the impact of volatility derivatives on s&p500 volatility

The authors are grateful to Robert Faff, Mark Flannery, Philip Hamill, Elena Kalotychou, David McMillan,Jayaram Muthuswamy, Lorenzo Trapani, George Wang, and John Wilson for their helpful comments on ear-lier drafts, as well as to Steven Haberman, Chris Hendry, and Mark Holder for eagerly providing their sup-port. The funding from Cass Business School, Kent State University, and the data assistance from Bloombergare greatly appreciated. We also thank the participants at the FMA 2006 Annual Meeting, EuropeanFinancial Management Association 2007 Annual Meeting, Computational and Financial Econometrics 2007Conference, FMA Europe 2007 Conference, Financial Markets and Institutions Group in the BritishAccounting Association 2008, the Midwest Finance Associate 2008 Annual Meeting, and the Asia-PacificFutures Research Symposium 2009 for their constructive feedback. Special thanks are due to Gang Zhao forthe excellent research assistance at the early stages of this study. The usual disclaimer applies.

*Correspondence author, College of Business Administration, Kent State University, Kent, Ohio 44242. Tel: �1-330-672-1242, Fax: �1-330-672-9806, e-mail: [email protected]

Received May 2009; Accepted May 2009

■ Paul Dawson is at the College of Business Administration, Kent State University, Kent, Ohio.

■ Sotiris K. Staikouras is at Cass Business School, City University, London, UK and ALBAGraduate Business School, Athens, Greece.

The Journal of Futures Markets, Vol. 29, No. 12, 1190–1213 (2009)© 2009 Wiley Periodicals, Inc.Published online in Wiley InterScience (www.interscience.wiley.com).DOI: 10.1002/fut.20424

THE IMPACT OF VOLATILITY

DERIVATIVES ON S&P500VOLATILITY

PAUL DAWSON*SOTIRIS K. STAIKOURAS

This study investigates whether the newly cultivated platform of volatility deriva-tives has altered the volatility of the underlying S&P500 index. The findings sug-gest that the onset of the volatility derivatives trading has lowered the volatility ofboth the cash market volatility and the cash market index, and significantlyreduced the impact of shocks to volatility. When big sudden events hit financialmarkets, however, the volatility of volatility seems to elevate in the U.S. equitymarket as a result of increased global correlations. Regardless of the period underexamination and the estimator employed, long-run volatility persistence is pres-ent. The latter drops significantly when the credit crunch period is excluded from

The Impact of Volatility Derivatives 1191

Journal of Futures Markets DOI: 10.1002/fut

the post-event date sample period. The correlation between the broad equityindex and the return volatility remains low, which in turn strengthens the role ofvolatility derivatives to facilitate portfolio diversification. The analysis also showsthat volatility is mean reverting, whereas market data support the impact of infor-mation asymmetries on conditional volatility. In the post-event date phase, noasymmetries are found when the recent crisis is not accounted for. Finally, com-parisons with other international equity indices, with no volatility derivatives list-ed, unveil that these indices exhibit higher volatility and slower recovery fromshocks than the S&P500 index. © 2009 Wiley Periodicals, Inc. Jrl Fut Mark29:1190–1213, 2009

INTRODUCTION

The impact of derivatives trading on market volatility has been watched closelyby academics, practitioners, regulators, and policy makers worldwide. On occa-sion, faced with the concern that derivative markets destabilize spot markets,state intervention has mandated bans on the trading of certain derivatives,either temporarily or indefinitely. On the other hand, proponents of derivativeshave argued that they benefit market welfare, by facilitating risk management,asset allocation, and price discovery.1

Theoretical arguments can be found to support both sides. Friedman(1953) notes that, in the long run, market players who are willing to take riskswould contribute to the smoothing of prices. The latter is countered byBaumol’s (1957) trend-following strategies, whereas Peck (1976) asserts thatproduction and storage decisions, made on the basis of commodity futuresprices, help to alleviate commotions in the spot market. According to Seiders(1981), what determines the level of disruption in the cash market is the spec-ulators’ (poor) forecasting ability. Board, Sandmann, and Sutcliffe (2001) arguethat contemporaneous future trading does not destabilize the spot market,whereas Powers (1970) and Stoll and Whaley (1988), based on a limited sam-ple, conclude that futures increase the routes and the speed with which infor-mation is disseminated. The seminal work by Miller, Muthuswamy, and Whaley(1994) goes beyond the index arbitrage argument to explain the dynamics inthe S&P500 index basis changes. Cox (1976) derives a relation between infor-mation, expected prices, and spot price volatility, and defines information con-tent as knowledge regarding random disturbances having an impact on demandin the real economy. Nonetheless, due to the lack of modeling conditional vari-ances (Engle & Ng, 1993) at that time, Cox does not show how volatility is afunction of the information flow per se.

1See Kalotychou and Staikouras (2009) for an overview of the volatility issue and Staikouras (2004) for arecent evidence on the price discovery and risk premia topics.

