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The informational role of option trading volume in theS&P 500 futures options marketsGhulam Sarwara Department of Finance , Insurance and Real Estate, St. Cloud State University , St. Cloud,MN 56301-4498 E-mail:Published online: 02 Feb 2007.

To cite this article: Ghulam Sarwar (2004) The informational role of option trading volume in the S&P 500 futures optionsmarkets, Applied Financial Economics, 14:16, 1197-1210, DOI: 10.1080/0960310042000280483

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The informational role of option trading

volume in the S&P 500 futures options

markets

GHULAM SARWAR

Department of Finance, Insurance and Real Estate, St. Cloud State University,St. Cloud, MN 56301-4498E-mail: gsarwar@stcloudstate.edu

This paper analyses the dynamic relations between future price volatility of theS&P 500 index futures and trading volume of S&P 500 futures options toexamine the informational role of the option volume in predicting the futureprice volatility. Using a pooled cross-sectional and time-series data framework,the paper uses the error components and dummy variable models to allow forthe relations between volatility and volume to vary by the option’s time-to-maturityand moneyness. The results suggest that previous call and put volumes have astrong predictive ability with respect to the future price volatility. The results alsoindicate that the future price volatility has a leading positive effect on the optionvolume, but that the rises and falls in volatility exert asymmetric influences on theoption volume. These findings support the hypothesis that both the information-and hedge-related trading explain most of the trading volume of S&P 500 futuresoptions.

I . INTRODUCTION

Options on equity index futures are widely used for

hedging the risk of equity positions and for speculativepurposes. Several recent studies investigate whether the

trading volume of equity options contain information

about the future stock price movements (Easley et al.,

1998; Llorence et al., 2002; Chan et al., 2002). Black(1975) and Mayhew et al. (1995) argue that lower transac-

tion costs and greater financial leverage of the options

markets may induce informed traders to trade in the

option market rather than in the stock market. Further,Back (1993) and Cherian (1993) argue that investors

who possess private information about the future

volatility of the stock price may be more attracted to

the option market instead of the stock market because

they can only make their bet on volatility in the option

market.Easley et al. (1998) examine the lead–lag relations

between the trading volume of options on individual stocks

and the prices of the underlying stocks, and show that theoption trading volume indeed contains information about

the future stock prices. However, Chan et al. (2002) report

that the option net trade volume has no strong predictiveability for stock quote revisions. Similarly, many studies

examine the links between option prices and stock prices,option volume and stock volume, option prices and stock

volume, and stock prices and stock volume (Manaster

and Rendleman, 1982; Bhatacharya, 1987; Anthony,1988; Vijh, 1988, 1990; Stephen and Whaley, 1990; Chan

et al., 1993; Sheikh and Ronn, 1994; Mayhew et al., 1995;

Fleming et al., 1996; Llorence et al., 2002). However, none

Applied Financial Economics ISSN 0960–3107 print/ISSN 1466–4305 online # 2004 Taylor & Francis Ltd 1197

http://www.tandf.co.uk/journalsDOI: 10.1080/0960310042000280483

Applied Financial Economics, 2004, 14, 1197–1210

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of these studies examine the direct links between the option

trading volume and the stock price volatility expected in

the future. The ability to predict price volatility is impor-

tant for portfolio selection and asset management as well as

for the pricing of primary and derivative securities (Engle

and Ng, 1993). Because informed traders can make direct

bets on their private information of the future price

volatility only in the option market (Back, 1993), an

examination of the interrelations between the future price

volatility and the option trading volume could provide use-

ful insights about the volatility-related information content

of option trades. The option pricing theory is unclear about

the exact nature of such volume–volatility relations.

Because the hedging and speculative uses of options arise

from the asset’s price volatility, some researchers may

argue that the option trading volume should unilaterally

follow the price volatility. For example, a perceived or an

unexpected actual increase in the stock price volatility

could lead to a higher trading volume of stock options as

traders increase their risk management and speculative

activities to cut the potential losses or to enhance the

potential gains on their equity positions. In fact, Sears

(2000a, b) and Tan (2001a) cite a positive relation between

the higher perceived price volatility and the trading volume

of stock options. However, the argument for the unidirec-

tional link from the price volatility to the option trading

volume implicitly assumes perfect markets and symmetric

information across traders, and views the trading volume

as a non-informative outcome of the trading process.

If some traders are better informed than others, and if

traders cannot accurately forecast the price volatility, the

unidirectional link from the price volatility to the option

trading volume may break down.

Because informed traders may be more attracted to

the options markets than to the stock markets due to the

low transaction costs and higher leverage available in

the options markets, option trades may first reflect the

information on the future price volatility due to the fact

that option pricing formulas need this volatility to deter-

mine the option price (Easley et al., 1998). Thus, the option

trading volume may precede the future price volatility

if the option trades are largely initiated by informed

traders. However, the hedge-related uses of options suggest

that the future price volatility may precede the option trad-

ing volume because a higher future price volatility leads to

a greater use of options. So far, Sarwar (2003) appears to

be the only study that examines the direct relations between

the future price volatility and the option trading volume in

currency options markets for the British pound. His results

suggest that the volume of British pound options has

a strong predictive power for the future volatility of the

US dollar/British pound exchange rate. Whether such

results hold in other options markets remain to be seen,

however.

This study examines the informational role of the tradingvolume of equity index futures options in predicting thefuture price volatility of the underlying index futures.The sample options markets examined here and the pro-cedures used to analyse the volume-volatility relations inthese markets are distinctly different from those of Sarwar(2003). Specifically, the present sample options marketsdiffer from those studied by Sarwar in the followingrespects. First, unlike the thinly-traded market for theBritish pound options examined by Sarwar, this studyexamines the market for the S&P 500 index futures optionswhich is the largest equity futures options market on theChicago Mercantile Exchange in terms of daily tradingvolume. Second, jumps are less likely to occur in equityindices than in individual currencies because of the diversi-fication afforded by the indices. Third, Sarwar examinesonly the European currency options written on theBritish pound, while the S&P 500 futures options of thisstudy are all American-style options. Finally, because theS&P 500 futures options market allows traders a widerange of trading choices with respect to the expirationdates and strike prices, this multidimensional tradingchoice enhances the ability of informed traders to hidetheir trades in the market than is possible in the thinly-traded British pound options market. Hence, the volume–volatility relations in the S&P 500 futures options marketcould be very different from those uncovered by Sarwar(2003) in the British pound options market. Moreover,the study uses a pooled cross-sectional and time-seriesdata framework to adequately capture the subtle volume-volatility relations that could emerge from the multidimen-tional trading aspects of the S&P 500 futures options.

