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Price volatility, trading volume, and market depth:evidence from the Japanese stock index futuresmarketToshiaki WatanabePublished online: 07 Oct 2010.

To cite this article: Toshiaki Watanabe (2001) Price volatility, trading volume, and market depth: evidence from theJapanese stock index futures market, Applied Financial Economics, 11:6, 651-658, DOI: 10.1080/096031001753266939

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Price volatility, trading volume, and market

depth: evidence from the Japanese stock

index futures market

TOSHIAKI WATANABE

Faculty of Economics, Tokyo Metropolitan University, 1-1 Minami Ohsawa, Hachioji-shi, Tokyo 192-0397, JapanE-mail: twatanab@bcomp.metro-u.ac.j p

This article examines the relation between price volatility, trading volume and openinterest for the Nikkei 225 stock index futures traded on the Osaka SecuritiesExchange (OSE) using the method developed by Bessembinder and Seguin (1993).The OSE regulation for trading of the Nikkei 225 futures decreased beginning14 February 1994. Results for the period beginning 14 February 1994 con®rmthe ®ndings by Bessembinder and Seguin (1993) of a signi®cant positive relation be-tween volatility and unexpected volume and a signi®cant negative relation betweenvolatility and expected open interest. However, no relation between price volatility,volume and open interest is found for the period prior to 14 February 1994, when theregulation increased gradually. This result provides evidence that the relationbetween price volatility, volume and open interest may vary with the regulation.

I . INTRODUCTION

The price-volume relation on ®nancial markets has longattracted the attention of many ®nancial economists. A

widely documented phenomenon is the positive contem-

poraneous correlation between price volatility and trading

volume. KarpoV (1987) reviews previous studies on the

price-volume relation on various ®nancial markets, in

which he cites 18 studies that document the positive corre-

lation between volatility and volume. Several theoreticalmodels to explain this correlation have been proposed

such as mixture of distributions models (Clark, 1973;

Tauchen and Pitts, 1983; Andersen, 1996) and sequential

information models (Copeland, 1976; Jennings et al.,

1981). Most empirical research in this area has, however,

been limited to the US and European markets.

This article examines the relation between price volatilityand trading volume for the Nikkei 225 stock index futures

traded on the Osaka Securities Exchange (OSE), which is a

major stock index futures in Japan. An advantage of inves-

tigating the Nikkei 225 futures traded on the OSE is that

the OSE changed regulation such as margin requirements,price range and time interval in updating quotaion several

times. It is interesting to examine whether changes in

regulation may in¯uence the eVects of volume on volatility.

Speci®cally, the regulation decreased beginning 14

February 1994. Therefore, the samples prior to and begin-

ning 14 February 1994 are analysed separately.

The analysis in this article is based on the methoddeveloped by Bessembinder and Seguin (1993). Their

analysis is not based on any theoretical models1 but

diVer from the other empirical studies on the price-

volume relation on several points. First, they also examine

the relation between volatility and open interest. Studies

on the relation between open interest and volatility are

scarce while the volume-volatility relation has been ana-lysed by many researchers. They use open interest as a

proxy for market depth, which Kyle (1985) de®nes as the

Applied Financial Economics ISSN 0960±3107 print/ISSN 1466±4305 online # 2001 Taylor & Francis Ltd

http://www.tandf.co.uk/journals

Applied Financial Economics, 2001, 11, 651±658

651

1 Watanabe (2000) analysed the relation between volatility and volume for the Nikkei 225 futures based on mixture of distributionsmodels.

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order ¯ow required to move prices by one unit. Second,they allow the eVects of trading volume and open interestshocks on volatility to vary depending on whether shocksare expected or unexpected. Third, they also allow theeVects of unexpected trading volume and open interestshocks on volatility to vary with the sign of shocks. Foreight agricultural, metal, currency, and bond futures tradedin the USA, they ®nd that (i) unexpected volume shockshave a signi®cant positive eVect on volatility, (ii) expectedopen interest shocks have a signi®cant negative eVect onvolatility, and (iii) the impact of positive unexpectedvolume shocks on volatility is larger than the impact ofnegative shocks.

