to choose the optimal ARIMA model. The criteria are that the estimate coefficients are all significant, a minimum AIC value, and residual term has no series correlation. Thus, the optimal ARIMA models of the TAIEX spot and the TAIEX options are ARMA (3,3) and ARMA (3,1), respectively. The expected volatility of volumes can be evaluated by the actual trading volumes subtracted by the optimal residual terms, which are estimated from the ARIMA model, and the residual value can be seen as the unexpected volatility portion of volumes. Dividing the unexpected volatilities by zero into positive and negative threshold effects, the dummy variables can be expressed as: UEV þ ¼
UEV ¼
1; if UEV N 0 0; if UEV b 0
ð6Þ
1; if UEV b 0 : 0; if UEV N 0
ð7Þ
By setting up the threshold dummy variables, we may account for whether information asymmetric relations do exist between the trading volumes of the TAIEX and TAIEX options. Similarly, it is better to say that we can demonstrate that the volatility transmission mechanism is asymmetric, i.e., negative innovations in a given market increase the volatility in the next market, resulting in considerably more trading than that under positive innovations.
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3.2.2. Bivariate GARCH (1,1) model The bivariate GARCH model not only is able to test for the time-varying variance or volatility in the spot and options markets, but can also investigate volatility transmission between the two markets. Many previous studies indicate that the time series data within the GARCH (1,1) model accesses the appropriateness of the GARCH specification; for instance, Bollerslev (1990), Wang and Wang (1999), Kearney and Patton (2000), and Wang and Wang (2001). Thus, this paper adopts a bivariate GARCH (1,1) model to investigate the dynamic relationships in both markets and accounts for the phenomenon of feedback influence which arises from options that have a better hedging performance for the spot market. After evaluating the expected and unexpected variables from the ARIMA model in each series, we change the conditional mean equation so that both variables are included. We then divide the positive and negative unexpected volatilities of the trading volumes by zero and add these two dummy variables into the conditional variance equation. With the bivariate GARCH (1,1) model, we can write the equation as: 2 2 2 X X X VS;t ¼ a10 þ a1i VS;ti þ b1i EV O;ti þ c1i UEV þ O;ti i¼0
þ
2 X
i¼0
i¼0
d1i UEV O;t1 þ eS;t
ð8Þ
i¼0
VO;t ¼ a20 þ
2 X
a2i VO;ti þ
i¼1
þ
2 X
2 X i¼0
b2i EV S;ti þ
2 X
c2i UEV þ S;ti
i¼0
d2i UEV S;t1 þ eO;t
ð9Þ
i¼0
eS;t jXt1 fN ð0; Ht Þ eO;t
h2 Ht ¼ S;t hO;S;t
hS;O;t h2O;t
ð10Þ
h i 2 2 2 hS;t ¼ c211 þ a2þ 1;11 DO þ a1;11 ð1 DO Þ eO;t1 þ g1;11 hS;t1
ð11Þ
ð12Þ
nh i i h þ þ hS;O;t ¼ c12 c11 þ aþ 1;11 a1;22 DO DS þ a1;11 a1;22 DO ð1 DS Þ io h i h þ þ a e1;t1 e2;t1 1;11 a1;22 ð1 DO ÞDS þ a1;11 a1;22 ð1 DO Þð1 DS Þ
hO;t
þ g1;11 g1;22 hS;O;t1 h i
2þ 2 2 2 ¼ c222 þ c212 þ a2þ 1;22 þ a2;22 DS þ a1;22 þ a2;22 ð1 DS Þ e2;t1
2 2 þ g1;22 þ g2;22 h22;t1 :
ð13Þ
ð14Þ
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where V S,t is the logarithm of the ratio of the TAIEX trading volume at time t and V O,t is the logarithm of the ratio of the TAIEX option trading volume at time t. EVi,t is the expected change rate of trading volume at time t (i=S, O; S represents the spot, O represents the option). UEV+ and UEV represent the unexpected positive and negative volatilities of volumes, respectively, EV and UEV are estimated from the ARIMA model. The residuals of the ARIMA model are UEV, however, EV could be evaluated by Vi,t subtracting the residuals. D S and D O are calculated as follows: 1; if UEV O N 0 ð15Þ DS ¼ 0; if UEV O b 0 DO ¼
1; if UEV S N 0 0; if UEV S b 0
ð16Þ
Easley, O’hara, and Srivivas (1998), Fase (1994), and Vijh (1990) indicated that the period of volatility transmission in both the spot and options markets does not exceed 30 min. Thus, the time lag length of this model is two periods per series.
4. Empirical results The setup of this section is as follows. First, we introduce the relationship between moneyness, expiration, and daily trading volumes of the options market in Taiwan. Second, we use intraday data to examine the asymmetric effects of the GARCH. 4.1. Preliminary findings Table 1 presents summary statistics for each series, including the mean, standard deviation, skewness, and kurtosis for the first differences of each intraday trading volume. The mean changes of the volume are 0.2611 for the spot and 0.0809 for the option market. Moreover, the standard deviations of the volatility are close between the spot and the options during the investigated period. Both of the first-differenced series are highly
Table 1 Preliminary statistics on spot and options series of intraday volume volatilities, 2002.9.25–2002.12.27 Statistics
Series
Mean Std. Dev. Skewness Kurtosis Jarque–Bera normality test
TAIEX
TAIEX Option
0.2611 65.8025 3.1729*** 10.8718*** 7718.6239***
0.0809 58.2017 0.3269*** 1.5386*** 136.1293***
Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively. Jarque–Bera (1987) normality test, which follows a chi-squared distribution, with two degrees of freedom. The 3
statistic is JB ¼ N ½ skewness þ ðkurtosis3Þ . 6 24 2
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Fig. 1. The trend of the TSEC Capitalization Weighted Price Index, 2001.12.24–2002.12.27.
skewed and leptokurtotic relative to the normal distribution, although only the spot series exhibits negative skewness. In addition, the Jarque–Bera normality tests strongly reject normality for all trading volume changes, with a critical value of 9.21 at the 1% significance level.2 Fig. 1 illustrates the trend of the TAIEX from the beginning of options listing; showing a decline in the long run. On the day data of basic statistics, we include the options’ moneyness and expiration of the options’ trading volume. We first observe the change in the daily option volume. Fig. 2 shows the trading behavior of options during this period. The volume has continually risen up to the present time and it reveals that options are now more acceptable and understandable for investors. At the beginning of options listing, the options market was very illiquid and the total number of contracts was only 1100 per day. However, the trading volume rose to 5000 contracts per day from the end of April 2002. We notice that the volume rose to between 10,000 and 20,000 contracts for the sample period and both call and put volumes have risen in the same way. We should not ignore here that the trading volume of calls is relatively larger than puts. During this sample period, Taiwan’s economy was still in a recession and the stock market was a bear market. These conditions caused most investors to expect the stock market to rise. At the same time, the Taiwan’s government announced some good policies3 to improve the stock market. When investors received these sorts of news, they expected that stock prices would rise and hoped that they could buy stocks with lower prices, which induced the call volumes to be larger than the put volumes. On the other hand, the Taiwan warrant market was established in 1997. The warrant and call are similar. So the investors can utilize the
2
The J-B (Jarque & Bera, 1987) tests whether a series is normally distributed. Under the null hypothesis of normality, the J-B statistic is distributed chi-squared with two degrees of freedom. 3 The Central Bank of China (CBC) lowered the discount rate, the rate on accommodations with collateral, and the rate on accommodations without collateral each by 25 basis points from 1.875%, 2.25%, and 4.125% to 1.625%, 2.0%, and 3.875%, respectively, effective from November 12, 2002. In addition, the remunerative rate on banks’ reserve accounts with the CBC was reduced from 2.5% to 2.25%, also effective from November 12, 2002.