Besides examining the informational role of the futuresoptions volume for the future volatility of the underlyingfutures index, the study also investigates if the relationsbetween option trading and price volatility vary betweenthe rises and falls in the expected future price volatility.Examining such relations may uncover certain volatilitymovements that attract a greater trading activity fromthe informed and uninformed traders.

II . METHODOLOGY

This study uses variants of the causality testing approachesof Granger and Newbold (1977) and Granger (1969)to investigate the relations between price volatility andoption trading volume. Many researchers conductGranger causality tests by estimating a vector autoregres-sive (VAR) model and testing zero restrictions on thelagged parameters (see, for example, Chan and Chung,1993; Chatrath et al., 1995, 1996). The VAR model speci-fies that each endogenous variable depends upon its ownlagged values and the lagged values of the other endogen-ous variable (s) involved. To account for the possibility

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of contemporaneous interaction among the variables, onecan add the current value of one variable as an additionalexplanatory variable in the VAR equation of the othervariable (s) involved (Koch, 1993; Easley et al., 1998;Kyriacou and Sarno, 1999; Chan et al., 2002).

The VAR equations for analysing the dynamic relationsbetween the expected future price volatility and optionvolume series are specified as:

It ¼ 8 þXk

j¼1

91jIt�j

þXm

i¼0

81iVt�i þ et, t ¼ 0, 1, . . . , n ð1Þ

and

Vt ¼ 9 þXk

j¼0

92jIt�j

þXm

i¼1

82iVt�i þ kt, t ¼ 0, 1, . . . , n ð2Þ

where It denotes the future price volatility, Vt is the optiontrading volume, 8 and 9 denote the intercepts, and et and ktare the disturbance terms.

The series It and Vt are assumed to be stationary tocircumvent the problem of spurious regressions. If theseseries are nonstationary, they can be transformed tostationarity by differencing prior to parameter estimation(Griffiths et al., 1993).

Most investigators using aggregate data on optionsestimate parameters of Equations 1 and 2 either by theordinary least-square method or by a simultaneous equa-tion estimator (Chan and Chung, 1993; Koch, 1993;Chatrath et al., 1995, 1996; Kyriacou and Sarno, 1999).Similarly, researchers employing interday or intradaydata on stock options use the ordinary least-square methodto estimate variants of Equations 1 and 2 (Bhar andMalliaris, 1998; Easley et al., 1998; Chan et al., 2002).Such estimation approaches make no distinction betweenthe time series and cross-sectional properties of the optionsdata even though option observations are actually clus-tered in time and across cross-sections.

Previous empirical research on option pricing and actualdata on options trading strongly suggest the considerationof three estimation issues in Equations 1 and 2. First, vola-tility smiles studies provide ample evidence that impliedvolatilities of the underlying assets, which approximatethe expected future price volatility of the assets, vary bythe option’s moneyness (Heston, 1993; Bakshi et al., 1997;Das and Sundraram, 1999). Second, since price vola-tilities vary overtime as shown by several studies on thestochastic-volatility option pricing models (Melino andTurnbull, 1990; Heston, 1993; Nandi, 1996; Bakshi et al.,1997), the future price volatility expected at a given point-

in-time for, say, the next thirty days is likely to be differentfrom volatilities expected for other future time periods. Infact, Whaley (1982, 1986) and Dumas et al. (1998) empha-size the use of maturity-specific implied volatilities for pri-cing options. Thus, the future price volatility is expected tovary with the option’s time-to-maturity, which in turn sug-gests variation of the volatility–volume relations withrespect to the option’s time-to-maturity. In a related con-text, Nandi (1996) and Whaley (1982) recognize the impor-tance of the option’s time-to-maturity and moneynessclasses in explaining the option pricing biases, and thusthey estimate separate regressions for each of the severalsuch classes defined for their data. Third, actual optionsmarkets trade a series of options with different expirationdates and strike prices, allowing traders a wide range oftrading choices at any given time. This multidimensionaltrading choice enhances the ability of informed traders tohide their trades in the market, and thus it may blur theevidence of information-related trading in options if thevolatility–volume relations are analysed using data aggre-gated over the option’s moneyness and time-to-maturityclasses. These three considerations strongly suggest thatthe volume–volatility relations in options markets varyacross the option’s time-to-maturity and moneynessclasses. Thus, VAR Equations 1 and 2 need to be modifiedto account for such inter-class distinction of the volatility–volume relations.

This paper attempts to capture the cross-sectionaland time-series properties of the options data, as well asthe possible inter-class distinction of the volume-volatilityrelations, in a single pooled cross-sectional and time-seriesequation for each endogenous variable. To implement thisapproach, the time-series observations of options are firstordered by the option’s time-to-maturity classes, so that alloptions with a time-to-maturity of T months are stackedfirst, followed by options with a time-to-maturity of Tþ1months, and so on. These options are then divided intothree moneyness classes: near-the-money, in-the-money,and out-of-the-money. The product of the time-to-maturityclass and the moneyness class yields a cross-section whosedaily observations are tracked overtime until the option’sexpiration date. In this data scheme, the time-series obser-vations of cross-section one (near-the-money options withT maturity) are stacked on top, followed by observationsof cross-section two (in-the-money with T maturity) andcross-section three (out-of-the-money with T maturity),respectively. Similarly, cross-section four (near-the-moneywith Tþ1 maturity) is stacked under cross-section three,and this scheme is continued for other cross-sections.The resulting data show unequal number of observationsunder each cross-section, yielding an unbalanced pooledcross-sectional and time-series data structure.

