We investigate the volatility structure of gold, trading as a futures contract on the Chicago Board of Trade (CBOT) using intraday (high frequency) data from January 1999 to December 2005. Apart from investigating the now familiar GARCH properties we also utilize a rarely used measure of volatility–the Garman Klass estimator – to provide new insights in intraday and interday volatility. This nonparametric measure incorporates the open, close, high and low price within a particular time interval. Both sets of results suggest significant variation across the trading day and week consistent with microstructure theories, although volatility is only slightly positively correlated with volume when measured by tick-count.Garman Klass estimator; volatility; gold; intraday patterns; futures

Brian M. Lucey

Jonathan A. Batten

English

Research Papers in Economics

Institute for International Integration Studies  
IIIS Discussion Paper  
No.225 / June 2007
Volatility in the Gold Futures Market
Jonathan A. Batten 
Graduate School of Management, Macquarie University,
Australia
Dep. of Finance, Hong Kong University of Science &
Technology 
Brian M. Lucey
Institute for International Integration Studies and School
of Business, Trinity College Dublin, Ireland 
 
IIIS Discussion Paper No. 225 
 
 
 
 
 
 
Volatility in the Gold Futures Market 
 
 
 
 
 
Jonathan A. Batten 
 
Brian M. Lucey 
 
 
 
 
 
 
 
 
 
 
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Volatility in the Gold Futures Market 
 
Jonathan A Batten and Brian Lucey 
 
 
Jonathan A. Batten 
Graduate School of Management, Macquarie University 
CBD Campus Level 6, 51-57 Pitt St 
Sydney, NSW 2000, Australia 
Tel: ++61-2-8274-8344,  
Fax: ++61-2-8274-8370 
Email: jonathan.batten@mgsm.edu.au 
 
Department of Finance 
Hong Kong University of Science & Technology 
Clear Water Bay, Kowloon, Hong Kong 
Tel: ++852-2358 8202 
Fax: ++852-2358 1749 
Email: jabatten@ust.hk 
 
Brian M Lucey 
Trinity College, Dublin - School of Business and Institute for International Integration 
Studies,  
The Sutherland Centre, Level 6, Arts Building 
Dublin 2,  Ireland 
Tel: +353 1 608 1552 
Fax: +353 1 679 9503 
Email: blucey@tcd.ie 
 
Abstract: 
We investigate the volatility structure of gold, trading as a futures contract on the 
Chicago Board of Trade (CBOT) using intraday (high frequency) data from January 
1999  to  December  2005.  Apart  from  investigating  the  now  familiar  GARCH 
properties  we  also  utilize  a  rarely  used  measure  of  volatility–the  Garman  Klass 
estimator  –  to  provide  new  insights  in  intraday  and  interday  volatility.  This  non-
parametric  measure  incorporates  the  open,  close,  high  and  low  price  within  a 
particular time interval. Both sets of results suggest significant variation across the 
trading day and week consistent with microstructure theories, although volatility is 
only slightly positively correlated with volume when measured by tick-count. 
 
Key words: Garman Klass estimator; volatility; gold; intraday patterns; futures 
 
JEL: C22; C32; E31; F31   2 
Volatility in the Gold Futures Market 
 
Abstract: 
We investigate the volatility structure of gold, trading as a futures contract on the 
Chicago Board of Trade (CBOT) using intraday (high frequency) data from January 
1999  to  December  2005.  Apart  from  investigating  the  now  familiar  GARCH 
properties  we  also  utilize  a  rarely  used  measure  of  volatility–the  Garman  Klass 
estimator  –  to  provide  new  insights  in  intraday  and  interday  volatility.  This  non-
parametric  measure  incorporates  the  open,  close,  high  and  low  price  within  a 
particular time interval. Both sets of results suggest significant variation across the 
trading day and week consistent with microstructure theories, although volatility is 
only slightly positively correlated with volume when measured by tick-count. 
 