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Fig. 2. The trend of trading volumes (number of contracts) of options, 2001.12.24–2002.12.27.
call more acceptably than put in processing the investments. For reasons mentioned above, we understand that the volume of call is larger than put. We also observe the distribution of the relationships between moneyness and options volume using day data from the listing of options to December 27, 2002. The moneyness is defined as the stock index divided by the exercise price. Fig. 3 and Table 2 show that most of the trading volume in put and call options during this period was concentrated in near-the-money and somewhat out-of-the-money options.4 Moreover, the trading volume fell monotonically as the options moved away from at-the-money. The result is consistent with the findings of Kamara and Miller (1995). In addition, Fig. 4 and Table 3 show the relationship between the expiration date and the trading volume. The result indicates that options are most active with 2 to 4 weeks’ expiration. That is because the time value of an option will become low when the option is closer to the expiration date. Whatever the high and low time values of an option are due to uncertainty, the option will only have an intrinsic value at the expiration day. In other words, investors can almost accurately anticipate the change of the TAIEX in the short run leading to a reduction in the option’s value. Therefore, an option with lower trading activity is closer to its expiration date. 4.2. Asymmetric effect on the GARCH (1,1) model The empirical model of this paper is the bivariate GARCH (1,1) model with asymmetric information terms. According to Fig. 2, the trading volume shows activity at the beginning of the options’ listing and do not affect the trading volume of the spot market. Therefore, we eliminate data before September 25, 2002. The investigated period spans from September 25, 2002 to December 25, 2002. The total number of the intraday observations is 1170 by 15-min intervals. After taking a first difference, the series is stationary. We then utilize the ARIMA (p,0,q) to estimate the expected and unexpected 4
Near-the-money is defined as 0.98bS/XV1.02, while somewhat out-of-the-money is defined as 0.96bS/ XV0.98 for calls and 1.02bS/XV1.04 for puts.
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Fig. 3. The relationships between moneyness and trading volumes of options.
trading volumes, and the criterion of the optimal ARIMA model is that all coefficients are significant and have a minimum Akaike Information Criterion (AIC) value (Enders, 2003). Therefore, the optimal models of the change in volumes of the spot and option series are ARIMA (3,3) and ARIMA (3,1), respectively. The lag periods in this model are chosen in two lags by the AIC criterion and SBC criterion. The optimal lags of both criterions are the same. Accordingly, expected and unexpected volatility transmissions do not exceed 30 min. Karpoff (1987) indicated that a financial market with relative information reflects it in its trading volume. Trading volume with high activity means that there is more information, which will increase the volatility in the market. Table 4 presents the estimates for the conditional mean equation of the trading volume volatilities. It shows that the spot and options markets are strongly influenced by their own past innovations.
Table 2 The relationships between moneyness and trading volumes of options Daily data Moneyness
Whole sample
Percentage of all quotes
Call options
Percentage of all call quotes
Put options
Percentage of all put quotes
1.08bS/X 1.06bS/XV1.08 1.04bS/XV1.06 1.02bS/XV1.04 1.00bS/XV1.02 0.98bS/XV1.00 0.96bS/XV0.98 0.94bS/XV0.96 0.92bS/XV0.94 S/Xb0.92 All Quotes
116,922 81,912 131,655 157,529 219,446 231,135 210,650 155,164 110,672 125,730 1,540,815
7.588 5.316 8.545 10.224 14.242 15.001 13.671 10.070 7.183 8.160 100.000
10,895 10,472 23,452 43,886 97,881 153,806 172,495 139,819 101,884 114,709 869,299
1.253 1.205 2.698 5.048 11.260 17.693 19.843 16.084 11.720 13.196 100.000
106,027 71,440 108,203 113,643 121,565 77,329 38,155 15,345 8,788 11,021 671,516
15.789 10.639 16.113 16.923 18.103 11.516 5.682 2.285 1.309 1.641 100.000
S is the index price and X is the exercise price.
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Fig. 4. The relationships between expiration and trading volumes of options.
Moreover, the parameters b ij (i=1,2; j=0,1,2) are all positive and significant, implying that the expected option (spot) volume with a larger volatility during this interval causes the spot (option) volume to have larger volatility during the next interval and the directions of the volatility are the same. We also find that the effect of the expected change in the option (spot) volume impacts the spot (option) volume to become smaller over time. More noteworthy is that b 1j bb 2j ; namely, the expected and the unexpected parts of these two conditional mean equations are that the spot effect to the options has a larger influence than the options do on the spot. This is because Taiwan’s stock market is more mature and the trading volume is more steadily related to the options market, which is an emerging market in Taiwan. We can be fairly certain that the spot market has a powerful influence over the whole financial market. In other words, the main purpose of utilizing an option is for hedging. When the spot market generates volume volatilities, investors increase their demand for options. The
Table 3 The relationships between expiration and trading volumes of options Daily data Expiration
Whole sample
Percentage of all quotes
Call options
Percentage of all call quotes
Put options
Percentage of all put quotes
TV7 7bTV14 14bTV30 30bTV60 60bTV90 90bTV120 120bTV150 150bTV180 180bTV210 TN210 All Quotes
217,880 289,873 802,513 204,493 14,287 4,381 4,037 2,322 531 498 1,540,815
14.141 18.813 52.084 13.272 0.927 0.284 0.262 0.151 0.034 0.032 100.000
127,019 160,374 454,085 115,123 5,762 2,430 2,796 1,181 234 295 869,299
14.612 18.449 52.236 13.243 0.663 0.280 0.322 0.136 0.027 0.034 100.000
90,861 129,499 348,428 89,370 8,525 1,951 1,241 1,141 297 203 671,516
13.531 19.285 51.887 13.309 1.270 0.291 0.185 0.170 0.044 0.030 100.000
T is the expiration days of options.
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Table 4 Maximum likelihood estimates of the bivariate GARCH (1,1) on spot and options conditional mean equation Variables
Coefficient
Standard error
Conditional mean equation: V S,t a 10 a 11 a 12 b 10 b 11 b 12 c 10 c 11 c 12 d 10 d 11 d 12
0.5892*** 0.1338*** 1.1878*** 0.0932*** 0.0709*** 0.0564*** 0.1158*** 0.1033*** 0.0521*** 0.2810*** 0.1313*** 0.0279***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001
Conditional mean equation: V O,t a 20 a 21 a 22 b 20 b 21 b 22 c 20 c 21 c 22 d 20 d 21 d 22
0.1030*** 0.5018*** 0.2587*** 0.2712*** 0.1539*** 0.1282*** 0.2272*** 0.1113*** 0.0111*** 0.3406*** 0.1657*** 0.1446***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 0.0002 b0.0001 0.0003
Standard error is less than 0.0001. Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively.