This pooled cross-sectional and time-series data struc-ture is used to analyse the volatility–volume relationsin the sample options. The volume–volatility relations are

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estimated using the error components and dummy variablemodels. To express these models succinctly, the VAREquations 1 and 2 are rewritten as:

Irt ¼ 8r þXK

J¼1

91jIrt�j

þXm

i¼0

81iVrt�i þ ert, t ¼ 0, 1, . . . , n ð3Þ

and

Vrt ¼ 9r þXk

j¼0

92jIrt�j

þXm

i¼1

82iVrt�i þ urt t ¼ 0, 1, . . . , n ð4Þ

where r refers to a cross-sectional unit (r¼ 1, 2, . . . ,N ), Irt�j

is the price volatility of cross-section r at time t�j, Vrt�i isthe option volume of cross-section r at time t�i, 8r (9r) isthe intercept of cross-section r in Equations 3 and 4, andert (urt) is the random error of cross-section r at time t inEquations 3 and 4. The random errors ert and urt areassumed to be independently and identically distributedwith a zero mean and constant variance.

The error components and dummy variable modelsassume that all behavioural differences between cross-sections are captured by the intercept. Thus, the modelsassume that each cross-section has its own, distinct inter-cept but all cross-sections share the same slope coefficients(see Griffiths et al., 1993 for details of these models). Thedummy variable model assumes that the intercepts arefixed parameters. However, the error components modelassumes that the intercepts are independent random vari-ables, so that we can write 8r¼8þ qr and 9r¼9þ 0r, where8 and 9 are unknown mean intercepts and qr and 0r areunobservable random disturbances that account for indi-vidual differences in cross-sections. Both models are usedfor analysis of the volume–volatility relations because thechoice between fixed and random effects is unclear a priorifrom the sample data.

If the volume and volatility series in Equations 3 and 4have contemporaneous interactions, then only 810 and 920are expected to be significant. However, if the linkages takesome time, the coefficients of the lagged price volatility oroption volume series would be significant. The null hypoth-esis, H0, that the future price volatility does not havea predictive power for the option trading volume isexpressed as:

H0 : 921 ¼ 922 ¼ � � � ¼ 92k ¼ 0 ð5Þ

that is, under H0 past values of the future price volatilitydo not have a predictive power for option volume. Thenull hypothesis is a joint hypothesis of zero-value lagged

coefficients that can be tested using an F-statistic for therestricted 921 ¼ 922 ¼ � � � ¼ 92k ¼ 0 and unrestricted equa-tion system (Griffiths et al., 1993; Koch, 1993). Similarly,the null hypothesis that the option volume does not have apredictive power for the future price volatility can be testedby simply replacing coefficients 92j in Equation 5 with 81i(i¼ 1, . . .,m). A rejection of the joint hypothesis of zero-value lagged 81i would be consistent with the information-related uses of options (Easley et al., 1998). Similarly, arejection of the joint hypothesis of zero-value lagged 92jis considered to be supportive of the hedge-related usesof options. If the null hypothesis in Equation 5 is rejected,the timing and direction of the predictive power of laggedvolatility terms can be examined by testing the significanceof individual lagged coefficients on the basis of a t-test(Easley et al., 1998). The number of lagged terms to includein Equations 3 and 4 is determined from the Schwartz andAkaike information criteria.

III . THE DATA

This study uses the daily closing transaction data forthe S&P 500 equity futures and futures options traded onthe Chicago Mercantile Exchange (CME) for the period2 January 2000 to 31 December 2000. The data areobtained from the Futures Industry Institute. The datalist for each futures option the opening, high, low, andclosing option prices; the date of the trade, maturity, andexercise price; and actual trading volume, open interest,and implied volatility. Similarly, the equity futures datalist for each contract the opening, high, low, settle, andclosing futures prices; the date of the trade and contractmaturity; and actual trading volume, delivery intent, andopen interest. The closing prices for the S&P 500 index(S&P) futures and futures options correspond to 3:15 PMcentral time, and both contracts are traded side by side onCME. The underlying futures for a futures option contractis the next expiring futures.

The daily data on futures options have a beginning sam-ple of 44,757 observations. Following Aı̈t-Sahalia and Lo(1998), options with time-to-maturity of less than a dayand with price less than $0.05 are dropped. In addition,options with a trading volume of less than two contractsare excluded. Aı̈t-Sahalia and Lo argue that prices ofoptions with a very low trading volume are notoriouslyunreliable. These filters yield a final sample of 37 883 obser-vations, which include 15 447 call observations and 22 436put observations.

The S&P futures options are American-style, and theunderlying asset is an index futures, the most likely casefor which jumps in prices are less likely to occur because ofthe diversification afforded by the index. Since the S&Pfutures options trade alongside the highly liquid futurescontracts, Daigler (1994) argue that the pricing of futures

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options will be more accurate than that of options on cash

assets because traders know the current price of the under-

lying futures.

The future price volatility of the S&P futures is approxi-

mated by the implied volatility using the procedures of

Whaley (1986) and Barone-Adesi and Whaley (1987).

Empirical evidence appears to favour an implied volatility

estimate over a historical volatility estimate as a predictor

of ex-post volatility. Chirac and Manaster (1978), Merville

and Pieptea (1989), Poteshman (2000) and Chernov (2001)

argue that implied volatilities should theoretically provide

the best forecasts of the expected future volatilities because

option prices can impound all publicly available informa-

tion. Their empirical results from the US equity index

options markets generally support the superiority of

the implied volatility as an estimate of expected future

volatility. Mayhew and Stivers (2003) show that for the

most actively traded CBOE stock options during 1988

and 1995, implied volatilities outperform GARCH volati-

lities and subsume all information in return shocks. They

also show that compared to GARCH volatilities, implied

volatilities of equity index options provide reliable incre-

mental information about the future firm-level volatility.1

In addition, Sarwar (2003) demonstrates that the overall

relations between the option volume and the expected

future price volatility in the British pound options markets

are unaffected whether the future price volatility is approxi-

mated by the implied volatility or by the GARCH volati-

lity.