Results for the period beginning 14 February 1994, whenthe regulation decreased gradually, con®rm the above®ndings by Bessembinder and Seguin (1993). In contrast,no relation between price volatility, volume, and openinterest is found for the period prior to 14 February1994, when the regulation increased gradually.

The remainder of this article is organized as follows:The next section reviews the method developed byBessembinder and Seguin (1993). Section III provides adescription of the OSE regulation for trading of theNikkei 225 futures. Section IV explains the data used,and Section V summarizes the estimation results. SectionVI concludes the article.

II . METHODOLOGY

Basic model

The analysis in this paper is based on the methoddeveloped by Bessembinder and Seguin (1993).Speci®cally, the following two equations are estimated.

Rt ˆ ¬ ‡Xn

jˆ1

®jRt¡j ‡X4

iˆ1

»idit ‡Xn

jˆ1

ºj¼¼t¡j ‡ Ut …1†

¼¼t ˆ ¯ ‡Xn

jˆ1

!jUUt¡j ‡X4

iˆ1

²idit ‡Xn

jˆ1

­ j¼¼t¡j

‡Xm

kˆ1

·kAAkt ‡ °t …2†

where Rt is the percentage change, which is called return, inthe futures price on day t, and ¼¼t is its conditional standarddeviation, which is called volatility. The method for esti-mating ¼¼t will be explained below. dit (i ˆ 1; . . . ; 4) are day-of-the week dummy variables. Speci®cally, d1t takes onewhen day t is Monday and zero otherwise, d2t takes onewhen day t is Tuesday and zero otherwise, and so on. Thesedummy variables capture diVerences in mean and standarddeviation by day of the week. AAkt (k ˆ 1; . . . ; m) are thetrading activity variables that represent how actively the

futures are traded. Bessembinder and Seguin (1993) parti-tion trading volume and open interest into expected andunexpected components and use them as trading activityvariables, i.e. m ˆ 4, to take into account the possibility

that expected and unexpected shocks may have a diVerentimpact on volatility.

The mean and volatility are allowed to depend on day ofthe week, lagged volatilities, and unexpected returns

de®ned as residuals UUt from Equation 1. The reason toinclude lagged volatilities in Equation 2 is to accommodatethe well-known phenomenon of high persistence involatility shocks, which is called volatility-clustering.

Another well-documented phenomenon in stock marketsis that negative return shocks have a larger eVect onsubsequent volatilities (see Black, 1976; Christie, 1982;Nelson, 1991). The reason to include lagged unexpected

returns in Equation 2 is to capture this asymmetry involatility.

The volatility ¼¼t is estimated using the residual UUt fromEquation 1. Speci®cally, UUt is transformed into ¼¼t based onthe following equation.

¼¼t ˆ jUUtj��������º=2

p…3†

This transformation produces the unbiased estimates ofconditional return standard deviations (see Bessembinderand Seguin, 1993 for details).

Using this transformation, Equations 1 and 2 are esti-mated as follows. Equation 1 is ®rst estimated withoutlagged volatilities, using ordinary least squares (OLS).The obtained residuals are then transformed to the volati-lities using Equation 3. Given the obtained volatilities,

Equations 1 and 2 are estimated using OLS. For this pro-cedure, see also Davidian and Carroll (1987), Schwert(1990), and Bessembinder and Seguin (1992) .

Asymmetry in the eVects of volume and open interestshocks

Bessembinder and Seguin (1993) also estimates the modelthat allows the eVects of unexpected volume and openinterest shocks on volatility to vary with the sign of shocks.Speci®cally, Equation 2 is replaced by

¼¼t ˆ ¯ ‡Xn

jˆ1

!jUUt¡j ‡X4

iˆ1

²idit ‡Xn

jˆ1

­ j¼¼t¡j ‡Xm

kˆ1

·kAAkt

‡ ³Voldumt ‡ ÀOpIndumt ‡ "t …4†

where Voldumt is the dummy variable that takes one whenunexpected volume on day t is positive and zero otherwise,

and OpIndumt is the dummy variable that takes one whenunexpected open interest on day t is positive and zerootherwise.