Key words: Garman Klass estimator; volatility; gold; intraday patterns; futures 
 
JEL: C22; C32; E31; F31 
 
 
I.  INTRODUCTION 
 
Despite the importance of gold as a key component of global monetary reserves, for 
trading  and  currency  hedging  (Capie, Mills  and Wood,  2005), there  is a  paucity  of 
studies  that  investigate  the  dynamics  of  the  gold  price  in  spot  and  futures  markets. 
Studies  investigating  the  dynamics  of  prices  in  futures  markets,  which  have  the 
advantage of greater transparency than over-the-counter spot markets, offer explanations 
concerning the empirical distribution of speculative prices and the importance of public 
and private information, as well as the relationship to other commodities and currencies 
(Adrangi, Chatrath and Christie, 2000). 
 
The objective of this study is to report the volatility structure of gold, trading as a 
futures contract on the Chicago Board of Trade (CBOT). We utilise high-frequency 
intraday, as well as interday prices, from January 1999 to December 2005. Apart from 
investigating the GARCH properties of the return series we also estimate the Garman 
and Klass (1980) statistic, termed the GK estimator (GKe). The novelty of the GKe 
approach  lies  in  the  use  of  use  of  the  open,  close,  high  and  low  price  within  a 
particular time interval in its calculation. The GKe therefore provides an alternative, 
volatility measure to the standard deviation and GARCH approach, which utilises the 
price  change  between  consecutive  time  intervals  (Ding,  1999).  The  within  period 
focus allows us to peer more deeply into the highfrequency dynamics than do other 
methods 
  
The empirical literature on volatility in key financial asset markets, such as stocks, 
currencies  and  bonds,  suggests  regularities  in  the  pattern  of  volatility  across  the 
trading day and week. Financial market microstructure theory (Lockwood and Linn, 
1990;  Park,  1993)  argues  that  this  pattern  occurs  as  a  consequence  of  the  price 
discovery actions of traders. While information is assumed to affect financial prices in 
a random manner, asymmetries in the information between different traders ensures 
that markets are most volatile as traders seek out and discover relevant information 
from one another. This leads to volatility patterns, which tend to be “U-shaped”, being 
higher  at  the  start  and  close  of  trading.  Earlier  researchers  postulated  specific   3 
relationships with trading volume; of importance is the expected positive correlation 
between trading volume and volatility (Karpoff, 1987; Oliver and Verrecchia, 1991; 
Cyree and Winters, 2001) due to the information seeking actions of traders. A unique 
feature of our data is that we are able to monitor tick-flow (quotes from traders) over 
time,  which  enables  a  direct  test  to  be  undertaken  of  the  correlation  between 
information flows and gold price changes. To our knowledge this has not been done 
previously for gold.  
 
In the next section we provide information on the data utilised, thereafter we present 
the results, with the final section allowing for some concluding remarks. 
 
II.  DATA 
 
The New York Mercantile Exchange (NYMEX) offers futures trading in a 100 troy oz 
nominal COMEX contract that is deliverable (settled) against both cash and physical 
gold of the same standard (0.995 fineness, cast either in one bar or in three one-
kilogram bars). This contract is available for the near month as well as any February, 
April,  August,  and  October  falling  within  a  23-month  period;  and  any  June  and 
December  falling  within  a  60-month  period  beginning  with  the  current  month 
(www.nymex.com).  In  this  sense  the  futures  contract  is  fully  arbitrageable  in  an 
economic sense against gold trading in a variety of other worldwide cash and futures 
markets. Open-outcry trading commences at 08:20h and ends at 13:30h. Trading is 
also  available  simultaneously  (termed  side-by-side  trading)  on  the  GLOBEX 
electronic trading system available on the Chicago Mercantile Exchange (CME).  
 
Our data comprises 56,814 observations of price quotes of the near month COMEX 
gold contract spanning the period 8:20 to 15:30, with the period from 13:30 to 15:30 
being GLOBEX trading. We group these price quotes into 10-minute intervals. The 
number of price-quotes within an interval is termed the tick-count. The tick-count 
across the trading day (including both open-outcry and the overlap with GLOBEX 
trading) is plotted in Figure 1. 
 