This study uses Whaley’s (1986) approach to estimate

the maturity-specific implied volatility for each traded

option. These maturity-specific volatilities are updated

daily until the option’s expiration date.2 This approach to

volatility estimation is similar in spirit to that of Dumas

et al. (1998) in which they estimate maturity-specific

implied volatility for each traded option and then

revise volatility weekly. The continuously compounded

Treasury bill rate interpolated to match the maturity

of the option is used for the risk-free rate needed for

estimation of volatilities. The T-bill rates are the average

of the ask and bid discounts, and are hand-collected

from the Wall Street Journal. The estimation of implied

volatilities does not require the time series of dividends

on the S&P 500 index since the transaction prices of S&P

futures reflect these dividends.

The time-series data of implied volatilities and trading

volume is ordered by cross-sections according to

the pooled cross-sectional and time-series data structure

of section II. Since the data contain multiple options

for a cross-section defined with respect to the option’s

moneyness and time-to-maturity on many trading days

(for example, several in-the-money March 2000 options

traded on 3 January 2000), the average of maturity-specific

implied volatilities and the sum of the trading volume of

options are used to represent the daily volatility and

volume, respectively, for such cross-sections.3

IV. RESULTS

Table 1 presents the summary statistics of the sample data

on S&P futures options. The implied volatility of the index,

a proxy for the expected future price volatility, is very

unstable, varying from 2.14% to 93.85% during 2000.

The trading volume shows a wide range across the options,

with a mean value of 105 contracts and a standard devia-

tion of 279 contracts. The time to expiration of the options

averaged about two months for calls and two and a half

months for puts. The mean exercise value of the options is

at 94% of the mean spot value of index futures, but the

exercise value is nearly three times more volatile than the

spot value.

Table 2 presents the Phillips–Perron unit root tests for

examining the stationarity of the option volume and

implied volatility series. The hypothesis that the option

volume series is nonstationary is rejected at the 0.01

level.4 The implied volatility series is, however, nonstation-

ary at the 0.01 level. When first-differenced, the volatility

series is stationary. Therefore, the option volume and first-

differenced volatility (volatility change) series are used in

the subsequent analysis of volume – volatility relations to

circumvent the problem of spurious regressions.

1 In addition, unlike the implied volatilities in which each specific option maturity has its own distinct implied volatility, the GARCHvolatilities do not distinguish between maturity-specific volatilities and thus the same conditional volatility is used for the expected futurevolatility of all option maturities. Thus, GARCH procedures do not provide maturity-specific volatilities which are important inour pooled cross-sectional and time-series analysis of the volume-volatility relations.2Although the futures options data from the CME list implied volatility of the futures options, the CME does not specify the nature ofthese volatilities and the procedures used to compute them. Thus, implied volatilities are estimated using Whaley’s (1986) procedure.However, the mean and variance of the estimated implied volatilities are very close to those reported by the CME.3A futures option is considered to be near the money when the ratio of the spot index value to the exercise index value is between 0.975and 1.025. A call (put) option is out-of-the-money (in-the-money) when the spot index to exercise index ratio is less than 0.975, and a call(put) option is in-the-money (out-of-the-money) when the spot index to exercise index ratio is greater than 1.025. Slight variations inthese upper and lower limits of the moneyness classes do not materially affect the results in Tables 3–7.4 The results of the Phillips–Perron unit root tests are not affected when both trend and intercept terms are allowed or ignored in the tests.

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Table 3 reports the regression results of the relation of

option volume and future price volatility from the error

components and dummy variable models. The table

also presents the results from the ordinary least-square

method, which assumes the same intercept and slope coef-

ficients across cross-sections, for comparative purposes.

The Akaike information and Schwartz criteria suggest

the use of five lags in the regressions. The partial autocor-

relation functions of the series also indicate that the partial

autocorrelation coefficients for both option volume and

price volatility are not significant beyond five lags.5

In Table 3, the results of Hausman test under the error

components model strongly suggest the existence of cross-

sectional random effects in intercepts. Similarly, the F-test

of the dummy variablemodel supports the presence of cross-

sectional fixed effects in intercepts.6 These results indicate

5 The results that follow are not materially affected when estimation is executed using an asymmetric lag structure that allows for higherthan five lagged terms in either the volatility or the volume series.6 The estimation of dummy variable model for Equations 3 and 4 also provides the intercept and t-value for each of the 40 distinct cross-sections in the data. These intercepts are not reported in Table 3 for brevity.

Table 1. Summary statistics for S&P 500 futures options data

Panel A: Aggregate datavariable Mean Standard deviation Minimum Maximum

Panel A: Aggregate dataOption price ($) 27.81 57.75 0.05 704.5Implied volatility (%) 24.21 7.71 2.14 93.85Days to expiration 75.20 64.34 2.00 335.00Exercise price (index points) 1388.09 180.86 850.0 2050.00Spot index value (index points) 1478.33 67.76 1279.60 1673.20Volume (option contracts) 105.32 279.62 2.0 7199.0

Panel B: Call optionsOption price ($) 31.18 67.38 0.05 653.00Implied volatility (%) 20.16 5.23 2.14 81.54Days to expiration 64.70 58.20 2.00 335.00Exercise price (index points) 1510.76 132.07 900.0 2050.0Spot index value (index points) 1479.24 68.01 1277.82 1672.03Volume (option contracts) 101.99 280.92 2.0 5805.00

Panel C: Put optionsOption price ($) 25.49 49.93 0.05 704.50Implied volatility (%) 27.17 7.83 2.14 93.85Days to expiration 78.06 68.00 2.00 335.00Exercise price (index points) 1303.64 160.40 850.00 2025.00Spot index value (index points) 1477.75 67.45 1283.82 1676.03Volume (option contracts) 107.61 278.69 2.0 7199.0

Notes: This table provides summary statistics for the daily closing prices of Chicago Mercantile Exchange call and put options on theS&P 500 index futures for the period 4 January 2000 to 31 December 2000. The aggregate sample has 37 883 observations, which include15 447 call and 22 436 put observations.