1192 Dawson and Staikouras


The purpose of this study is to examine the impact of the volatility deriva-tives trading on the S&P500 volatility index. The CBOE’s trademark volatilityindex, VIX, was initially based on a design by Whaley (1993)2 and subsequent-ly revised in 2003 (CBOE, 2009). The first exchange-traded products, VIX(implied volatility) and VT futures (realized variance), were introduced by theCBOE in March 26 and May 18, 2004, respectively,3 aiming to hedge the vari-ability in the stock market. Although a number of studies have concentrated onthe impact of commodity and financial derivatives, this is the first study thatconcentrates on the impact of volatility derivatives and their effects on theirunderlying asset. The research is primarily motivated by the lack of similarstudies, and by the increased number of traders working on the basis of volatil-ities rather than prices. Volatility itself has become an asset class (Gangahar,2006; Zhang & Zhu, 2006) and a group of volatility derivatives—bothexchange-traded and over-the-counter (OTC)—is now widely traded by hedgefund managers and proprietary traders.4 Thus, the present study offers a freshperspective on the issue of spot market volatility.

The remainder of the article is structured as follows. The following sectionpresents a brief discussion on the volatility debate. The next two sections formthe main body of the article where the data, methodology, and econometricresults are discussed. Finally, the last section summarizes the empirical find-ings, draws some conclusions, and points out avenues for future research.

A BRIEF REVIEW OF THE DEBATE

The relationship between cash and derivatives markets5 usually sparks discus-sions revolving around the term “financial stability.” The latter is usually trans-lated into volatility, an inevitable experience mirroring market expectations andinformation arrival. In fact, fundamentally justified volatility is not a bad thing,as it can form the basis for efficient price discovery. The aforesaid discussion isa vivid example of scholarly debate, with the views divided as to how much spotprice volatility is induced by derivatives trading.

2Note that the idea of writing options on volatility was originally suggested by Brenner and Galai (1989, 1993).3The VIX futures contract is the most liquid within the CBOE family of volatility products. For a completedescription of the VIX and VT contracts, see http://cfe.cboe.com/Products/Products_VIX.aspx and http://cfe.cboe.com/Products/Spec_VT.aspx, respectively.4The benefits of volatility derivatives include: (a) users being unaffected by directional moves in the underly-ing asset, (b) the contracts enabling cross-index volatility arbitrage, (c) the risk exposure mirroring volatilitymovements rather than delta hedging, and (d) participants trading their views on realized volatility levelsagainst market implied volatility or trade their expectation in the volatility term structure.5To keep the task manageable, this section presents a brief overview of some empirical findings with no inten-tion to lessen the importance of any research excluded. A detailed survey is beyond the scope of the currentstudy. An extended list of papers is available from the authors upon request.



Research has been conducted in various segments of financial marketssuch as interest rates, equities, foreign exchange, and commodities, with eachstudy using a different definition of volatility, methodology, and time period.One strand in the literature has documented no apparent change in the vari-ability of the spot market upon the arrival of derivatives trading. Using the hedge ratio between weekly spot prices of Government National MortgageAssociation (GNMA) and long-term T-bonds, Froewiss (1978) shows that thereis no apparent change in that ratio and concludes that the spot market hasbecome more informationally efficient. In the same market, Simpson andIreland (1982) find analogous results by using either daily or weekly data. Theyemploy a multivariate model aiming to eliminate any time dependency in theirsample. The above results are further corroborated by Corgel and Gay (1984)who illustrate, via intervention analysis,6 that futures have improved cash mar-ket efficiency. Later, Moriarty and Tosini (1985) reexamine Figlewski’s (1981)findings by extending his sample period.7 Based on the same methodologicalframework, they conclude (contrary to Figlewski) that GNMA futures tradinghas no effect on the spot market volatility. However, they do point out that dif-ferences in results could be contingent on the sub-periods analyzed. Extendingtheir previous work, Simpson and Ireland (1985) notice a reduction in spot T-bill yield volatility, but this was short-lived as the volume of futures tradingstarted rising and the market became more mature. Bessembinder and Seguin(1992) argue that active futures markets lead to stability by enhancing thedepth and liquidity of the cash market.

In contrast, other scholars have identified significant changes in thenature of volatility as a result of futures trading. Based on GNMA data,Figlewski (1981) detects an increase in the monthly price volatility transmittedfrom the futures arena. A possible explanation of that increase could be theexistence of an ill-informed group of futures traders. In a similar vein, Aggarwal(1988) finds an increased volatility trend in the stock index futures marketbetween 1981 and 1987. She does acknowledge, however, that such anincrease is common to other markets, during that period, which do not havefutures contracts. Elsewhere, Stoll and Whaley (1990) find a mild and tempo-rary swing in spot prices at the expirations of futures contracts, which isreversed on the following day. Examining the variance homogeneity, Brorsen(1991) shows that stock index futures have increased the market efficiency(reduced autocorrelations) as well as the variance of the S&P500 cash market.

6The interested reader is referred to Box and Tiao (1975).7Their period (1975–1983) is characterized by Fed’s shift in monetary policy (October 6, 1979) and financialderegulation in the years following 1979. The Fed directed the trading desk to focus on monetary aggregates,letting the federal funds rate move more freely, which resulted in high interest rate volatility. Figlewski’s(1981) sample period goes until 1979.