spot market effect on the options market is more significant, and there is a bilateral causality (feedback effect) within both markets. Regarding the assessment of lead/lag effects, the estimated parameters of the expected and the unexpected parts are all significant. This represents that the two markets have the lead behaviors with one another. When the spot market has new information, it will transmit the volatility to the options market. After reflecting the volatilities, the option market will influence the spot market. This result should be consistent with the reason why we employed the bivariate GARCH (1,1) model. Considering the unexpected terms of the two equations in Table 4, c and d represent the unexpected positive and negative volatilities of volumes, respectively. A significant positive c coupled with a positive d implies that the unexpected volume changes in the same direction for both markets. Moreover, the parameters c and d are higher than b. This reveals that the unexpected innovations have a higher impact on the volatility than the expected innovations in each market. Table 4 also reports that the parameters, which are estimated from Eq. (9), are higher than Eq. (8), implying that options are effected by the
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Table 5 Asymmetric information effect test Likelihood ratio
Hypothesis test
LR1 LR2 LR3 LR4 LR5 LR6
H 0: H 0: H 0: H 0: H 0: H 0:
cˆ10+cˆ11+cˆ12=0 dˆ10+dˆ 11+dˆ 12=0 cˆ 20+cˆ 21+cˆ22=0 dˆ20+dˆ 21+dˆ 22=0 cˆ10+cˆ11+cˆ12=dˆ10+dˆ11+i12 cˆ20+cˆ21+cˆ22=dˆ20+dˆ21+dˆ22
Estimated value
Test statistics
0.2712 0.4402 0.3496 0.6509 0.1690 0.3013
5.396783e+010*** 1.069186e+011*** 89696604.5462*** 2939369.3747*** 1.593882e+011*** 6879839.5551***
LR is the likelihood ratio test. LR1~LR6 are all v 2 (1) distributions. Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively.
spot market with a greater influence than the spot market is effected by the options market. Furthermore, the LR1, LR2, LR3, and LR4 are the likelihood ratio (LR) statistics to test whether information asymmetric effects exist between volumes in the spot and options markets. Table 5 shows that LR1, LR2, LR3, and LR4 are significant, which represent that the positive and negative unexpected volatilities of volume do indeed impact the spot and options markets. Note that the changes in the volume are the same direction. After the spot volume increase, the options volume will also increase. The LR5 and LR6 test whether negative past innovations cause a larger current volatility than positive innovations. The results of the estimations are all significantly negative and fit the assumption of the information asymmetric theory on financial securities (such as Braun, Nelson, and Sunier (1995)). If investors ignore the asymmetric characteristics in expecting the volatilities of a financial market, then investment risks will increase and profits may be lost. Table 6 shows the estimated parameters of two conditional variance equations; namely, to consider how asymmetric information is for the volatilities of trading volumes. The result reveals that unexpected positive and negative volatilities of spot (option) volumes have an impact on the option (spot) volumes. Fig. 5 presents the conditional correlation coefficient between these two markets. It is evaluated from the bivariate GARCH model and is between (0.793, +0.792). This result reveals that the conditional variances and
Table 6 Maximum likelihood estimates of the bivariate GARCH (1,1) on spot and options conditional variance equation Conditional variance equation h S,t h S, O,t h O,t Variables
Coefficient
Standard error
Variables
Coefficient
Standard error
c 11 c 12 c 22 + a 1,11 + a 1,22 + a 2,22
0.1472*** 0.1849*** 0.1194*** 0.1153*** 0.1744*** 0.1341***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001
a 1,11 a 1,22 a 2,22 g 1,11 g 1,22 g 2,22
0.1252*** 0.1610*** 0.1509*** 0.1602*** 0.1215*** 0.1119***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001
Standard error is less than 0.0001. Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively.
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Fig. 5. The conditional correlation coefficient with spot and options.
conditional covariance are indeed time-varying; and as a result the conditional correlation coefficient between the spot and options markets also changes over time.
5. Conclusions Diversification is the best reason to explain why the index option can be so popular. Whether investors have long or short spot positions, when the market takes adverse direction, investors can prevent their spot market holdings from losing profits by trading options. This makes the portfolios have the efficient arbitrages and hedging effects. That is the reason why the volumes between the stock and options markets may generate an interaction with each other. In previous studies, futures were the main topic in studying the influence of derivatives markets on stock markets, and few attempts have been made to demonstrate the spot market’s effect that derivatives have on volatilities. The purpose of this paper is to investigate the volatility transmission (feedback) effects between options and the underlying spot market and information asymmetry in financial markets. The ARIMA model is used to evaluate the change of the expected and the unexpected volumes and then the process divides the change in the unexpected volume into the positive and negative dummy variables. Finally, we add these variables into the bivariate GARCH (1,1) model. The results indicate that most of the trading volume in put and call options during this period is concentrated in near-the-money and somewhat out-of-the-money options.
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Moreover, trading volume falls monotonically as options move away from at-the-money. In addition, the options most active are those with 2 to 4 weeks’ expiration. This is because an option will only have its intrinsic value at the expiration day. In other words, investors can almost accurately expect that the change in the TAIEX over the short run will reduce the option’s value. Therefore, an option with lower trading activity is closer to its expiration date. Regarding the volatility transmissions, the expected option (spot) volume with a larger volatility during this interval causes the spot (option) volume to have a larger volatility during the next interval and the directions of the volatility are the same. We also find that the effect of the expected change in the option (spot) volume impacts the spot (option) volume to become smaller over time. When the spot market generates volume volatilities, investors will increase their demand for the option. That causes the spot market’s effect on the option market to be more significant, and there is bilateral causality (feedback effect) within both markets. Regarding the assessment of lead/lag effects, the result reveals that these two markets have lead behaviors with one another. The volatility of unexpected volumes is shown to move with the same direction in both the spot and options markets. The unexpected innovations have a higher impact than the expected innovations on the volatility in each market. The options are impacted by the spot market with a greater influence than the spot market is impacted by the options market. Furthermore, the likelihood ratio statistics represent that the positive and negative unexpected volatilities of volume indeed impact the spot and options markets and that the changes in volume are in the same direction. It is noteworthy that the results of testing whether negative past innovations cause a larger current volatility than positive innovations do fit the assumption of the information asymmetric theory on financial securities. If investors ignore the asymmetric characteristics from expecting volatilities in the financial market, then investment risks increase and profits may be lost. Finally, the estimated parameters of the two conditional variance equations reveal that the unexpected positive and negative volatilities of spot (option) volumes have an impact on the option (spot) volumes. We concluded for investors that the most important thing is that they need to be sensitive to the asymmetric ripple effects of volume volatility in the spot and options markets.
References Bollerslev, T. (1990). Modeling the coherence in short-run nominal exchange rates generalized ARCH. Review of Economics and Statistics, 72(3), 498 – 505. Boluch, M. L., & Chambrelain, T. W. (1997). Option volume and stock price behavior: Some evidence from the Chicago Board Options Exchange. Atlantic Economic Journal, 25(4), 358 – 370. Braun, P. A., Nelson, D. B., & Sunier, A. M. (1995). Good news, bad news, volatility, and beta. Journal of Finance, 50(5), 1575 – 1603. Chamberlain, T. W., Cheung, C. S., & Kwan, C. C. Y. (1993). Options listing, market liquidity and stock behaviour: Some Canadian evidence. Journal of Business Finance and Accounting, 20(5), 687 – 698. Chen, K. C., & Wu, L. (2001). Introduction and expiration effects of derivative equity warrants in Hong Kong. International Review of Financial Analysis, 10, 37 – 52. Corredor, P., Lechon, P., & Santamaria, R. (2001). Option-expiration effects in small markets: The Spanish stock market. The Journal of Futures Markets, 21(10), 905 – 928. Draper, P. B., Mak, S. C., & Tang, G. Y. N. (2001). The derivative warrant market in Hong Kong: Relationships with underlying assets. Journal of Derivatives, 8(4), 72 – 84.