Table 2. Tests for stationarity of the volume and volatility series

Phillips – Perron unit root Z-test

Variable Aggregate sample Call options Put optionsVolume (level form) �38.56 �24.80 �26.03Implied volatility (level form) �2.99 �2.47 �2.02Implied volatility (first difference form) �28.19 �17.74 �19.25Critical Z-test value �6.25 �6.25 �6.25Total observations 37 883 15 447 22 436

Notes: This table shows the results of the Phillips – Perron unit root tests for the trading volume and implied volatilityseries of S&P 500 futures options from 4 January 2000 to 31 December 2000. The critical Z-test value for a sample ofinfinite observations came from Table 6 of Dickey and Fuller (1981, p. 1063).

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that the relations between option volume and expected

future price volatility vary across the time-to-maturity and

moneyness classes, and that the error components and

dummy variable models provide a reasonable framework

to capture these distinct cross-sectional effects. The results

undermine the use of ordinary least-square method and

other estimators that do not account for the differential

cross-sectional effects in volume–volatility relations.

The aggregate results in Table 3 do not show significant

contemporaneous feedbacks between price volatility and

option volume under the error components and dummy

variable models. Since the aggregate results average out

the contemporaneous effects of the call and put results,

the absence of contemporaneous effects in the aggregate

sample does not necessarily imply the absence of such

effects in the call and put samples. It is possible to get

insignificant contemporaneous feedbacks in the aggregate

sample if these feedbacks are positive for puts and negative

for calls, or vice versa. Interestingly, the least-square

method indicates significant and positive contemporaneous

interactions between volatility and option volume in the

aggregate sample. Hence, procedures that ignore the differ-

ential cross-sectional effects in volume–volatility relations

may provide misleading conclusions about the simulta-

neous effects between volatility and volume.

The lagged volatility terms jointly have a significant

positive effect on the option volume. The positive and

significant responses of volume to volatility at lags two

through five are consistent with the hedge-related uses of

S&P futures options. Thus, a rise in the expected future

volatility has a delayed persistent, positive influence over

the trading volume of futures options. Such a hedging role

Table 3. Option volume and implied volatility regressions: aggregate results

Dependent variable

Independent variableVolume (Vt) Implied volatility change (It)

EC Model DV Model OLS EC Model DV Model OLS

Intercept 234.4 �0.11 249.6 0.0001 0.01 �0.0006(4.62) (0.00) (11.75) (0.03) (2.16) (0.69)

It 568.2 346.0 1207.7 – – –(1.34) (0.74) (3.60)

It�1 471.2 618.8 177.68 �0.86 �0.85 �1.16(0.91) (1.17) (0.35) (83.73) (83.1) (90.5)

It�2 2765.2 2750.2 2936.3 �0.66 �0.66 �0.97(4.78) (4.74) (4.95) (45.94) (45.5) (48.9)

It�3 2787.5 2827.2 2624.9 �0.34 �0.33 �0.49(4.87) (4.95) (4.43) (21.11) (20.9) (21.7)

It�4 1902.7 1857.1 2110.3 �0.21 �0.21 �0.28(3.94) (3.85) (4.24) (15.65) (15.5) (14.5)

It�5 1441.6 1372.9 1673.7 �0.16 �0.15 �0.28(4.47) (4.26) (5.02) (17.07) (16.7) (21.46)

Vt – – – 0.00003 0.00003 0.00002(0.82) (0.74) (3.60)

Vt�1 0.008 0.018 �0.015 0.00003 0.00003 0.00004(0.61) (1.38) (1.13) (7.79) (7.71) (8.90)

Vt�2 0.12 0.12 0.13 �0.00007 �0.00007 �0.00007(9.23) (9.32) (9.61) (2.00) (1.93) (1.30)

Vt�3 0.31 0.29 0.35 �0.00001 �0.00001 �0.00002(24.4) (23.67) (28.08) (3.50) (3.43) (4.53)

Vt�4 0.13 0.13 0.14 �0.00002 �0.00001 �0.00002(10.34) (10.37) (11.02) (4.24) (4.17) (3.31)

Vt�5 0.03 0.03 0.04 �0.00003 �0.00002 �0.00001(2.73) (2.90) (2.68) (0.83) (0.72) (2.63)

R2 0.18 0.33 0.24 0.64 0.87 0.71F-statistic 15.04** 13.0** 27.0** 15.8** 15.4** 23.3**Hausman test 527.6** – – 3167.0** – –

(H0: No random effects)F-test – 7.7** – – 65.8** –(H0: No fixed effects)

Notes: The OLS, EC model, and DV model denote the ordinary least-square, error components model, and dummy variable model,respectively. Absolute t-values are reported in parentheses. The F-statistic tests the joint hypothesis that the five lagged coefficientsof Vt (It) are zero when the dependent variable is It (Vt). Two asterisks (**) indicate significance at the 0.01 level.

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of futures options is both expected and reasonable. A find-

ing that did not support the hedging role of options would

be difficult to reconcile with the extensive use of options

markets for portfolio protection purposes. The positive

effects of lagged volatilities on the option volume may also

be related to the response structure of volume itself in

which the current volume displays a delayed but persistent

positive response to its lagged values over five trading days.

Like the lagged volatility terms, the lagged option

volumes jointly have a significant predictive power for

the future volatility of the S&P futures, a result consistent

with the information-related uses of S&P futures options.

However, the individual effects of lagged volumes on

volatility are mixed, with the volatility initially rising with

a rise in the previous-day volume and then subsequently

falling with rises in volumes on days two to five. These

volatility reactions to volume could be consistent with an

overreaction effect. Also, such reactions of volatility to

lagged volumes may be related to the response structure

of volatility itself in which the current volatility displays a

delayed but persistent negative response to its lagged values.

The individual effects of lagged volumes on volatility

also show subtle differences between the results of error

components and dummy variable models and those of

the least-square method. The least-square method indicates

that lag-two and lag-five volumes have statistically insig-

nificant and significant effects on volatility, respectively,

but the error components and dummy variable models

show exactly the opposite effects. These differential results

stem from the assumption of non-differential cross-

sectional effects under the least-square method.7 By con-

trast, the signs and statistical significance of all regression

coefficients, except the intercept, are similar between the

error components and dummy variable models. However,

the dummy variable model has a larger R2 value in both

regressions, and thus it may provide a better fit of the

volume–volatility relations than the error components

model.