The latter is evident in daily price changes, whereas for weekly and monthlydata the variance remains the same. In a similar vein, Damodaran (1990) findsthat the introduction of futures trading increases the cash market volatility.Examining the period around the 1987 crash, Koutmos and Tucker (1996)show that innovations originating in the futures markets increase the volatility inthe stock market in an asymmetric fashion i.e. bad news increases volatilitymore than good news. The picture looks different when Edwards (1988a,b)demonstrates either a decrease in the volatility for the S&P500, 90-day T-bill,and 90-day Eurodollar markets or no significant change for the Value LineIndex. His research excluded the volatile interest rate phase of 1979–1982.Similar results are reported by Bortz (1984) and Baldauf and Santoni (1991).Based on Australian individual share futures, McKenzie, Brailsford, and Faff(2001) unveil a reduction in the systematic risk and the unconditional volatili-ty on individual stocks after the listing of futures, whereas they report mixedevidence concerning the impact on the conditional volatility. More recently,using a conditional volatility approach and 25 years of daily data, Staikouras(2006) finds a decrease in the U.K. short-term interest rates variability sincethe onset of futures trading in 1982.

Black (1982) goes further to separate the notion of causation from corre-lation. Based on causality tests, Bhattacharya, Ramjee, and Ramjee (1986) pro-vide some evidence of casual influence running from futures to spot GNMAmarkets, but no direct findings are reported to support the stabilization ordestabilization hypothesis. No evidence of speculative destabilization both inthe futures and spot T-bill markets is also reported by Dale and Workman(1981). The stock market volatility inflation could be due to the use of hedgingstrategies by fund managers in the spot market (Grossman, 1988), where sud-den orders of large volumes will cause unusual movements; or it could beattributed to other index-related phenomena (Harris, 1989). Harris rightlyargues that foreign ownership may be concentrated on the S&P500, whereinformation is widely available, and overreaction might be a problem. He alsodiscusses the booming of index funds, which replicate a number of these equityindices. Further research by Becketti and Roberts (1990) unveils that neitherthe level of futures trading nor the existence of the derivatives contributes tothe equity spot market volatility. Pericli and Koutmos (1997) find that pastinnovations have been reduced but the persistence has risen. They note, how-ever, that the incremental impact of derivatives trading, the flexible exchange-rate regime, and the liberalization of brokerage commission rates cannot beassessed independently.

Overall, the empirical and theoretical work so far provides conflicting sig-nals as to what drives the spot market volatility across different markets. Most ofthe work has been concentrated in the U.S. financial and commodities markets



and thus a more global verification seems necessary. A common ground foropinion convergence may never be achieved, and essentially the debateremains still in the battlefield of empirical research.

DATA AND METHODOLOGY

The analysis focuses on the S&P500 volatility and whether this has beenaffected by the trading on volatility derivatives. The onset of the CBOE volatil-ity derivatives in May 2004 is chosen as the event date to examine the impactof these new hedging vehicles on the equity spot market variability. We areaware of the significant OTC trading in volatility derivatives in the form of vari-ance swaps (Gangahar, 2006) and recognize that these can also be expected tohave an influence on the spot market. May 2004 is chosen as the event date, asthis is the point by which OTC volatility derivatives trading had gained suffi-cient critical mass for the exchanges to introduce their own varieties. The sam-ple consists of daily data from January 3, 2000, to May 30, 2008. Daily data arechosen on the basis of providing more degrees of freedom and closely trackingthe dynamics of the equity index volatility. The S&P500 three-month volatilityseries is calculated by Bloomberg on a daily rolling-over basis, excluding non-trading days, public holidays, and any other market interruptions. Panel A inthe Appendix illustrates the return of the S&P500 and its three-month volatili-ty over the period examined.

Because of the methodology’s well-established nature and the extensivematerial available on these estimators, a brief description will suffice forthe purpose of the present study. Conditional heteroscedastic processes, asoriginally proposed by Engle (1982), Bollerslev (1986, 1987), and Engleand Bollerslev (1986), are the ideal tool for this research. Such frameworkmakes it possible to simultaneously model the conditional mean and vari-ance of a series, and hence capture most of the variation in stock returns.To make this operational, let the general representation of the regressionequation be

x� denotes a vector of predetermined exogenous variables, which could includelagged values of y; b denotes the vector of parameters to be estimated; vt is ani.i.d. sequence with zero mean and unit variance; � is the information set at acertain period; u(L) and d(L) are lag polynomials of orders p and q, respectively,and L is the backward shift operator; Z denotes other stochastic exogenous

E(e2t ƒ�t�1) � ht ht � m � u(L)e2t � d(L)ht � gz.

yt � x�b � et, E(et) � E(vt2ht) � 0,



variables, which will be employed to test our hypotheses; non-negativity of ht

implies the identification condition that m > 0 and (u, d) � 0.Financial time series data are influenced by time-dependent information

flows, which result in pronounced temporal volatility clustering. The above formulation adequately captures such a phenomenon, and when correctlystructured produces insightful and reliable results. When conditional het-eroscedasticity is present, but not correctly modeled, the parameters from anOLS regression are still unbiased, but the estimator is inefficient as it does notdeploy the information on the time-varying nature of volatility. The nonlinearmaximum likelihood estimator, however, produces greater efficiency gains(Engle, 1982); hence, its application in conditional volatility models. A surveycovering the family of conditional volatility models is provided by Bollerslev,Chou, and Kroner (1992). The increased importance of equity variability inglobal financial markets along with the recent derivatives trading on volatilityprovides a fertile and unexplored terrain, and this is what the article turns to next.