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Easley, D., O’Hara, M., & Srinivas, P. S. (1998). Option volume and stock prices: evidence on where informed traders trade. Journal of Finance, 53(2), 431 – 465. Enders, W. (2003). Applied econometric time series (2nd ed.). New York7 John Wily and Sons. Etling, C., & Miller, T. W., Jr. (2000). The relationship between index option moneyness and relative liquidity. Journal of Futures Markets, 20(10), 971 – 987. Fase, M. M. G. (1994). The interaction between trading volume of stocks and options: some statistical evidence. Journal of International Money and Finance, 13(5), 587 – 601. Hagelin, H. (2000). Index option market activity and spot market volatility under different market conditions: An empirical study from Sweden. Applied Financial Economics, 10(6), 597 – 613. Jarque, C. M., & Bera, A. K. (1987). A test for normality of observations and regression residuals. International Statistical Review, 55, 163 – 172. Kamara, A., & Miller, T. W. (1995). Daily and intradaily tests of European put-call parity. Journal of Financial and Quantitative Analysis, 30(4), 519 – 539. Karpoff, J. M. (1987). The relation between price changes and trading volume: A survey. Journal of Financial and Quantitative Analysis, 22(1), 109 – 126. Kearney, C., & Patton, A. J. (2000). Multivariate GARCH modeling of exchange volatility transmission in the European monetary system. Financial Review, 35(1), 29 – 48. Park, T. H., Switzer, L. N., & Bedrossian, R. (1999). The interactions between trading volume and volatility: Evidence from the equity options markets. Applied Financial Economics, 9(6), 627 – 637. Stephan, J. A., & Whaley, R. E. (1990). Intraday price change and trading volume relations in the stock and stock option markets. Journal of Finance, 45(1), 191 – 220. Vijh, A. M. (1990). Liquidity of the CBOE equity options. Journal of Finance, 45(4), 1157 – 1179. Wang, P., & Wang, P. (1999). Foreign exchange market volatility in Southeast Asia. Asia-Pacific Financial Markets, 6(3), 235 – 252. Wang, P., & Wang, P. (2001). Equilibrium adjustment, basis risk and risk transmission in spot and forward foreign exchange markets. Applied Financial Economics, 11(2), 127 – 136.
The intraday behaviors and relationships with its underlying assets: Evidence on option market in Taiwan Mingchih Lee*, Chun-Da Chen Department of Banking and Finance, Tamkang University, Tamsui, Taipei 251, Taiwan Available online 26 November 2004
Abstract In this paper, we use daily data to investigate the information asymmetric effects and the relationships between the trading volume of options and their underlying spot trading volume. Our results reveal that options with higher liquidity are near-the-money and expiration periods with 2 to 4 weeks have higher trading activity. We classify them into two parts with the ARIMA model: the expected trading activity impact and the unexpected trading activity impact. Using the bivariate generalized autoregressive conditional heteroscedasticity (GARCH) model, we investigate the trading activity effect and information asymmetric effect. In conclusion, the trading volume volatility of the spot and options markets move together, and a greater expected and unexpected trading volume volatility of the spot (options) market is associated with greater volatility in the options (spot) market. However, both markets generate higher trading volume volatility when people expect such an impact rather than when they do not. We also find that there are feedback effects within these two markets. Furthermore, when the spot (options) market has negative innovations, it generates a greater impact on the options (spot) market than do positive innovations. Finally, the conditional correlation coefficient between the spot and the option markets changes over time based on the bivariate GARCH model. D 2005 Elsevier Inc. All rights reserved. JEL classification: G14 Keywords: ARIMA model; GARCH model; Options market; Volatility transmission; Information asymmetric effect
* Corresponding author. Tel.: +886 2 26215656x2855; fax: +886 2 26214755. E-mail address: [email protected] (M. Lee). 1057-5219/$ - see front matter D 2005 Elsevier Inc. All rights reserved. doi:10.1016/j.irfa.2004.10.021
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1. Introduction Options on stocks were first traded on an organized exchange in 1973. Ever since then, there has been a dramatic growth in the options market, as options are now traded on many exchanges throughout the world. Huge volumes of options are also traded over the counter by banks and other financial institutions. The underlying assets include stocks, stock indices, foreign currencies, debt instruments, commodities, and futures contracts. In Taiwan the first option (call and put) was listed by the Taiwan Futures Exchange (TAIFEX) on the TSEC Capitalization Weighted Price Index (TAIEX) on December 24, 2001. The TAIEX option is a European-style bphysical deliveryQ option. In the beginning, investors unfamiliar with the new derivatives caused the trading volume to be very illiquid. However, following the options trading activities of South Korea and the United States, options with a better hedge performance have now become the most popular derivative in financial markets. Therefore, if investors can understand the applications and trading systems of options, then the options market in Taiwan has high growth potential. The Taiwan index future has the same underlying TAIEX listed on July 21, 1998. The investors hold the futures can utilize the option to hedge, and the option writers can also employ the index futures to hedge risk of the short position. Under these inter-applications, the futures market will become more perfect, and the option market will develop successfully. There are many uncertainties in the stock market that cause it to be unstable and this makes options very attractive. The main purpose of trading an option is for hedging. After the option lists, investors have more tools for hedging, and investment operations have more elasticity. The risks and costs of trading options are different from trading futures. Using an option not only reduces portfolio risks, but also lowers the investment cost. Applying options and futures at the same time will not cause crowding effects. However, the spot market will become more perfect, because of diverse hedging methods. There are many relationships between spot and option markets through speculating, arbitraging, and hedging by investors. In Taiwan the relationships and the volatility transmissions between the volume in the options and spot markets have never been examined. Therefore, the objectives of this paper are as follows: First, we analyze the relationships between the moneyness, expiration, and trading activities. We then consider the effects of the spot trading volumes after options became available in Taiwan. Finally, we investigate the information asymmetric effects and volatility transmissions on the trading volume between the spot and the options markets. Section 2 summarizes the previous literature. Section 3 describes the data and methodology. Section 4 explains the empirical results. Section 5 summarizes the results.