652 T. Watanabe

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II I . REGULATION FOR TRADING OF THENIKKEI 225 FUTURES

There are two major stock index futures in Japan. One isTokyo Stock Price Index (TOPIX) futures traded on the

Tokyo Stock Exchange (TSE) and the other is Nikkei 225futures traded on the Osaka Securities Exchange (OSE).

This article focuses on the Nikkei 225 futures because the

trading of the Nikkei 225 futures has almost always domi-nated that of the TOPIX futures.

The trading of the Nikkei 225 futures on the OSE startedon 3 September 1988. The OSE changed the regulation for

trading of the Nikkei 225 futures several times. Table 1shows margin rates, where the member’s margin is depos-

ited by the OSE’s regular members and special participantswith the OSE, and the customer’s margin is deposited by

the customers with the OSE’s regular members and specialparticipants. Both margin requirements can be ful®lled by

depositing either cash or securities, but minimum cashrequirements are imposed. Both margin rates and mini-

mum cash requirements (in parentheses) were reducedbeginning 14 February 1994.

Table 1 also shows price range and time interval in

updating quotation. Unlike the US stock markets, revisionof quotes for the Nikkei 225 futures is gradual and pro-

gressive, which may necessitate a waiting period to com-plete transition. As far as I know, there is no literature that

describes the details of the adjustment of quotes on theOSE, but Hamao and Hasbrouck (1995) explained it for

the Tokyo Stock Exchange, which is another major stockexchange in Japan that adopts a trading rule similar to that

of the OSE. The larger the price range is and the shorter thetime interval is, the shorter are the intervals of waiting. The

price range increased beginning 14 February 1994, and thetime interval decreased beginning 27 June 1991.

To sum up, the OSE regulation for trading of the Nikkei225 futures decreased beginning 14 February 1994, except

for the time interval in updating quotation, which

decreased beginning 27 June 1991. Therefore, this articleanalyses the periods prior to and beginning 14 February1994 separetely.

IV. DATA AND ADJUSTMENTS

Data description

The data used are daily closing prices, trading volume, andopen interest for the Nikkei 225 futures traded on the OSE.These data were generously provided by the OSE. Thesample period extends from 24 August 1990, to 30December 1997. As explained in the previous section, theOSE regulation for trading of the Nikkei 225 futuresdecreased beginning 14 February 1994. Therefore, thesample is divided into two diVerent periods; One is from24 August 1990, to 10 February 1994, which we call periodA, and the other is from 14 February 1994, to 30 December1997, which we call period B. These two periods areanalysed separately.

Trading in any particular contract (that expires onMarch, June, September, or December) begins about ayear and three months before the expiration date andhence ®ve contracts are traded in each day. FollowingBessembinder and Seguin (1993), return is de®ned as thepercentage change in the closing price of the contractclosest to expiration, except within the delivery month,when the change in the second nearest contract is used.As for trading volume and open interest, we simply usethe total for all contracts. Period A includes the dayswhen the price hits the limit and hence trading volume isextremely small. Speci®cally, the total trading volume onsuch dates are: 153 (2 October 1990), 658 (6 January 1992),167 (27 August 1992), 63 (24 January 1994), 0 (31 January1994), 0 (1 February 1994). Such data are simply omitted.

Descriptive statistics for returns, absolute returns,trading volume and open interest in each period aresummarized in Table 2. The statistics reported are the

Price volatility, trading volume and market depth 653

Table 1. Margin rates, price range, and time interval in updating quotation for the Nikkei 225stock index futures

Margin rates Updating quotation

Date Customer Member Price range Time interval

3 September 1988 9% (3%) 6% (0%) 90 yen 3 minutes24 August 1990 15% (5%) 10% (0%) 50 yen 6 minutes31 January 1991 20% (7%) 15% (2%) 50 yen 6 minutes27 June 1991 25% (8%) 20% (5%) 30 yen 5 minutes18 December 1991 30% (13%) 25% (10%) 30 yen 5 minutes

20 yen*14 February 1994 25% (8%) 20% (5%) 60 yen 3 minutes15 August 1994 20% (5%) 15% (2%) 60 yen 3 minutes13 February 1995 15% (3%) 10% (2%) 60 yen 3 minutes

Numbers in parentheses are minimum cash requirements. * After 3 p.m.