The results are somewhat different when the aggregate

option volume is decomposed into the call and put

volumes. The main new result is that volatility and volume

have now significant contemporaneous feedbacks.

In Table 4, the put results show significant and positive

contemporaneous feedbacks between option volume and

future price volatility, suggesting that arbitrage and other

market forces operate efficiently to produce quick and

strong daily interactions between volume and volatility.

As in the aggregate results, the lagged volatilities jointly

have a significant positive effect on the put volume.

This positive influence suggests the lead of the expected

future price volatility over the put trading volume and is

consistent with the hedging-based uses of futures put

options. Also like the aggregate results, the lagged put

volumes jointly have a significant predictive power with

respect to the future price volatility, a result supportive

of the information-related uses of futures put options.

Hence, the trading volume of futures options is not a

non-informative outcome of the trading process, but it

actually contains valuable information about the future

price volatility. The lagged put volumes individually have

mixed effects on volatility, which are again similar to the

effects in the aggregate analysis. Further, the Hausman and

F tests continue to suggest the existence of significant

random and fixed effects in cross-sectional intercepts,

respectively.

The call results in Table 5 are nearly similar to the put

and aggregate results, with the exception of contempora-

neous relations between volatility and call volume. The call

results suggest significant and negative contemporaneous

feedbacks between volume and volatility, rather than

positive feedbacks as under the put options. The negative

feedbacks suggest that a rise in volatility quickly leads to

a fall in the call trading volume, and this fall in volume in

turn raises volatility. Such a negative impact of volatility

on volume may occur if the actual price volatility turned

out to be lower than the expected price volatility even

though the change in volatility is still positive.

However, similar to the put and aggregate results, the

call results show that lagged volatilities jointly have a sig-

nificant positive effect on the call volume. This positive

influence suggests the lead of the expected future price

volatility over the call trading volume and points to the

hedging role of futures call options. Also, like the aggregate

and put results, the lagged call volumes jointly have a sig-

nificant predictive ability for the expected future volatility,

a result that reinforces the information-related uses of S&P

futures options. In a related study, Easley et al. (1998) find

support for the information-based uses of stock options

when they examine the relations between the stock price

changes and the informationally defined option volume.

The results discussed so far implicitly assume that the

rises and falls in volatility have symmetric effects on the

option volume. It is probable that option traders are more

sensitive to increases in volatility (bad news) than they are

to decreases in volatility (good news). For instance, an

unexpected increase in volatility may increase the perceived

riskiness of equity positions, thus inducing portfolio

managers to seek additional risk protection from options.

But portfolio managers may not be willing to cut their

option positions at the first sign of a lower than expected

volatility because of the potential financial risks associated

with such a move. Tan (2001b) cites support for such asym-

7The equations for It and Vt are also estimated by the seemingly unrelated regression (SUR) method to check the possible impactof accounting for error-related bias on the estimated parameters. The SUR-based results are very similar to the OLS results in Table 3.

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metric effects of price volatility on option trading volume.

Nelson (1990), Schwert (1990) and Engle and Ng (1993)

suggest that good and bad news in returns have asymmetric

effects on the future price volatility. The present study

examines if good and bad news in the expected future

price volatility have asymmetric effects on the trading

volume of futures options.

Table 6 reports the asymmetric effects of positive and

negative changes in volatility on the option volume in the

aggregate sample.8 The results indicate that the latest

reduction in volatility individually as well as the previous

reductions in volatility jointly have significant downward

effects on the option volume. Similarly, the lagged increases

in volatility jointly have significant positive effects on

the option volume. These results clearly illustrate the role

of options markets as venues for hedging risks. Since

the lagged increases in volatility as well as the lagged

reductions in volatility have a significant predictive power

for the trading volume, it is not surprising to find that the

combined effect of the lagged rises and falls in volatility on

8The negative (positive) change in volatility variable in Table 6 is constructed as the product of the negative (positive) change in volatilityand a dummy variable that takes the value one when the volatility change is negative (positive) and zero otherwise.

Table 4. Option volume and implied volatility regressions: put options

Dependent variable

Volume (Vt) Implied volatility change (It)

IndependentVariable

ECmodel

DVmodel

ECmodel

DVmodel

Intercept 285.5 �137.4 �0.012 0.016(4.28) (0.50) (2.06) (2.90)

It 7425.3 7910.4 – –(9.90) (9.10)

It�1 5116.0 5692.8 �0.85 �0.85(5.39) (5.83) (63.84) (63.2)

It�2 6248.9 6686.2 �0.58 �0.57(6.06) (6.44) (29.83) (29.57)

It�3 4557.6 4724.9 �0.29 �0.28(4.50) (4.67) (13.95) (13.82)

It�4 1870.0 2126.3 �0.16 �0.16(2.20) (2.51) (8.92) (8.86)

It�5 999.4 983.0 �0.08 �0.08(1.92) (1.88) (7.77) (7.68)

Vt – – 0.00004 0.00004(9.20) (9.10)

Vt�1 0.020 0.026 0.00005 0.00005(1.08) (1.35) (13.9) (13.8)

Vt�2 0.11 0.11 �0.00002 �0.00002(6.05) (6.03) (4.31) (4.17)

Vt�3 0.25 0.25 �0.00001 �0.00001(13.8) (13.6) (2.83) (2.78)

Vt�4 0.16 0.16 0.00007 0.00001(8.91) (8.86) (0.19) (0.27)

Vt�5 0.07 0.08 �0.00002 �0.00001(3.95) (4.17) (2.88) (2.79)

R2 0.22 0.35 0.68 0.90F-statistic 8.39** 8.97** 44.4** 44.04**Hausman test 44.5** – 44.6** –(H0: No random effects)F-test – 5.95** – 102.06**(H0: No fixed effects)

Notes: The EC model and DV model denote the error components model and dummy variable model, respectively.Absolute t-values are reported in parentheses. The F-statistic tests the joint hypothesis that the five laggedcoefficients of Vt(It) are zero when the dependent variable is It(Vt) Two asterisks (**) indicate significance at the0.01 level.