EMPIRICAL RESULTS

This section looks at the empirical (ir)regularities, which are related to the tri-angular relation between information, spot market volatility, and volatilityderivatives trading activity. The three series of main interest employed in thisstudy are the daily change in the volatility of the S&P500 and the daily returnon the S&P500, as the endogenous variables (DV and Rsp), and the return onthe world stock market index, as the exogenous variable (Rwi). The latter aims tocapture any market and macroeconomic effects. The study focuses on threetime frames, which span the overall period, the pre-event date, and the post-event date phases. The pre-credit crunch period is separately examined toeliminate the impact of the credit crisis. This time segmentation is followedthroughout the econometric analysis to provide an insight into the effect ofvolatility derivatives trading on the equity spot market volatility. Table I providessome descriptive statistics of the series involved in the empirical investigation.

Although the data do not exhibit considerable skewness, they do sufferfrom excess kurtosis relative to the normal distribution. The Ljung–Box Q test,for serial correlation up to 30 lags, is significant at the 1% tolerance level(50.89) indicating that changes in volatility (DV) are highly forecastable, butthis is not the case for equity returns (Rsp). Analyzing the difference in means,between the pre- and post-derivatives era, for the volatility variable (DV) yieldsa z-value of 0.46, which is insignificant at any conventional level, and thus theequality of the means is not rejected. Turning to the variance of the sameseries, a visual inspection confirms that the difference between the two regimes



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is noticeable. The F-statistic for the variance equality of the two samples showsa value of 2.57, which is well above the critical value, at the 1% level (1.15),and thus rejecting the null hypothesis. However, this is only a preliminary testdivulging a potential change in equity returns’ variability.

Econometric estimations, under the assumption of conditional normality,reveal that the GARCH models can capture some, although not all, of the lep-tokurtosis in the unconditional distribution of the series. In light of this evi-dence, some models are estimated based on a conditional Student-t densityfunction.8 Under the conditional t distribution, the additional parameter 1/df isestimated. The log likelihood function for the conditional t distribution con-verges to the log likelihood function of the conditional normal GARCH modelas 1/df tends to zero.

Using a likelihood ratio test and after experimentation with up to five lagsfor each parameter p and q, the GARCH(1, 1) representation is found to be the most appropriate structure. In the mean equation of the GARCH model, theimpact of the wide market effects is tested by using the S&P500 and theMorgan Stanley Capital International (MSCI) world equity index.9 Usingeither index, the estimation outputs are the same. The U.S. market is the dom-inant player worldwide and thus its covariation with a global index is in linewith the standard capital asset pricing framework. Lastly, in the conditionalvariance equation, a time dummy is constructed to capture the possible effectof the onset of the CBOE volatility derivatives trading, which is the event dateof interest. In what follows the results of the analysis on the underlying asset,namely the volatility of the S&P500 index, are presented. Similar results areseen when a comparable analysis on the returns, rather than the volatility, ofthe S&P500 index is undertaken. For the sake of parsimony, the results of thissecond analysis are not presented here.10 One aspect of their similarity is shown in Figure 1. The results of the estimation process are presented inTable II.

8The log likelihood function, under the assumption that the residuals follow a conditional Student-t density,is given by

where n is the sample size, df is the degree of freedom (>2), and �(.) is the gamma function. The estimatedcoefficients are obtained by using the Berndt, Hall, Hall, and Hausman (1974) algorithm.9The Morgan Stanley world index measures the total return attributable to the largest capitalized companieson the world’s major stock exchanges. The index is compiled and reported monthly in local and common cur-rencies, and has more than $800 billion in assets indexed to it.10These results are obtainable upon request.

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Apart from the wide equity market factor, in the mean equation, the analysishas also employed lagged dependent variables as well as dummy variables. The former produces white noise residuals and indirectly supports a unit roottest, which is later discussed when all findings are considered. The use of theunit root test helps us to identify whether changes in volatility are mean revert-ing.11 The dummies, which are not reported here, are related to certain events,which could possibly have had an effect on the volatility of the equity index.12

None of these dummy variables is found to be statistically significant. The over-all construction of the mean equation is based on the general to specificapproach aiming to identify the pertinent significant factors.

Looking at the whole-period column, the event date dummy coefficient (k)exhibits a negative value, which is statistically significant, clearly supportingthe reduction of volatility in the post-event date period. Both the autoregressive(d) and moving average (u) coefficients in the conditional variance equation arealso highly significant. The sum of ARCH and GARCH effects is 0.816 indicating

FIGURE 1Conditional volatilities for the S&P500 three-month volatility and returns.

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Point A: The event date Point B: The Chinese stock market decline & the emergence of the US subprime

The conditional volatility of returns is divided by 2, while the three-month volatility is reduced by 0.002 for clearer exposition.