2. Literature review Because Taiwan’s options market is an emerging market, few attempts by researchers have been made at investigating options. Prior empirical research can be classified into three parts: First, there are some previous studies about the impact of an expiration on the trading volume of options (warrants can be call options). Chen and Wu (2001) showed that the expiration of warrants causes a positive price effect on the expiration day, a negative
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price effect after expiration for in-the-money warrants, and a negative price effect prior to the expiration for out-of-the-money warrants. In their study there also appears to be a strong relationship between price and trading volumes of warrants. Corredor, Lechon, and Santamaria (2001) found that the expiration of Ibex-35 index derivatives (Spanish Equity Derivatives Exchange) has no significant effect on either the underlying asset prices or the level of volatility on the expiration day. However, the expiration of stock options does have a significant impact on their underlying assets. They showed a downward pressure on prices, a reduction of the volatility level in the week before the expiration date, and a significant increase in trading volume on the expiration day. Chamberlain, Cheung, and Kwan (1993) by contrast analyzed the effect of the listing of options on the price behavior, trading volume, and liquidity of underlying stocks on Canadian stock exchanges. The results indicate that return volatility declines, trading volume increases, and liquidity is enhanced, though the findings are not statistically significant. They also tested whether the impact of listing on volume depends on the pre-listing liquidity of a stock. However, they failed to detect any statistically significant relationship. The second part of the literature investigates the nature of the relationship between moneyness and three liquidity proxies for options. Etling and Miller (2000) conducted their study on the Standard & Poor’s (S&P) 100 and S&P 500 indexes. They used bid-ask spreads, volume, and time between quotes as liquidity proxies. Their statistical analysis rejected the hypothesis of a simple quadratic relationship between moneyness and liquidity in these markets. Although liquidity was maximized near the money, liquidity did not decrease symmetrically when option strikes moved deeper into the money or deeper out of the money. Kamara and Miller (1995) avoided the early exercise problem by testing putcall parity using S&P 500 European options. The result shows that most of the trading volume of put and call options during 1986 to 1989 was concentrated in near-the-money options (0.98bS/Xb1.02, where X is the exercise price and S represents the S&P index price) and somewhat out-of-the-money options (calls with 0.96bS/Xb0.98 and puts with 1.02bS/Xb1.04). Moreover, the trading volume fell monotonically as the options moved away from at-the-money options. The third part in the literature (and the most important argument of this paper) examines the cross-sectional relationship of volatility transmissions of trading volume between stock and option markets. Darper, Mak, and Tang (2001) examined the impact of warrant introductions on price, volatility, and volume of trading in the underlying security. An increase in trading volume is found as a result of the introduction, but has little impact on volatility. Price effects are also identified, although these effects appear to be temporary and do not persist much beyond the listing of the warrants. On delisting, however, a large negative price effect is observed. Hagelin (2000) investigated the relationship between options market activity and spot market volatility on Sweden’s OMX index. The findings show that for the complete sample period there is unidirectional causality from spot market volatility to options market activity for calls and puts jointly, as well as for calls and puts, respectively. While unidirectional causality from spot market volatility to call options market activity is documented for both subperiods, bilateral causality between put option market activity and spot market volatility was found for one of the subperiods. The interesting findings are that both the lagged expected and unexpected put options market activities were found to be positive and significant for the first period. For the second
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period, the lagged expected put options market activity was found to be negative and significant, while the unexpected component was reported to be negative, but insignificant. Overall, the evidence suggests that calls and puts may affect spot market volatility differently and that this potential impact can vary under different market conditions. Park, Switzer, and Bedrossian (1999) wrote that unexpected options trading activity contributes to enhanced volatility in the underlying equity returns. Moreover, the analysis indicates that expected options trading activity significantly affects equity volatility in only a minority of firms. This is consistent with the contention that trading in the equity options market does not systematically lead to price destabilization in the underlying equity market. Boluch and Chamberlain (1997) indicated that the option volume/stock price relationship is largely characterized by feedback, with the option volume causing the stock price to change and vice versa. Fase (1994) demonstrated the feedback hypothesis for trading volume on the Amsterdam stock and options markets. The most important finding is that very often causality runs from options to the stock market, which seems to support the feeling of the business profession and the main hypothesis of his analysis. Stephan and Whaley (1990) used intraday data to examine the lead/lag relation between price changes in the option market and stock market. The results indicate that price changes in a stock lead the options market by as much as 15 min. The analysis of trading volume indicates that the stock market lead may be even longer.
3. Data and methodology 3.1. Data Among the many stock indices of the TSEC (Taiwan Stock Exchange) that have listed derivatives, the most frequently quoted one is the TSEC Capitalization Weighted Price Index (TAIEX). The TAIEX has been used since 1971 and is based on the average capitalization in 1966. Other weighted indices include non-finance, non-electronics, and 22 sector indices by individual industries. Index options on the TAIEX were introduced by TAIFEX (Taiwan Futures Exchanges) on December 24, 2001. At present, there are only European options. During the beginning of their listing, there was little activity within the trading volumes, because investors at that time did not understand how to use an index option to hedge their investment risk. Currently, the trading activities of call options are still higher than put options. In this paper, we use the daily and intradaily data for the trading volume of the TAIEX and TAIEX options. Taiwan Stock Exchange (TSE) transaction data together with contemporaneous options trading volume were obtained from the Taiwan Economic Journal (TEJ), which is a local data vendor, and from the Taiwan Futures Exchanges (TAIFEX). The investigated period in this study for the 92 days is from September 25, 2002 to December 27, 2002. The period before September 25, 2002 was omitted due to low trading activities in the options market.1 After eliminating non-transaction days, the 1
The standard deviation of the trading volume volatility of options is 0.3055 during the investigated period, but is 0.4004 from when the options began in December 24, 2001 up until September 24, 2002.
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estimated period is 65 days. The data was filtered in a series so as to satisfy various criteria. All transactions after 1:30 p.m. Taiwan Time were eliminated since the TSEC closes its market at that time. New information that comes to the options market between 1:30 and 2:00 p.m., when the TAIFEX is closed, can be acted upon immediately, whereas the corresponding change in the TSEC may not occur until the next trading day. We therefore chose the intraday sampling interval. The interval has to be large enough so that trading is sufficiently heavy in each interval to provide useful information, but small enough to capture a short-term causal relationship. After inspecting the data, an interval of 15 min was set up. The data was then aggregated for the trading volumes of the TAIEX market and TAIEX options based on this 15-min time interval in order to give the total number of put and call contracts traded, as well as the total number of put and call transactions in each interval. In those cases, the total amount of the intraday sampling interval data at 15-min intervals was 1170 observations per series. In order to capture the volatility transmissions between the TAIEX spot market and TAIEX options on the trading volumes, we have to derive the ordinary series data with the rate of volume changes. Two points need to be considered. The first point is that the intraday data from the database come in 1-min intervals. Before an analysis with the empirical model, we need to sum the trading volumes in 15-min intervals per series. We next process first-order difference to become stationary-I(0) series. We define the change rate of trading volume as a logarithm of the ratio of the daily trading volume as: VS;t ¼ log ms;t =ms;t1 100
ð1Þ
VO;t ¼ log mo;t =mo;t1 100;
ð2Þ
where m s,t represents the 15-min interval trading volume of the TAIEX spot market at time t; and m o,t represents the 15-min interval trading volume of TAIEX options at time t. Time t1 is the last 15-min interval trading volume, while V S and V O are the rate change of volume in the TAIEX and TAIEX options, respectively. 3.2. Methodology In this study the main point falls on demonstrating the feedback relationship of trading volumes and information asymmetric effects between the TAIEX and TAIEX options. We first employ the autoregressive integrated moving average ARIMA (p,0,q) model to classify the rate change of TAIEX and TAIEX option volumes into expected and unexpected activity variables (terms). Investors may follow their expectations from the trading volumes in this market to adjust their investment strategies. We thus conclude that using the intraday data with 15-min intervals to consider volatility transmissions and their influences between these two securities can obtain better expectations. The residual term that is derived from the ARIMA model is separated into positive and negative threshold effects; specifically, separating the unexpected volatility into positive and negative volatility effects. Finally, these two threshold dummy variables are added into the bivariate generalized autoregressive conditional heteroscedasticity (GARCH) (1,1) model. The models of this study are given below.