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option volume is also positive. More importantly, however,is the finding that the rises and falls in volatility do nothave symmetric influences on the option volume. Rather,increases in lagged volatilities jointly exert a larger positiveeffect on option volume than do decreases in laggedvolatilities. Thus, option traders appear to be more sensi-tive to the rises in the expected future volatility (bad news)than to the falls in the expected future volatility (goodnews) of similar magnitude.

The asymmetric call and put results in Table 7 are simi-lar, and they corroborate the aggregate asymmetric resultsin Table 6. In both the call and put options, the jointpositive effects of lagged increases in volatilities on theoption volume are larger than those of lagged reductionsin volatilities. The only notable exception in the call andput results is the effect of the latest rise and fall in volatility

on the option trading volume. Under the put options, thecurrent rise and fall in volatility have the expected positiveand significant effects on the option volume. However,under the call options, the latest increase in volatilityalone has a significant effect on the option volume, butthis effect is unexpectedly negative. Such mixed effects incalls are perhaps not too unexpected, and they may resultfrom the difference between the expected and actual pricevolatilities and the subsequent adjustments in volatilityexpectations.

Overall, the results overwhelmingly support the conten-tion that the markets for S&P futures options are venuesfor information-related trading. The results also clearlyillustrate the role of markets for S&P futures options asvenues for hedging risks. In hedging their risks with the useof futures options, portfolio and risk managers appear to be

Table 5. Option volume and implied volatility regressions: call options

Dependent variable

Volume (Vt) Implied volatility change (It)

Independent variable EC model DV model EC model DV model

Intercept 334.8 2073.5 0.017 0.13(4.68) (5.24) (2.68) (8.92)

It �3626.8 �3945.4 – –(7.31) (7.44)

It�1 �2091.8 �1923.1 �0.81 �0.80(3.48) (3.13) (49.84) (49.36)

It�2 48.81 �244.1 �0.70 �0.69(0.07) (0.37) (34.15) (33.9)

It�3 2247.5 2313.3 �0.34 �0.33(3.39) (3.48) (14.29) (14.1)

It�4 1251.6 1127.9 �0.26 �0.26(2.23) (2.02) (13.27) (13.24)

It�5 1249.1 1352.6 �0.18 �0.18(3.11) (3.37) (12.78) (12.43)

Vt – – �0.00005 �0.00005(7.46) (7.44)

Vt�1 �0.038 �0.027 0.00006 0.00004(1.95) (1.41) (0.80) (0.62)

Vt�2 0.14 0.13 �0.00002 �0.00002(7.23) (6.66) (2.28) (2.35)

Vt�3 0.35 0.34 �0.00003 �0.00003(19.4) (18.7) (0.35) (0.40)

Vt�4 0.07 0.06 �0.00004 �0.00004(3.85) (3.45) (5.73) (5.81)

Vt�5 �0.003 �0.003 �0.00007 �0.00006(0.19) (0.14) (1.04) (0.94)

R2 0.21 0.36 0.66 0.86F-statistic 16.12** 15.9** 9.83** 10.15**Hausman test 63.9** – 75.97** –(H0: No random effects)F-test – 8.09** – 45.8**(H0: No fixed effects)

Notes: The EC model and DV model denote the error components model and dummy variable model, respectively.Absolute t-values are reported in parentheses. The F-statistic tests the joint hypothesis that the five lagged coefficients ofVt(It) are zero when the dependent variable is It(Vt) Two asterisks (**) indicate significance at the 0.01 level.

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more responsive to the rises in the expected future volatilitythan they are to the falls in the expected future volatility.Compared to Sarwar (2003) who reports that the informa-tion-related trading explains more of the trading volume ofBritish pound options than hedging, the present study findsthat both the hedge-related and information-related trad-ing are significant forces in explaining most of the tradingvolume of S&P futures options.

V. CONCLUSIONS

This paper examines the dynamic relations between theexpected future price volatility of the S&P 500 indexfutures and the trading volume of S&P 500 futures optionsduring 2000 to explore the informational role of the optionvolume in predicting the future price volatility of the indexfutures. The future price volatility is approximated by theimplied volatility of the S&P 500 futures options. Using a

pooled cross-sectional and time-series data framework, thepaper uses the error components and dummy variablemodels to allow for the relations between volatility andvolume to vary by the option’s moneyness and time-to-maturity.

The results indicate that the relations between the optionvolume and the future price volatility vary across cross-sections defined with respect to the option’s time-to-matur-ity and moneyness. The error components and dummyvariable models provide a reasonable framework tocapture such cross-sectional effects in volume-volatilityrelations. These results undermine the use of estimatorsthat do not account for the differential cross-sectionaleffects in volume-volatility relations.

This study uncovers the presence of strong contempora-neous feedbacks between the price volatility and the trad-ing volume of call and put options, suggesting thatarbitrage forces operate efficiently to produce quick andstrong interactions between volume and volatility.

Table 6. Asymmetric effects of volatility on option volume: aggregate sample

Dependent variable: Volume (Vt)

Independent variable Error components model Dummy variable model

Intercept 40.28 (0.71) �152.7 (0.59)It(þ) 655.03 (1.24) 1095.3 (1.89)It(�) 3510.4 (4.08) 3018.6 (3.39)It�1(þ) 3206.1 (3.58) 3130.7 (3.43)It�1(�) 4057.7 (4.81) 4352.9 (5.14)It�2(þ) 7822.0 (8.54) 7958.5 (8.67)It�2(�) 2821.3 (3.17) 2684.7 (3.03)It�3(þ) 4748.3 (4.99) 4720.5 (4.97)It�3(�) 3996.6 (4.72) 3963.2 (4.70)It�4(þ) 4983.6 (5.51) 4798.3 (5.32)It�4(�) 2017.9 (2.60) 2103.1 (2.70)It�5(þ) 3236.1 (3.86) 3361.1 (4.02)It�5(�) 701.1 (1.80) 566.9 (1.45)Vt�1 �0.005 (0.43) 0.003(0.24)Vt�2 0.113 (8.54) 0.114(8.64)Vt�3 0.28 (22.48) 0.27(21.58)Vt�4 0.12 (9.07) 0.12 (9.05)Vt�5 0.02 (1.89) 0.03 (2.06)R2 0.20 0.35F-statistic (þI1�5¼0) 18.25** 18.59**F-statistic (�I1�5¼0) 7.20** 7.67**F-statistic (þI1�5¼�I1�5) 20.39** 20.40**F-statistic (all I1�5¼0) 18.38** 17.43**Hausman test 61.26** –(H0: No random effects)F-test (H0: No fixed effects) – 7.67**