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mean, the standard deviation, the Ljung-Box (LB) statisticsfor 10 lags corrected for heteroscedasticity followingDiebold (1988). The mean of returns in period A is larger

than that in period B. The standard deviation of returns

and the mean of absolute returns in period A are largerthan those in period B. The mean of volume in period A islarger than that in period B, while the mean of open inter-

est in period A is smaller than that in period B. The LBstatistic for the return series in period A does not reject the

null hypothesis of no autocorrelation at any standard level,while that for the return series in period B rejects the null at

the 10% level. In contrast, the LB statistics for the squaredreturn series in both periods reject the null hypothesis of no

autocorrelation at any standard level, indicating signi®cantpersistence in volatility. The LB statistics for tradingvolume and open interest in both periods strongly reject

the null hypothesis of no autocorrelation, demonstratingthat trading volume and open interest are also highly auto-

correlated.

Unit root tests for volume and open interest

The stationarity of the volume and open interest series ineach period is tested using the Augmented Dickey±Fuller

(ADF) tests. Speci®cally, the following regression equationis estimated:

¢Yt ˆ · ‡ ­ t ‡ ¬0Yt¡1 ‡X5

iˆ1

¬i¢Yt¡i ‡ ut …5†

where ¢Yt ˆ Yt ¡ Yt¡1:The results of ADF tests are presented in Table 3, where

the statistics t¬ and t­ are t-statistics to test the null ¬0 ˆ 0and the null ­ ˆ 0 respectively, and the statistics ©2 and ©3

are F -statistics to test the null …·; ¬0; ­ † ˆ …0; 0; 0† and thenull …¬0; ­ † ˆ …0; 0† respectively. The statistics t¬, ©2, and

©3 are signi®cant at any standard level for the volume andopen interest series in both periods except t¬ for the volumeseries in period B, which is signi®cant at the 5% level.Thus, the presence of unit root is rejected for the volumeand open interest series in both periods. The statistic t­

rejects the null hypothesis of no linear time trend for thevolume and open interest series in both periods at anystandard level except for the volume series in period B,for which the null is not rejected at any standard level.

The conclusion is that volume in period A and openinterest in both periods are trend-stationary while volumein period B is stationary and has no trend. Therefore, vol-ume in period A and open interest in both periods aredetrended by regressing them on a constant and on timet ˆ 1; . . . ; T .

Expected and unexpected components of volume and openinterest

The detrended volume in period A, the raw volume inperiod B, and the detrended open interest in both periods

654 T. Watanabe

Table 2. Summary statistics of futures return, volume, and openinterest

Period A Period BSample period 24 August 1990± 14 February 1994±

10 February 1994 30 December 1997Sample size 847 960

Return (%)Mean 70.023 70.028St.Dev. 1.632 1.384LB(10) 3.32 16.12*

Absolute return (%)Mean 1.224 1.005St.Dev. 1.079 0.951LB(10) 174.39*** 116.49***

VolumeMean 57 075 28 459St.Dev. 27 271 11 989LB(10) 5569.83*** 1698.36***

Open interestMean 162 549 192 110St.Dev. 40 350 73 832LB(10) 6705.45*** 8027.78***

LB(10) and LB2(10) are the heteroscedasticity-corrected LjungˆBox statistics (e.g. Diebold, 1988) for up to tenth order auto-correlation in the returns and the squared returns respectively.The asymptotic distribution of these statistics is À2 with tendegrees of freedom. À2…10† critical values: 15.99 (10%), 18.31(5%), 23.21 (1%). *, **, and *** signi®cant at the 10%, 5%,1% level, respectively.