A B

11See also Miller et al. (1994) for a thorough examination of the mean reversion in the S&P500 index basischanges.12The events tried in the current study are the Gujarat earthquake on January 26, 2001; the New York terrorattacks on September 11, 2001 (no prices until 9/14); the Asian tsunami on December 26, 2004 (Sunday);the hurricane Katrina on August 29, 2005; and the South Asian earthquake on October 8, 2005.



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Vt�

i�e

t



a relatively small degree of persistence13 in the volatility of the endogenousvariable (DV). Older news, however, does feed through to the next day’s volatil-ity as denoted by the highly significant d coefficient. Moreover, a 1% change inthe “recent news” variable will increase the next day’s volatility by 0.069% (u),whereas a similar change in the “old news” variable14 will result in a 0.746% (d)rise in the volatility. As shown, the ARCH term has a higher impact on thevolatility, whereas older innovations are of progressively minor importance.

Interestingly, the broad market index comes out with insignificant or nega-tive coefficients. This is in line with the wide market perception that volatilitycontracts could be used to reduce risk and/or increase portfolio diversificationinstead of using other assets such as commodities, precious metals, property,etc. Market realities often support a negative/low correlation between volatilityand equity indices. That is, volatility is higher during bearish markets com-pared to bullish trends, and tends to stay high when prices tumble. Thus, in aportfolio framework, one appealing feature of volatility derivatives is their con-tribution to lower risk significantly.

When the whole period is split into the pre- and post-event date intervalsthe results provide a useful insight. The wide market index continues to haveeither a negligible or a negative impact on the volatility, whereas long-runvolatility persistence (d) seems to dominate the conditional variance in eitherphase. Long-run volatility persistence is higher in the pre-event date, whichdrops by 2.94% in the following period. On the other hand, the importance ofrecent innovations (u) increases in the post-event date stage by 113.11%.Overall, the comparison reveals that although persistence remains at similarlevels, the contribution of recent news (shocks) is more pronounced in thepost-event date sample. Figure 1 illustrates the evolution in the conditionalvolatility of the S&P500 three-month volatility when the whole sample periodis considered. The graph also incorporates the conditional volatility of theS&P500 equity returns, showing the similarity referred to above. Note that toachieve a combined and clear graph of the two series the original conditionalvolatility of returns is divided by 2, whereas that of the three-month volatility isreduced by 0.002.

Research in financial markets has usually looked at the relationshipbetween derivatives trading and their underlying assets, due to the informa-tional efficiency transmitted from futures to the spot market (Cox, 1976;

13This phenomenon simply addresses the question: how quickly do financial markets forget large volatilityshocks?14The conditional lagged volatility can be also expressed as , which in turn is afunction of past news through the “news” coefficient theta (u) or even much older news through delta (d).Note that the GARCH model is an infinite-order ARCH process.

ht�1 � m � ue2t�2 � dht�2



Whitakker, Bowyer, & Klein, 1987), as well as the futures markets’ distinctivecharacteristics (highly visible, centralized, low cost, arbitrage). Figure 1 alsoshows the conditional volatility of a related, but more distant, variable, theS&P500 returns. Although there is not a direct link between the derivativesvolatility contracts and the equity index returns, lower variability of theS&P500 returns could provide further support to our empirical investigation.

The graph shows the drop in conditional volatilities (point A) around theevent date. The post-event date volatility seems to remain at a notably lowerlevel, compared with the pre-event date period, until Spring 2007—when thetwo high spikes emerge (point B). A closer look unveils that on February 27,2007, a huge sell-off in the Chinese stock market managed to depress DJIA by416.02 points.15 It was only a few weeks later when discussions regarding thesize of the U.S. subprime mortgage market surfaced sending more shock wavesinto international markets. Both of these events are captured in Figure 1—point B. On the basis of these findings, the article estimates another post-eventdate GARCH model until February 26, 2007. The results are presented in thelast column of Table II. It seems that during this period long-run volatility per-sistence has weakened by 28.2%, whereas ARCH effects are almost similar.The market risk remains uncorrelated with the volatility variable.

As the current data set is characterized by long-run volatility persistence, itis expected that volatility can persevere for some time, if a shock strikes the U.S. stock market. Thus, the above discussion is extended by looking at theimpact of unexpected shocks (impulse response) on the conditional variance ofthe S&P500 three-month volatility. To assess the effect of possible macroeco-nomic and/or financial shocks, a one standard deviation shock hits the condi-tional variance. Figure 2 presents the impulse response analysis, over a 15-daytrading horizon, for the three sub-periods. Impulse responses measure the timeprofile of the effect of a shock, on the expected future values of a variable—inour case the conditional variance of equity volatility.

It is noticeable that a shock in the pre-event date period increases thevolatility by a much bigger scale than in the post-event date period. It also takesmuch longer, before the event date, for the volatility to settle down after theshock is introduced. When the post-event estimation period is constrained upto February 26, 2007, the impact of shocks is almost negligible. The amplifiedimpact of shocks for the full post-event date sample is attributed to theunanticipated events that took place during that period—point B in Figure 1.