Notes: This table reports the results of causality regressions when positive and negative changes in implied volatility aretreated as separate explanatory variables for the option volume. Positive (negative) changes in volatility at lag k aredenoted as kþ (k�) Absolute t-values are reported in parentheses. The results of the regressions when the dependentvariable is volatility change (It) are omitted for brevity as they are similar to the results in Table 3. The F-statistic (þI1�5)and F-statistic (�I1�5), respectively, test the joint hypothesis that the coefficients of positive and negative changes involatility at lags 1–5 are zero. Similarly, the F-statistic (þI1�5¼�I1�5) tests the joint hypothesis that the coefficients ofpositive and negative changes in volatility at lags 1–5 are equal to each other, and the F-statistic (all I1�5) tests the jointhypothesis that the coefficients for both the positive and negative changes in volatility at lags 1–5 are zero. Two asterisks(**) indicate significance at the 0.01 level.

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The main result of the study is that the trading volume of

S&P 500 futures options has a strong predictive ability with

respect to the future price volatility of the S&P 500 index

futures, and that the markets for S&P 500 futures options

are venues for information-related trading. The study also

finds strong evidence that clearly illustrates the role of mar-

kets for S&P futures options as venues for hedging risks.

However, the rises and falls in the expected future price

volatility have asymmetric influences on the hedge-related

uses of futures options. In hedging their risk exposures,

portfolio and risk managers appear to be more responsive

to the rises in future price volatility than to the falls in

future price volatility.

The present results based on the interday data of index

options may have implications for the relations between

option volume and future price volatility in other options

markets. Because interactions between trading volume and

price volatility are likely to be stronger in intraday data of

index options and actively traded stock options than ininterday data of index options, the volume–volatilityresults of this study may also hold for such options data.This remains to be seen in future research, however.

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Table 7. Asymmetric effects of volatility on option volume: call and put options

Dependent variable: Volume (Vt)

Call options Put options

Error components Dummy variable Error components Dummy variableIndependent variable model model model model

Intercept 219.1 (2.88) 1839.3 (4.64) �11.1 (0.12) �297.5 (1.09)It (þ) �3577 (5.90) �3617.4 (5.49) 6164 (5.90) 7434.8 (6.51)It (�) �2066 (1.65) �2268.9 (1.77) 8045 (6.76) 7853.7 (6.09)It�1 (þ) �954 (0.73) �663.2 (0.50) 5202 (3.69) 5834.4 (4.09)It�1 (�) 3601 (2.76) 4053.2 (3.11) 6875 (5.83) 7136.2 (5.89)It�2 (þ) 5993 (4.40) 6100.6 (4.49) 1129.5 (7.94) 11320 (7.92)It�2 (�) 2251 (1.69) 1717.7 (1.29) 3327 (2.59) 3950.3 (3.07)It�3 (þ) 5683 (4.16) 5603.7 (4.00) 4844 (3.37) 4937.2 (3.42)It�3 (�) 3709 (2.86) 3886.1 (3.01) 5560 (4.52) 5564.4 (4.52)It�4 (þ) 3966 (2.87) 3850.0 (2.80) 4821 (3.65) 4803.1 (3.63)It�4 (�) 3108 (2.61) 3300.3 (2.78) 1874 (1.65) 2074.2 (1.83)It�5 (þ) 4668 (3.60) 5112.0 (3.95) 3676 (3.17) 3513.6 (3.03)It�5 (�) 365.8 (0.82) 436.6 (0.97) 110.2 (0.15) 83.8 (0.11)Vt�1 �0.04 (2.39) �0.03 (1.78) 0.02 (1.06) 0.02 (1.21)Vt�2 �0.12 (6.51) 0.12 (5.95) 0.10 (5.48) 0.11 (5.44)Vt�3 0.33 (18.16) 0.32 (17.59) 0.21 (11.32) 0.21 (11.28)Vt�4 0.06 (3.29) 0.03 (2.94) 0.15 (7.90) 0.15 (7.90)Vt�5 �0.01 (0.51) �0.007 (0.41) 0.05 (2.87) 0.06 (3.14)R2 0.23 0.38 0.24 0.36F-statistic (þI1�5¼ 0) 8.85** 9.16** 15.26** 15.07**F-statistic (�I1�5¼ 0) 3.31** 4.03** 8.64** 8.67**F-statistic (þI1�5¼�I1�5) 9.60** 10.30** 9.60** 8.06**F-statistic (all I1�5¼ 0) 13.70** 14.07** 9.01** 8.50**Hausman test 136.3** – 71.99** –(No random effects)F-test (No fixed effects) – 8.53** – 5.08**

Notes: This table reports the results of causality regressions when positive and negative changes in implied volatility are treated asseparate explanatory variables for the option volume. Positive (negative) changes in volatility at lag k are denoted as kþ (k�) Absolutet-values are reported in parentheses. The F-statistic (þI1�5) and F-statistic (�I1�5), respectively, test the joint hypothesis that thecoefficients of positive and negative changes in volatility at lags 1–5 are zero. Similarly, the F-statistic (þI1�5¼�I1�5) tests the jointhypothesis that the coefficients of positive and negative changes in volatility at lags 1–5 are equal to each other, and the F-statistic(all I1�5) tests the joint hypothesis that the coefficients for both the positive and negative changes in volatility at lags 1–5 are zero.Two asterisks (**) indicate significance at the 0.01 level.

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