(Insert Figure 1) 
 
This figure records a declining tick-count across the trading day commencing with a 
mean of 134.85 quotes in the 8:20-8:30 interval and ending with a mean of 81.03 in 
the 13:20-13:30 interval. Note that the tick-count across the trading day is statistically 
different  with  a  one-way  ANOVA  of  the  tick-count  versus  time  (as  a  10-minute 
interval), recording a F-Statistic = 141.65 (P-value = 0.000).  
 
III.  RESULTS 
(Insert Figure 2) 
 
We first estimate the returns for gold ￿Pt = logPt - logPt-1, where the interval t-1 to t, 
is  10-minutes.  Figure  2  plots  this  distribution,  which  has  a  mean  close  to  zero 
(0.000001)  and  a  standard  deviation  of  0.0000071.  The  series  is  slightly  skewed 
(1.48) and significantly leptokurtic (122.5). We allow for an ARMA(2,2) process to 
accommodate any autocorrelated innovations et, the consequence of illiquidity effects. 
In addition, we apply a GARCH(1,1) conditional variance specification, necessary 
given the volatility clustering clearly evident in the return series. Therefore:   4 
 
t t t t t t P P P e le le b b a + C + C + D + D + = D - - - - 2 2 1 1 2 2 1 1 0    
0 , , 0 , 2 1 0
2
1 2
2
1 1 0
2 ³ > + + = - - w w w s w e w w s t t t                                             (1) 
(Insert Table 1) 
 
The results of this estimation (Equation 1) are recorded in Table 1.The series all have 
significant ARMA(2,2) terms at the 95% level. Higher order ARMA terms were also 
estimated  but  these  were  not  significant  and  so  have  neither  been  recorded  nor 
estimated. This is consistent with price dependence (and potential arbitrage) being 
limited to at most 20 minutes (2 by 10-minute intervals). There are also significant 
GARCH  effects,  with  the  GARCH(1)  term  generally  more  significant  than  the 
ARCH(1)  term.  Both  the  coefficient  of  the  mean  and  variance  equation  is  not 
economically significant, with the mean equation coefficient being just statistically 
significant at the 90% level. The regression R-squared is also close to zero, suggesting 
that other factors drive changes in price other than the ARMA coefficients. This is 
consistent with trading in the gold futures market, at least across 20-minute intervals 
being efficient. 
 
While it is commonplace to measure asset volatility based on the standard deviation 
of the log difference across a regular time interval, we also utilise a more complex 
measure, the GKe measure, which incorporates information about the open, close, 
high and low prices within a particular time interval. From Garman and Klass (1980), 
the GKe is: 
 
GKe =  ) O (C-   0.383   -   C) (l-   C) 2 L- (H+   0)   (C-   0.019   -   ) L (H-   0.511   =  
2 2 2 s 1            (2) 
 
where  H =  log of interval high 
  L =  log of interval low 
  O =  log of interval open 
  C =  log of interval close 
 
(Insert Figures 3 and 4) 
 
Over  the  entire  sample  period  the  Gke  (10min)  has  an  average  of  0.000000335, 
skewness  of  50.79  and  kurtosis  of  4684.99.  The  results  of  the  GKe  analysis  for 
simplicity are presented in two figures, with the y-axis recording the Gke*100 and the 
x-axis recording time. Figure 3 plots the 10-minute gold Gke across the complete 
sample period from January 1999 to December 2005. There are a number of volatility 
spikes  clearly  evident  at  9/28/1999;  2/7/2000;  5/24/2000;  9/11/2001;  6/28/2002. 
Importantly only one of these can be directly associated with a significant political or 
economic event (9/11/2001), with the others therefore likely to be the consequence of 
portfolio rebalancing at close of trading.  
 