15This incident and the U.S. subprime crisis are vivid examples of the increased correlations in global mar-kets. The Chinese stock market downturn was triggered by the speculation that the government may takeaction to cool growth. This was the biggest DJIA decline (3.35%) since September 17, 2001, when the 30-share index dropped by 684.81 points (7.40%). The broader S&P500 index fell by 3.47%—its worst one-day percentage fall since March 24, 2003 (3.59%), whereas the NASDAQ composite plunged by 3.94%—itsbiggest percentage drop since early December 9, 2002 (3.97%).



The above findings indicate that (a) under normal market conditions volatilityderivatives trading does contribute to lowering the underlying asset’s variabilityand (b) even in times of turbulence (point B onward) volatility derivatives arestill able to dampen and shorten the effects of shocks to volatility.

Therefore, what insights do the findings so far provide about the deriva-tives-underlying interface? First, the decrease in volatility is evident by observingFigure 1, as well as the market’s response to possible unexpected macroeconomic/financial shocks (Figure 2). Second, the change in the impact of the recentinnovations coefficient, in the post-event date period, implies increased spotmarket efficiency in the sense of placing more weight on recent news (Table I).The latter is corroborated by the very low persistence of shocks (Figure 2) duringthe same period.

Thus, derivatives trading can be responsible for more stable (less volatile)underlying markets through their fundamental role as hedging devices. Thisrisk transfer (hedging) has two distinctive effects: (a) market participants arenot forced to change spot positions, and thus no extra upward/downward pres-sure is induced into rising/falling prices, and (b) market participants would bewilling to accept lower spot risk premia. Taken altogether, individual andinstitutional investors (possibly risk averse) will feel confident to take largerpositions, which in turn will result in more liquid markets.

Nonetheless, one should be very broad minded when such issues areexamined, as it is difficult to attribute excessive volatility levels solely to theactivities of “irrational” or probably uninformed speculators who hope forshort-term profits. Market realities are much more complicated than it appearsin any controlled-state hypotheses. Moreover, during the period examined inthis article, the U.S. economy has experienced the impact of both economic

FIGURE 2A unit size shock on the conditional variance of S&P500 volatility.

0.0E�00

2.0E�06

4.0E�06

6.0E�06

Trading days

1 4 7 10 13 16

Vol

atili

ty

S&P Pre-Futures

S&P Post-Futures

S&P Post-Futures 2/07



expansion and recession.16 Thus, further support for the impact of derivativestrading on the underlying asset would provide a useful insight.

In the literature so far, this issue has always been hanging over the head ofresearchers, as it is impossible to isolate the impact of derivatives per se. A wayto tackle this concern, in the current study, is to replicate the empirical investi-gation for assets with no listed volatility derivatives, and then compare themwith the S&P500 findings. Therefore, two international stock indices are con-sidered, namely the FTSE All Share index (United Kingdom) and theTOPIX500 index (Japan).17 Figure 3 illustrates and further confirmsthe change in the nature of volatility for the S&P500 since the event date bycomparing it with the U.K. index (FTSE All Share).

FIGURE 3Conditional volatilities for the U.S. and the U.K. equity indices’ volatility.

0.001

0.004

0.007

0.010

0.013

2000 2002 2004 2006 2008

S&P500

FTSE All

A B

Point A: The event datePoint B: The Chinese stock market decline & the emegrence of the US subprime

16According to the National Bureau of Economic Research (NBER), an official panel of senior economists,the U.S. economy reached its most recent trough in November 2001, “inaugurating a reversal.” The eco-nomic growth, since 1991, has been the longest period of expansion in the U.S. history according to theNBER.17The estimation results for the U.K. and the Japanese indices are available from the authors upon request.The structure of the U.K. and Japan GARCH equations is the same as that used for the U.S. equation inTable II, namely

In the case of the United Kingdom, the lagged dependent variables found with significant coefficients arelags 2–7, whereas in the case of Japan, the lagged dependent variables found with significant coefficients are lags 2–3 and 5–7.

ht � m � ue2t�1 � dht�1 � kdft.

DVt � c � bRwit � an

i�1biDVt� i � et



The above graph portrays the contrast between the U.K. and the U.S.indices, as well as the change in their volatility from one period to another (pre-and post-event date). The decrease in the conditional volatility of the S&P500volatility is significant, whereas FTSE All Share index’s conditional volatility doesnot experience any drop when moving from the pre- to the post-event phase.Similar results are obtained for the TOPIX500 Share index—see Appendix, PanelB, where the TOPIX series is increased by 0.003 for clearer exposition. As previ-ously discussed, the article further explores the volatility of returns for all threeequity indices. Panel C illustrates the conditional volatilities of the three stockindices. The obvious contrast is between the Japanese and the U.S. index, where-as the U.K. index seems to be more correlated with the S&P500.

When unit size shocks are launched on the conditional variances of theequity volatility series (see Appendix, Panel D), the different responses amongthe three volatility indices provide further support to our prior findings. Panel Dillustrates the impulse response analysis for all equity indices. FTSE’s responseto a unit size shock is above the S&P500, whereas TOPIX falls below theS&P500 due to its relatively lower volatility (see Panel B) when compared withthe S&P500. In both phases (under Panel D), FTSE seems to experience thehighest peaks as the result of the introduced volatility shocks. This is attributedto its higher variability as observed in the above figure over the last eight years.The shock’s effect on the FTSE index appears to persist for a long time, espe-cially in the post-event date era, given that its volatility does not decrease fastenough as time elapses. When the focus is on the post-event date period but upto the end of February 2007 (i.e. excluding the subsequent extraordinaryevents), then the S&P500 is the least affected index when the shock hits themarket, and thus providing further support to our discussion so far.