Table 3. Unit root tests for volume and open interest

Period A Period B

Volumet¬ 74.85*** 77.43***©2 7.97*** 18.57***©3 11.94*** 27.86***t­ 73.95*** 0.91

Open interestt¬ 74.38*** 73.76**©2 6.66*** 4.84***©3 9.96*** 7.20***t­ 73.70*** 2.61***

The regression ¢Yt ˆ · ‡ ­ t ‡ ¬0Yt¡1 ‡P5

iˆ1 ¬i¢Yt¡i ‡ ut isestimated, where ¢Yt ˆ Yt ¡ Yt¡1: t¬0

tests the null ¬0 ˆ 0. Thecritical values are: 73.12 (10%), 73.41 (5%), 73.96 (1%).©2 tests the null …·; ¬0; ­ † ˆ …0; 0; 0†. The critical values are 4.03(10%), 4.68 (5%), and 6.09 (1%). ©3 tests the null …¬0; ­ † ˆ …0; 0†.The critical values are 5.34 (10%), 6.25 (5%), and 8.27 (1%). t­

tests the null ­ ˆ 0. Under the null, t­ has a t-distribution. *, **,and *** signi®cant at the 10%, 5%, 1% level, respectively.

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are partitioned into expected and unexpected componentsusing the following regression.

yt ˆ ’ ‡X10

jˆ1

»jjrt¡jj ‡X10

kˆ1

¶kVolt¡k

‡X10

mˆ1

·mOpInt¡m ‡ ¿DTEt ‡ ¸t;

for yt ˆ Volt or OpInt …6†

where Volt is the detrended volume in period A or the rawvolume in period B, OpInt is the detrended open interest ineach period, and DTEt is day to expiration.

The residuals ^t from the above regression are used asthe unexpected component. The LB(10) statistics do notreject the null hypothesis of no autocorrelation at anystandard level for the unexpected components of volumeand open interest in each period. The expected componentis de®ned as the diVerence between the actual series and theunexpected component, yt ¡ ^t¸t.

This method is diVerent from the one used byBessembinder and Seguin (1993), who ®rst ®t an AR(10)or an ARIMA(10,1,0) model to volume and open interestand then use the obtained residuals as a dependent variablein Equation 6. Their method is also used, but the results arequalitatively unaltered.

V. ESTIMATION RESULTS

Conditional mean equation

Equations 1 and 2 are estimated for each of the two peri-ods. The results of estimating the conditional meanEquation 1 are presented in Table 4. Numbers in parenth-eses are t-statistics computed using White (1980) standarderrors for the individual coe� cients, and F statistics for thesum of 10 lagged volatilities and the sum of 10 laggedreturns.

Coe� cient estimate for the dummy variable associatedwith Thursday is signi®cant at the 10% level for period A,while that associated with Tuesday is signi®cant and at the5% level for period B. This result provides evidence thatreturns are higher on Thursday in period A and onTuesday in period B, but the evidence is weak. Laggedvolatilities are not signi®cant at any standard level foreach period. This result contrasts with the result ofBessembinder and Seguin (1993) who ®nd a signi®cantpositive relation between the conditional mean and laggedvolatilities, but is consistent with Nelson (1991) who doesnot ®nd a signi®cant relation between the conditional meanand volatility. Lagged unexpected returns have signi®cantexplanatory power for only period B, so that the adjustedR2 for period B is larger than that for period A. However,the adjusted R2 even for period B is 0.0217 and not large

enough to violate weak-form e� ciency, which states thatpast returns are not useful in predicting present returns.

The LB(10) statistic for the residual series in each period

does not reject the null hypothesis of no autocorrelation at

any standard level.

Volatility equation

The results of estimating the volatility Equation 2 are

presented in Table 5. The dummy variables that representthe day-of-the-week eVects are not signi®cant at any

standard level for each period. The sum of the estimated

coe� cients associated with 10 lagged volatilities are

positive and signi®cant at any standard level for both

periods, exhibiting signi®cant persistence in volatility

typical in ®nancial markets. The sum of the estimatedcoe� cients on lagged unexpected returns is negative and

signi®cant for both periods, con®rming the well-

documented regularity in stock markets that negative

return shocks have a larger eVect on subsequent volatilities(see Black, 1976; Christie, 1982; Nelson, 1991). However, it

contrasts with the ®nding by Bessembinder and Seguin

(1993), where the estimated coe� cients on lagged un-

Price volatility, trading volume and market depth 655

Table 4. Estimation results of the conditional mean Equation 1

Period A Period B

Intercept 70.2369 70.2739(71.1897) (71.5654)