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3.2.1. ARIMA model In order to use the ARIMA methodology, it is first necessary to identify whether each series is stationary. The ARIMA model can only be used on a stationary series, and if it is determined that a series is non-stationary, then it could be repeated until a stationary series results. Most of the spot and options volume series require first-order differencing. We take a first difference that produces a stationary series and apply the ADF and PP tests. The result shows that the spot and options volume series become stationary after being firstorder differenced, as denoted by I(0). We then employ the general ARIMA (p,0,q) model to divide the expected and unexpected variables from the change in the volume. The ARIMA (p,0,q) model can be written as follows: Vi;t ¼ a0 þ
p X
aj Vtj þ
j¼1
q X
bj etj
i ¼ TAIEX; TAIEX OPTION;
ð3Þ
j¼0
where V is composed of a logarithm of the ratio of the trading volume, and ! ! p q X X EV i;t ¼ a0 þ E aj Vtj þ E bj etj i¼1
UEV i;t ¼ Vi;t EV i;t ;
ð4Þ
j¼0
ð5Þ
where EVi,t represents the expected volatility of volumes and UEVi,t shows the unexpected volatility of volumes. One thing worth mentioning now is how to choose the optimal ARIMA model. The criteria are that the estimate coefficients are all significant, a minimum AIC value, and residual term has no series correlation. Thus, the optimal ARIMA models of the TAIEX spot and the TAIEX options are ARMA (3,3) and ARMA (3,1), respectively. The expected volatility of volumes can be evaluated by the actual trading volumes subtracted by the optimal residual terms, which are estimated from the ARIMA model, and the residual value can be seen as the unexpected volatility portion of volumes. Dividing the unexpected volatilities by zero into positive and negative threshold effects, the dummy variables can be expressed as: UEV þ ¼
UEV ¼
1; if UEV N 0 0; if UEV b 0
ð6Þ
1; if UEV b 0 : 0; if UEV N 0
ð7Þ
By setting up the threshold dummy variables, we may account for whether information asymmetric relations do exist between the trading volumes of the TAIEX and TAIEX options. Similarly, it is better to say that we can demonstrate that the volatility transmission mechanism is asymmetric, i.e., negative innovations in a given market increase the volatility in the next market, resulting in considerably more trading than that under positive innovations.
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3.2.2. Bivariate GARCH (1,1) model The bivariate GARCH model not only is able to test for the time-varying variance or volatility in the spot and options markets, but can also investigate volatility transmission between the two markets. Many previous studies indicate that the time series data within the GARCH (1,1) model accesses the appropriateness of the GARCH specification; for instance, Bollerslev (1990), Wang and Wang (1999), Kearney and Patton (2000), and Wang and Wang (2001). Thus, this paper adopts a bivariate GARCH (1,1) model to investigate the dynamic relationships in both markets and accounts for the phenomenon of feedback influence which arises from options that have a better hedging performance for the spot market. After evaluating the expected and unexpected variables from the ARIMA model in each series, we change the conditional mean equation so that both variables are included. We then divide the positive and negative unexpected volatilities of the trading volumes by zero and add these two dummy variables into the conditional variance equation. With the bivariate GARCH (1,1) model, we can write the equation as: 2 2 2 X X X VS;t ¼ a10 þ a1i VS;ti þ b1i EV O;ti þ c1i UEV þ O;ti i¼0
þ
2 X
i¼0
i¼0
d1i UEV O;t1 þ eS;t
ð8Þ
i¼0
VO;t ¼ a20 þ
2 X
a2i VO;ti þ
i¼1
þ
2 X
2 X i¼0
b2i EV S;ti þ
2 X
c2i UEV þ S;ti
i¼0
d2i UEV S;t1 þ eO;t
ð9Þ
i¼0
eS;t jXt1 fN ð0; Ht Þ eO;t
h2 Ht ¼ S;t hO;S;t
hS;O;t h2O;t
ð10Þ
h i 2 2 2 hS;t ¼ c211 þ a2þ 1;11 DO þ a1;11 ð1 DO Þ eO;t1 þ g1;11 hS;t1
ð11Þ
ð12Þ
nh i i h þ þ hS;O;t ¼ c12 c11 þ aþ 1;11 a1;22 DO DS þ a1;11 a1;22 DO ð1 DS Þ io h i h þ þ a e1;t1 e2;t1 1;11 a1;22 ð1 DO ÞDS þ a1;11 a1;22 ð1 DO Þð1 DS Þ
hO;t
þ g1;11 g1;22 hS;O;t1 h i
2þ 2 2 2 ¼ c222 þ c212 þ a2þ 1;22 þ a2;22 DS þ a1;22 þ a2;22 ð1 DS Þ e2;t1
2 2 þ g1;22 þ g2;22 h22;t1 :
ð13Þ
ð14Þ
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where V S,t is the logarithm of the ratio of the TAIEX trading volume at time t and V O,t is the logarithm of the ratio of the TAIEX option trading volume at time t. EVi,t is the expected change rate of trading volume at time t (i=S, O; S represents the spot, O represents the option). UEV+ and UEV represent the unexpected positive and negative volatilities of volumes, respectively, EV and UEV are estimated from the ARIMA model. The residuals of the ARIMA model are UEV, however, EV could be evaluated by Vi,t subtracting the residuals. D S and D O are calculated as follows: 1; if UEV O N 0 ð15Þ DS ¼ 0; if UEV O b 0 DO ¼
1; if UEV S N 0 0; if UEV S b 0
ð16Þ
Easley, O’hara, and Srivivas (1998), Fase (1994), and Vijh (1990) indicated that the period of volatility transmission in both the spot and options markets does not exceed 30 min. Thus, the time lag length of this model is two periods per series.
4. Empirical results The setup of this section is as follows. First, we introduce the relationship between moneyness, expiration, and daily trading volumes of the options market in Taiwan. Second, we use intraday data to examine the asymmetric effects of the GARCH. 4.1. Preliminary findings Table 1 presents summary statistics for each series, including the mean, standard deviation, skewness, and kurtosis for the first differences of each intraday trading volume. The mean changes of the volume are 0.2611 for the spot and 0.0809 for the option market. Moreover, the standard deviations of the volatility are close between the spot and the options during the investigated period. Both of the first-differenced series are highly
Table 1 Preliminary statistics on spot and options series of intraday volume volatilities, 2002.9.25–2002.12.27 Statistics
Series
Mean Std. Dev. Skewness Kurtosis Jarque–Bera normality test
TAIEX
TAIEX Option
0.2611 65.8025 3.1729*** 10.8718*** 7718.6239***
0.0809 58.2017 0.3269*** 1.5386*** 136.1293***
Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively. Jarque–Bera (1987) normality test, which follows a chi-squared distribution, with two degrees of freedom. The 3
statistic is JB ¼ N ½ skewness þ ðkurtosis3Þ . 6 24 2
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Fig. 1. The trend of the TSEC Capitalization Weighted Price Index, 2001.12.24–2002.12.27.