The Impact of Asymmetries on Volatility

One of the underlying contributions of the conditional volatility estimators isthe fact that they provide a link between volatility and information. Actually, in1976, Cox argued that derivatives trading has an impact on price expectationsby altering the flow of information into the market. Cox put forward the linkbetween information, expected prices, and spot price volatility. He defined infor-mation content as knowledge regarding random disturbances having an impacton demand in the real economy. However, the limitation of his approach, at thattime, was that although derivatives may increase the flow of information, he didnot show how volatility is a function of the information flow per se.

Thus the issue worth exploring is whether asymmetries have an impact onvolatility. The asymmetric effect measures the impact of negative or positiveinnovations, on conditional volatility, by allowing either the slope of the two sides



of the news impact curve to differ or the center of the news impact curve tolocate at a certain point. In essence, the article looks at the market’s reactionto the arrival of different news, and simultaneously engulfs the impact (if any) ofderivatives trading. In theory, the latter should have an effect on the wayinformed and knowledgeable market participants react to the information arrivalbased on the fact that alongside the cash equity market a hedging platform exists.

Engle and Ng (1993) show that failure to model asymmetries leads to mis-specification of the volatility process. For example, linear ARCH models tend tounder-predict volatility associated with negative innovations. Thus their usagein the past may have led to erroneous inferences regarding the role of deriva-tives on stock market volatility. It is also established by now that the role offinancial leverage is not the only factor that triggers asymmetries18 (Kalotychou &Staikouras, 2009). Developments in modern financial markets, such as volatil-ity derivatives trading, could well be behind the existence of information asym-metries affecting both the level and the nature of volatility.

Table III presents the results of a threshold GARCH (TGARCH) model,which serves this particular purpose. These estimators were introduced inde-pendently by Glosten, Jaganathan, and Runkle (1993) and Zakoian (1994).The conditional variance equation is amended to incorporate an extra term,which, in the current study, represents the negative innovations whose impactis captured by the gamma (g) coefficient. There is no reason, however, why one18Market interactions, noise trading, volatility feedback, and irrational behavior may well contribute to therise of asymmetries (Campbell & Hentschel, 1992; Christie, 1982).

TABLE III

Threshold GARCH Estimation for the S&P500 Three-Month Volatility

Post-Event DateWhole Period Pre-Event Date Post-Event Date —February 2007

Coefficient z-Value Coefficient z-Value Coefficient z-Value Coefficient z-Value

c 8.1E�06 0.10 �7.3E�05 �0.51 3.1E�06 0.03 �8.0E�05 �1.03b �0.0037 �0.68 0.0118 1.63 �0.0238 �2.73 �0.0027 �0.29m 3.6E�06 8.09 5.2E�06 6.01 1.2E�06 6.64 9.6E�07 3.28u 0.0407 4.19 0.1810 5.89 0.0215 2.16 0.1473 3.04d 0.7450 24.87 0.6309 10.60 0.7433 19.72 0.5983 6.18g 0.0783 6.97 �0.1554 �5.36 0.2075 9.78 0.0506 0.89k �2.2E�06 �7.84 – – – – – –

Note. DV is the daily change in the S&P500 three-month volatility; Rwi is the return on the world index. The post-event date—February 2007—period finishes on February 26, 2007—the day before the major U.S. stock market fall. Similar comments apply forthe coefficients on the lagged dependent variables as reported in Table II; df is the dummy variable signifying the event date; dt � 1 ifet 0 and zero otherwise, and measures the impact of asymmetries on the conditional volatility.

ht � m � ue2t�1 � dht�1 � ge2t�1dt�1 � k˛dft .

DVt � c � b˛Rwit � an

i�1bi˛DVt� i � et



cannot test for a model where the asymmetric effect stems from a positiverather than a negative innovation i.e. dt � 1 if et � 0 and zero otherwise.

The above equation differs from the standard equity TGARCH specifica-tion in the sense that the endogenous variable in the mean equation is thechange in volatility rather than the equity returns. In this case, negative inno-vations (et�1 0 ) imply a decrease (increase) in the observed volatility by more(less) than expected, whereas positive innovations imply a rise (decline) in thevolatility by more (less) than its estimated value. The impact of negative inno-vations is measured by the sum of the coefficients u � g, whereas the positiveinnovations have an impact of theta (u). For gamma (g) values, which are sta-tistically different from zero, the news impact is asymmetric.

The results, in Table III, confirm the change in the nature of volatility asthe event date dummy coefficient (k) is negative and statistically significant.Regarding the appearance of the conditional volatility, using a TGARCHmodel, this remains similar to that obtained from the estimator without theasymmetry factor (see Fig. 1).