Day-of-the-week dummiesMonday 70.2726 70.0252

(71.5099) (70.1768)

Tuesday 70.0130 0.2831(70.0785) (1.9942)**

Wednesday 0.0041 0.2214(0.0239) (1.6064)

Thursday 0.2870 0.1959(1.6534)* (1.4723)

Sum of 10 lagged volatilities 0.1446 0.0844(1.3217) (1.3212)

Sum of 10 lagged returns 0.0762 70.0684(0.4832) (2.3359)***

Adjusted R2 0.0049 0.0217LB(10) 1.1546 0.2344

Numbers in parentheses for individual coe� cients are t-statisticscomputed using White (1980) standard errors. Numbers in par-entheses for the sum of 10 lagged volatilities and the sum of 10lagged returns are F-statistics for the hypothesis that all of the 10coe� cients are zero. LB(10) is the heteroscedasticity-correctedLjungˆBox statistic (e.g. Diebold 1988) for up to tenth orderautocorrelation in the residuals. The asymptotic distribution ofLB2(10) is À2 with ten degrees of freedom. À2…10† critical values:15.99 (10%), 18.31 (5%), 23.21 (1%). *, **, and *** signi®cant atthe 10%, 5%, 1% level respectively.

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expected returns is not signi®cant for agricultural, metal,currency, and bond futures.

None of the coe� cient estimates associated with volumeand open interest are signi®cant at any standard level forperiod A, when the regulation increased gradually.

In contrast, coe� cient estimates for unexpected volumeand expected open interest are signi®cant at any standardlevel for period B, when the regulation decreased gradually.Coe� cient estimate for unexpected volume is positive andlarger than that for expected volume, demonstrating thatunexpected volume shocks have a positive and larger eVecton volatility. This result is consistent with the ®nding byBessembinder and Seguin (1993) and a widely documentedempirical regularity of the contemporaneous positivecorrelation between volatility and volume (see KarpoV,1987). A signi®cant negative coe� cient of expected openinterest indicates that an increase in expected open interestmitigates volatility. This result is also consistent with the®nding by Bessembinder and Seguin (1993), who explain

that this is because expected open interest is positivelyrelated to the number of traders or amount of capitala� liated with a market, and an increase in the number oftraders or amount of capital a� liated with a marketenhances market depth and hence lessens volatility.

Asymmetry in the eVects of volume and open interestshocks

Table 6 reports the estimation results of Equation 4 thatallows the eVects of unexpected changes in volume andopen interest on volatility to vary with the sign of shockby introducing dummy variables Voldumt and OpIndumt

that equal one for a positive unexpected shock and zero fora negative unexpected shock. The estimation is conductedfor period B only, because the eVects of volume and openinterest shocks on volatility are not signi®cant for period A.

Coe� cient estimate for Voldumt is positive andsigni®cant at the 10% level. Although the evidence is

656 T. Watanabe

Table 5. Estimation results of the volatility Equation 2

Period A Period B

Intercept 0.6162 0.4917(4.8322)*** (3.4136)***

Day-of-the-week dummiesMonday 0.1456 0.1633

(1.0337) (1.4472)

Tuesday 70.0564 70.0932(70.4710) (70.8392)

Wednesday 0.1073 70.0682(0.8374) (70.6540)

Thursday 70.0369 70.0378(70.2398) (70.3850)

Sum of 10 lagged volatilities 0.5512 0.5603(7.0716)*** (8.2934)***

Sum of 10 lagged unexpected returns 70.3070 70.2965(3.4324)*** (2.4429)***

Expected volume 70.2881 0.2329(70.8241) (0.5947)

Unexpected volume 0.7131 5.8019(1.4909) (9.4263)***

Expected open interest 70.0473 70.2017(70.2398) (72.6058)***

Unexpected open interest 70.8751 0.0648(71.5574) (0.2374)