skewed and leptokurtotic relative to the normal distribution, although only the spot series exhibits negative skewness. In addition, the Jarque–Bera normality tests strongly reject normality for all trading volume changes, with a critical value of 9.21 at the 1% significance level.2 Fig. 1 illustrates the trend of the TAIEX from the beginning of options listing; showing a decline in the long run. On the day data of basic statistics, we include the options’ moneyness and expiration of the options’ trading volume. We first observe the change in the daily option volume. Fig. 2 shows the trading behavior of options during this period. The volume has continually risen up to the present time and it reveals that options are now more acceptable and understandable for investors. At the beginning of options listing, the options market was very illiquid and the total number of contracts was only 1100 per day. However, the trading volume rose to 5000 contracts per day from the end of April 2002. We notice that the volume rose to between 10,000 and 20,000 contracts for the sample period and both call and put volumes have risen in the same way. We should not ignore here that the trading volume of calls is relatively larger than puts. During this sample period, Taiwan’s economy was still in a recession and the stock market was a bear market. These conditions caused most investors to expect the stock market to rise. At the same time, the Taiwan’s government announced some good policies3 to improve the stock market. When investors received these sorts of news, they expected that stock prices would rise and hoped that they could buy stocks with lower prices, which induced the call volumes to be larger than the put volumes. On the other hand, the Taiwan warrant market was established in 1997. The warrant and call are similar. So the investors can utilize the
2
The J-B (Jarque & Bera, 1987) tests whether a series is normally distributed. Under the null hypothesis of normality, the J-B statistic is distributed chi-squared with two degrees of freedom. 3 The Central Bank of China (CBC) lowered the discount rate, the rate on accommodations with collateral, and the rate on accommodations without collateral each by 25 basis points from 1.875%, 2.25%, and 4.125% to 1.625%, 2.0%, and 3.875%, respectively, effective from November 12, 2002. In addition, the remunerative rate on banks’ reserve accounts with the CBC was reduced from 2.5% to 2.25%, also effective from November 12, 2002.
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Fig. 2. The trend of trading volumes (number of contracts) of options, 2001.12.24–2002.12.27.
call more acceptably than put in processing the investments. For reasons mentioned above, we understand that the volume of call is larger than put. We also observe the distribution of the relationships between moneyness and options volume using day data from the listing of options to December 27, 2002. The moneyness is defined as the stock index divided by the exercise price. Fig. 3 and Table 2 show that most of the trading volume in put and call options during this period was concentrated in near-the-money and somewhat out-of-the-money options.4 Moreover, the trading volume fell monotonically as the options moved away from at-the-money. The result is consistent with the findings of Kamara and Miller (1995). In addition, Fig. 4 and Table 3 show the relationship between the expiration date and the trading volume. The result indicates that options are most active with 2 to 4 weeks’ expiration. That is because the time value of an option will become low when the option is closer to the expiration date. Whatever the high and low time values of an option are due to uncertainty, the option will only have an intrinsic value at the expiration day. In other words, investors can almost accurately anticipate the change of the TAIEX in the short run leading to a reduction in the option’s value. Therefore, an option with lower trading activity is closer to its expiration date. 4.2. Asymmetric effect on the GARCH (1,1) model The empirical model of this paper is the bivariate GARCH (1,1) model with asymmetric information terms. According to Fig. 2, the trading volume shows activity at the beginning of the options’ listing and do not affect the trading volume of the spot market. Therefore, we eliminate data before September 25, 2002. The investigated period spans from September 25, 2002 to December 25, 2002. The total number of the intraday observations is 1170 by 15-min intervals. After taking a first difference, the series is stationary. We then utilize the ARIMA (p,0,q) to estimate the expected and unexpected 4
Near-the-money is defined as 0.98bS/XV1.02, while somewhat out-of-the-money is defined as 0.96bS/ XV0.98 for calls and 1.02bS/XV1.04 for puts.
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Fig. 3. The relationships between moneyness and trading volumes of options.
trading volumes, and the criterion of the optimal ARIMA model is that all coefficients are significant and have a minimum Akaike Information Criterion (AIC) value (Enders, 2003). Therefore, the optimal models of the change in volumes of the spot and option series are ARIMA (3,3) and ARIMA (3,1), respectively. The lag periods in this model are chosen in two lags by the AIC criterion and SBC criterion. The optimal lags of both criterions are the same. Accordingly, expected and unexpected volatility transmissions do not exceed 30 min. Karpoff (1987) indicated that a financial market with relative information reflects it in its trading volume. Trading volume with high activity means that there is more information, which will increase the volatility in the market. Table 4 presents the estimates for the conditional mean equation of the trading volume volatilities. It shows that the spot and options markets are strongly influenced by their own past innovations.
Table 2 The relationships between moneyness and trading volumes of options Daily data Moneyness
Whole sample
Percentage of all quotes
Call options
Percentage of all call quotes
Put options
Percentage of all put quotes
1.08bS/X 1.06bS/XV1.08 1.04bS/XV1.06 1.02bS/XV1.04 1.00bS/XV1.02 0.98bS/XV1.00 0.96bS/XV0.98 0.94bS/XV0.96 0.92bS/XV0.94 S/Xb0.92 All Quotes
116,922 81,912 131,655 157,529 219,446 231,135 210,650 155,164 110,672 125,730 1,540,815
7.588 5.316 8.545 10.224 14.242 15.001 13.671 10.070 7.183 8.160 100.000
10,895 10,472 23,452 43,886 97,881 153,806 172,495 139,819 101,884 114,709 869,299
1.253 1.205 2.698 5.048 11.260 17.693 19.843 16.084 11.720 13.196 100.000
106,027 71,440 108,203 113,643 121,565 77,329 38,155 15,345 8,788 11,021 671,516
15.789 10.639 16.113 16.923 18.103 11.516 5.682 2.285 1.309 1.641 100.000
S is the index price and X is the exercise price.
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Fig. 4. The relationships between expiration and trading volumes of options.
Moreover, the parameters b ij (i=1,2; j=0,1,2) are all positive and significant, implying that the expected option (spot) volume with a larger volatility during this interval causes the spot (option) volume to have larger volatility during the next interval and the directions of the volatility are the same. We also find that the effect of the expected change in the option (spot) volume impacts the spot (option) volume to become smaller over time. More noteworthy is that b 1j bb 2j ; namely, the expected and the unexpected parts of these two conditional mean equations are that the spot effect to the options has a larger influence than the options do on the spot. This is because Taiwan’s stock market is more mature and the trading volume is more steadily related to the options market, which is an emerging market in Taiwan. We can be fairly certain that the spot market has a powerful influence over the whole financial market. In other words, the main purpose of utilizing an option is for hedging. When the spot market generates volume volatilities, investors increase their demand for options. The
Table 3 The relationships between expiration and trading volumes of options Daily data Expiration
Whole sample
Percentage of all quotes
Call options
Percentage of all call quotes
Put options
Percentage of all put quotes
TV7 7bTV14 14bTV30 30bTV60 60bTV90 90bTV120 120bTV150 150bTV180 180bTV210 TN210 All Quotes
217,880 289,873 802,513 204,493 14,287 4,381 4,037 2,322 531 498 1,540,815
14.141 18.813 52.084 13.272 0.927 0.284 0.262 0.151 0.034 0.032 100.000
127,019 160,374 454,085 115,123 5,762 2,430 2,796 1,181 234 295 869,299
14.612 18.449 52.236 13.243 0.663 0.280 0.322 0.136 0.027 0.034 100.000
90,861 129,499 348,428 89,370 8,525 1,951 1,241 1,141 297 203 671,516
13.531 19.285 51.887 13.309 1.270 0.291 0.185 0.170 0.044 0.030 100.000
T is the expiration days of options.