Looking at the impact of asymmetries, in the pre-event date period, thegamma coefficient comes out negative and significant. That is, in the pre-eventdate phase, the impact of volatility falls (2.56% � u � g) on the future condi-tional volatility (ht) is much smaller than the impact of volatility rises(18.1% � g). Thus, the market assigns more weight to volatility increases (rela-tive to expectations) as opposed to volatility declines. Note that during the pre-event date period, volatility is not traded as a hedging instrument and investorsare probably more concerned with abrupt changes in the underlying market.

On the other hand, the story is reversed in the post-event date period as theimpact of volatility falls (22.9%) is markedly higher than that of volatility rises(2.15%). Interestingly, when the post-event date estimation period is constrainedup to February 26, 2007, the asymmetric term becomes insignificant. The dispar-ity in these findings could be explained by the fact that the market was taken bysurprise with the Chinese downturn and the credit crunch events. The insig-nificant asymmetric term may imply that under normal market conditions:(a) investors are concerned with the level of spot market volatility, in the sense oftaking short/long positions in futures, and (b) any changes in volatility are not thatimportant, as traders can hedge their volatility exposure in the derivatives market.

Finally, there is another point worth discussing, which was briefly mentionedearlier in the article. Going back to the mean equation, an augmentedDickey–Fuller (ADF) test is employed to test for mean reversion (see Table I) inthe volatility variable. The statistic produces a value of �15.59, which is far belowtheADF critical value (�3.43) at the 1% level. The results indicate that changes involatility are mean reverting in any of the periods examined. Overall, the existenceof mean reversion has both economic and practical intuition. Based on market



experience, when changes in volatility reach high levels, then these are not expect-ed to persist on such levels, and likewise when changes in volatility are too small.

CONCLUDING REMARKS

Given the argument that spot and derivatives markets are linked by arbitrageoperations, then one would expect that participants in the forward lookingderivatives market would convey information to the equity cash market.Drawing upon this argument, the present study examines whether the onset ofthe volatility derivatives trading has conveyed enough information to alter thespot market volatility. Using conditional volatility estimators a number of inter-esting findings have emerged.

More specifically, the introduction of volatility derivatives has altered thevolatility of both the underlying asset (S&P500 volatility) and that of a related,but more distant, variable, the S&P500 index returns. Using impulse responseanalysis, unexpected shocks are easily absorbed and quickly disappear in the post-event date era—as a result of “risk neutrality” as participants have hedged theirexposure to market fluctuations. The volatility series is dominated by a long-runpersistence as past conditional volatility has an important role to play. Meanreversion is present confirming a wide market belief, whereas volatility’s low/neg-ative correlation with the wide market index validates the role of such contracts inreducing the portfolio risk. When information asymmetries are taken intoaccount, the importance of negative and positive innovations to volatility is foundto be sample period dependent. Finally, a cross-index comparison with the U.K.and the Japanese equity indices, for which no listed volatility derivatives contractsexist, reveals a considerably lower volatility and a faster recovery from shocks forthe S&P500 volatility during the post-event date period. The analysis also showsthat the U.K. equity index suffers from the persistence of shocks to volatility.

Looking forward, one could argue that the current study sheds light on theinformation signal per se, but remains silent as to the optimum amount of infor-mation required19 as well as the dispersion and quality of information flow.Although the U.S. economy is one of the dominant markets, empirical evidencefrom other economies has to corroborate/refute the present empirical findingsand further establish regional patterns, if any. Given the increasing interest intrading volatility, risk arbitrage, portfolio hedging, risk management of financialinstitutions, and overall market stability, such contributions seem worthy of anactual application.

19Market forces alone are insufficient to cause all material information to be disclosed. Information is mate-rial if it has an impact on securities prices when it becomes publicly available for the first time. If it has noimpact on price, it is largely irrelevant, although it may cause portfolio adjustments that leave pricesunchanged.



APPENDIX

Graphical illustrations of the equity indices’ returns and volatilities.

�0.20

0.00

0.20

0.40

2000 2002 2004 2006 2008

S&P500 three-month volatility

S&P500 return

The return series is multiplied by 2.5 for clearer exposition.

Panel A. Volatility and return of the S&P500.

0.001

0.003

0.005

0.007

0.009

0.011

2000 2002 2004 2006 2008

TOPIX500S&P500

Point A: The event datePoint B: The Chinese stock market decline & the emergence of the US subprime

The TOPIX500 is increased by 0.003 for clearer exposition.

A B

Panel B. Conditional volatilities for the U.S. and the Japanese equity indices volatility.



0.00

0.01

0.02

0.03

2000 2002 2004 2006 2008

S&P500FTSE AllTOPIX500

Panel C. Conditional volatility for the U.S., the U.K., and the Japanese equity indices returns.

Pre-futures trading

0.0E�00

2.0E�06

4.0E�06

6.0E�06

8.0E�06

1.0E�05

1 4 7 10 13 16

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Trading days

Vol

atili

ty

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2.0E�06

4.0E�06

6.0E�06

Vol

atili

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S&P Pre-Futures

TOPIX Pre-Futures

FTSE Post-Futures

S&P Post-Futures

TOPIX Post-Futures

Post-futures trading



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the impact of volatility derivatives on s&p500 volatility

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