Adjusted R2 0.1148 0.2564

LB(10) 0.9575 6.7739

Numbers in parentheses for individual coe� cients are t-statistics computed using White(1980) standard errors. Numbers in parentheses for the sum of 10 lagged volatilities andthe sum of 10 lagged unexpected returns are F-statistics for the hypothesis that all of the 10coe� cients are zero. LB(10) is the heteroscedasticity-corrected LjungˆBox statistic (e.g.Diebold 1988) for up to tenth order autocorrelation in the residuals. The asymptotic distri-bution of LB2(10) is À2 with ten degrees of freedom. À2…10† critical values: 15.99 (10%),18.31 (5%), 23.21 (1%). *, **, and *** signi®cant at the 10%, 5%, 1% level respectively.

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weak, this result is consistent with the ®nding byBessembinder and Seguin (1993) that the impact of positiveunexpected volume shocks on volatility is larger than theimpact of negative shocks. Coe� cient estimate forOpIndumt is not signi®cant at any standard level.

VI. CONCLUSIONS

This article investigates the relation between tradingactivity and price volatility for the Nikkei 225 stockindex futures traded on the OSE, employing the method

developed by Bessembinder and Seguin (1993). Followingthem, this article examines the relation of price volatility tonot only trading volume but also open interest as a proxyfor market depth, and allows the eVects of trading volumeand open interest shocks to diVer depending on whethershocks are expected or unexpected and on whether unex-pected shocks are positive or negative. The OSE regulationfor trading of the Nikkei 225 futures decreased beginning14 February 1994. Therefore, the samples prior to andbeginning 14 February 1994 are analysed separately.

A signi®cant positive relation between unexpected vol-ume and volatility and a signi®cant negative relationbetween expected open interest and volatility are foundfor the period beginning 14 February 1994, when theregulation decreased gradually. Although weak, it is alsofound that the impact of positive unexpected volumeshocks on volatility is larger than the impact of negativeshocks. These results con®rm the ®ndings by Bessembinderand Seguin (1993).

In contrast, no relation between price volatility, volume,and open interest is found for the period prior to 14February 1994, when the regulation increased gradually.This result is noteworthy because it provides evidencethat the relation between price volatility, volume, andopen interest may vary with the regulation.

ACKNOWLEDGEMENTS

The author would like to thank the Osaka SecuritiesExchange for generously providing data on the Nikkei225 stock index futures. Thanks are also due to MichiakiHashimoto and Toshinori Takayama for making some use-ful suggestions. Remaining errors are the authors’ alone.

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Price volatility, trading volume and market depth 657

Table 6. Estimation results of the volatility Equation 4

Period B

Intercept 0.4574(3.1512)

Day-of-the-week dummiesMonday 0.1460

(1.2912)

Tuesday 70.0886(70.8050)

Wednesday 70.0622(70.6040)

Thursday 70.0338(70.3457)

Sum of 10 lagged volatilities 0.5625(8.4280)***

Sum of 10 lagged unexpected returns 70.2884(2.4019)**

Expected volume 70.0433(70.1048)

Unexpected volume 3.7406(4.2015)***

Voldum 3.3649(1.8760)*

Expected open interest 70.2104(72.7213)***

Unexpected open interest 70.0007(70.0019)

OpIndum 0.4443(0.5561)

Adjusted R2 0.2595

LB(10) 5.9555

Numbers in parentheses for individual coe� cients are t-statisticscomputed using White (1980) standard errors. Numbers in par-entheses for the sum of 10 lagged volatilities and the sum of 10lagged unexpected returns are F -statistics for the hypothesis thatall of the 10 coe� cients are zero. LB(10) is the heteroscedasticity-corrected LjungˆBox statistic (e.g. Diebold 1988) for up to tenthorder autocorrelation in the residuals. The asymptotic distri-bution of LB2(10) is À2 with ten degrees of freedom. À2…10†critical values: 15.99 (10%), 18.31 (5%), 23.21 (1%). *, **, and*** signi®cant at the 10%, 5%, 1% level respectively.

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