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Table 4 Maximum likelihood estimates of the bivariate GARCH (1,1) on spot and options conditional mean equation Variables
Coefficient
Standard error
Conditional mean equation: V S,t a 10 a 11 a 12 b 10 b 11 b 12 c 10 c 11 c 12 d 10 d 11 d 12
0.5892*** 0.1338*** 1.1878*** 0.0932*** 0.0709*** 0.0564*** 0.1158*** 0.1033*** 0.0521*** 0.2810*** 0.1313*** 0.0279***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001
Conditional mean equation: V O,t a 20 a 21 a 22 b 20 b 21 b 22 c 20 c 21 c 22 d 20 d 21 d 22
0.1030*** 0.5018*** 0.2587*** 0.2712*** 0.1539*** 0.1282*** 0.2272*** 0.1113*** 0.0111*** 0.3406*** 0.1657*** 0.1446***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 0.0002 b0.0001 0.0003
Standard error is less than 0.0001. Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively.
spot market effect on the options market is more significant, and there is a bilateral causality (feedback effect) within both markets. Regarding the assessment of lead/lag effects, the estimated parameters of the expected and the unexpected parts are all significant. This represents that the two markets have the lead behaviors with one another. When the spot market has new information, it will transmit the volatility to the options market. After reflecting the volatilities, the option market will influence the spot market. This result should be consistent with the reason why we employed the bivariate GARCH (1,1) model. Considering the unexpected terms of the two equations in Table 4, c and d represent the unexpected positive and negative volatilities of volumes, respectively. A significant positive c coupled with a positive d implies that the unexpected volume changes in the same direction for both markets. Moreover, the parameters c and d are higher than b. This reveals that the unexpected innovations have a higher impact on the volatility than the expected innovations in each market. Table 4 also reports that the parameters, which are estimated from Eq. (9), are higher than Eq. (8), implying that options are effected by the
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Table 5 Asymmetric information effect test Likelihood ratio
Hypothesis test
LR1 LR2 LR3 LR4 LR5 LR6
H 0: H 0: H 0: H 0: H 0: H 0:
cˆ10+cˆ11+cˆ12=0 dˆ10+dˆ 11+dˆ 12=0 cˆ 20+cˆ 21+cˆ22=0 dˆ20+dˆ 21+dˆ 22=0 cˆ10+cˆ11+cˆ12=dˆ10+dˆ11+i12 cˆ20+cˆ21+cˆ22=dˆ20+dˆ21+dˆ22
Estimated value
Test statistics
0.2712 0.4402 0.3496 0.6509 0.1690 0.3013
5.396783e+010*** 1.069186e+011*** 89696604.5462*** 2939369.3747*** 1.593882e+011*** 6879839.5551***
LR is the likelihood ratio test. LR1~LR6 are all v 2 (1) distributions. Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively.
spot market with a greater influence than the spot market is effected by the options market. Furthermore, the LR1, LR2, LR3, and LR4 are the likelihood ratio (LR) statistics to test whether information asymmetric effects exist between volumes in the spot and options markets. Table 5 shows that LR1, LR2, LR3, and LR4 are significant, which represent that the positive and negative unexpected volatilities of volume do indeed impact the spot and options markets. Note that the changes in the volume are the same direction. After the spot volume increase, the options volume will also increase. The LR5 and LR6 test whether negative past innovations cause a larger current volatility than positive innovations. The results of the estimations are all significantly negative and fit the assumption of the information asymmetric theory on financial securities (such as Braun, Nelson, and Sunier (1995)). If investors ignore the asymmetric characteristics in expecting the volatilities of a financial market, then investment risks will increase and profits may be lost. Table 6 shows the estimated parameters of two conditional variance equations; namely, to consider how asymmetric information is for the volatilities of trading volumes. The result reveals that unexpected positive and negative volatilities of spot (option) volumes have an impact on the option (spot) volumes. Fig. 5 presents the conditional correlation coefficient between these two markets. It is evaluated from the bivariate GARCH model and is between (0.793, +0.792). This result reveals that the conditional variances and
Table 6 Maximum likelihood estimates of the bivariate GARCH (1,1) on spot and options conditional variance equation Conditional variance equation h S,t h S, O,t h O,t Variables
Coefficient
Standard error
Variables
Coefficient
Standard error
c 11 c 12 c 22 + a 1,11 + a 1,22 + a 2,22
0.1472*** 0.1849*** 0.1194*** 0.1153*** 0.1744*** 0.1341***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001
a 1,11 a 1,22 a 2,22 g 1,11 g 1,22 g 2,22
0.1252*** 0.1610*** 0.1509*** 0.1602*** 0.1215*** 0.1119***
b0.0001 b0.0001 b0.0001 b0.0001 b0.0001 b0.0001
Standard error is less than 0.0001. Significance levels of 10%, 5%, and 1% are represented by *, **, and ***, respectively.
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Fig. 5. The conditional correlation coefficient with spot and options.
conditional covariance are indeed time-varying; and as a result the conditional correlation coefficient between the spot and options markets also changes over time.
5. Conclusions Diversification is the best reason to explain why the index option can be so popular. Whether investors have long or short spot positions, when the market takes adverse direction, investors can prevent their spot market holdings from losing profits by trading options. This makes the portfolios have the efficient arbitrages and hedging effects. That is the reason why the volumes between the stock and options markets may generate an interaction with each other. In previous studies, futures were the main topic in studying the influence of derivatives markets on stock markets, and few attempts have been made to demonstrate the spot market’s effect that derivatives have on volatilities. The purpose of this paper is to investigate the volatility transmission (feedback) effects between options and the underlying spot market and information asymmetry in financial markets. The ARIMA model is used to evaluate the change of the expected and the unexpected volumes and then the process divides the change in the unexpected volume into the positive and negative dummy variables. Finally, we add these variables into the bivariate GARCH (1,1) model. The results indicate that most of the trading volume in put and call options during this period is concentrated in near-the-money and somewhat out-of-the-money options.
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Moreover, trading volume falls monotonically as options move away from at-the-money. In addition, the options most active are those with 2 to 4 weeks’ expiration. This is because an option will only have its intrinsic value at the expiration day. In other words, investors can almost accurately expect that the change in the TAIEX over the short run will reduce the option’s value. Therefore, an option with lower trading activity is closer to its expiration date. Regarding the volatility transmissions, the expected option (spot) volume with a larger volatility during this interval causes the spot (option) volume to have a larger volatility during the next interval and the directions of the volatility are the same. We also find that the effect of the expected change in the option (spot) volume impacts the spot (option) volume to become smaller over time. When the spot market generates volume volatilities, investors will increase their demand for the option. That causes the spot market’s effect on the option market to be more significant, and there is bilateral causality (feedback effect) within both markets. Regarding the assessment of lead/lag effects, the result reveals that these two markets have lead behaviors with one another. The volatility of unexpected volumes is shown to move with the same direction in both the spot and options markets. The unexpected innovations have a higher impact than the expected innovations on the volatility in each market. The options are impacted by the spot market with a greater influence than the spot market is impacted by the options market. Furthermore, the likelihood ratio statistics represent that the positive and negative unexpected volatilities of volume indeed impact the spot and options markets and that the changes in volume are in the same direction. It is noteworthy that the results of testing whether negative past innovations cause a larger current volatility than positive innovations do fit the assumption of the information asymmetric theory on financial securities. If investors ignore the asymmetric characteristics from expecting volatilities in the financial market, then investment risks increase and profits may be lost. Finally, the estimated parameters of the two conditional variance equations reveal that the unexpected positive and negative volatilities of spot (option) volumes have an impact on the option (spot) volumes. We concluded for investors that the most important thing is that they need to be sensitive to the asymmetric ripple effects of volume volatility in the spot and options markets.
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