Figure 4 provides a plot of the 10-minute gold Gke across the trading day. We include 
the NYMEX trading as well as the next 2-hours of GLOBEX trading. A one-way 
ANOVA of Gke (10min) versus Time shows statistically significant variation across 
the  trading  day  (F-Statistic  =  11.28,  P-value  =  0.000).  A  “U-shaped”  volatility   5 
structure  is  clearly  evident,  although  volatility  tends  to  decline  from  the  opening 
levels of 0.0000743 to 0.0000358 at the close of NYMEX trading. Notice that this 
also coincides with the declining tick volume shown in Figure 1. There is also a spike 
as GLOBEX opens, which is consistent with new information being provided by this 
market. 
 
(Insert Figure 5) 
 
Next  we  consolidate  price  and  tick-count  into  hourly  intervals  with  36,260 
observations of Gke matched with  the  specific number of quotes  within  the  hour. 
Price  quotes  proxy  for  trading  which  also  should  be  positively  correlated  with 
volatility.  Figure  5  records  the  correlation  between  tick  count  and  Gke  volatility 
across the hourly trading day and week. Note that there is not an obvious pattern to 
the direction of the correlation over the trading day. For the entire sample there is a 
positive correlation of 0.28 between GKe and tick-count for positive changes in price 
and  -0.30  for negative changes in  price.  Note that there is clear  evidence  of time 
varying hourly correlations (from 0.10 to 0.52) across the trading week. This may be 
interpreted within the recent microstructure models (such as Oliver and Verrecchia, 
1991), where information content varies as well as information asymmetry 
 
IV. CONCLUSIONS 
 
The results suggest significant variation across the trading day and week in volatility, 
which  is  only  slightly  correlated  with  tick-count:  a  proxy  for  information.  The 
stochastic  nature  of  volatility  in  the  gold  market  is  therefore  consistent  with  the 
complex  interaction  of  price  sensitive  information  from  other asset  markets  rather 
than  the  price  discovery  actions  of  traders  within  the  gold  market  itself.  These 
findings  are  of  considerable  importance  for  gold  investors  and  traders.  Arbitrage 
between gold products for example, will be more difficult than otherwise expected 
based  on  historic  short-term  correlation  and  long  term  cointegration  relationships. 
Thus,  derivatives  portfolios  should  be  constantly  rebalanced  to  accommodate  the 
changing dynamics from these  same short-lived price interactions with  other asset 
markets.   6 
REFERENCES 
 
Adrangi, B., Chatrath, A. and Christie, R. C. (2000) Price discovery in strategically-
linked markets: the case of the gold-silver spread, Applied Financial Economics, 10, 
227-234. 
 
Capie, F., Mills, T.C., Wood, G. (2005) Gold as a hedge against the dollar, Journal of 
International Financial Markets, Institutions and Money 15, 343-352. 
 
Cyree,  K.,  and  D.  Winters  (2001)  An  intraday  examination  of  the  federal  funds 
market: implications for the theories of the reverse-J pattern, Journal of Business 74, 
535–556. 
 
Ding, D. (1999) The determinates of bid-ask spreads in the foreign exchange futures 
market: a microstructure analysis, Journal of Futures Markets 19, 307-324. 
 
Garman, M., and Klass, M. (1980) On the estimation of security price volatilities from 
historical  data, Journal of Business, 53, 67-78. 
 
Karpoff, J. M. (1987) The relation between price changes and trading volume: a survey,  
Journal of Financial and Quantitative Analysis, 22, 109-126. 
 
Lockwood, L. and Linn, S. (1990) An examination of stock market return volatility 
during overnight and intraday periods, 1964–1989, Journal of Finance 45, 591–601. 
 
Oliver, K. and Verrecchia, R. (1991) Trading volume and price reactions to public 
announcements, Journal of Accounting Research, 29, 302-321,  
 
Park,  H.  Y.  (1993)  Trading  mechanisms  and  price  volatility:  spot  versus  futures, 
Review of Economics & Statistics, 75, 175-179.   7 
Table  1:  Gold  returns  across  a  10-minute  interval  using  an  ARMA-GARCH 
specification 
 
  Coefficient  Standard 
Error 
z-Statistic  Probability  
  Mean Equation 
0 a   0.00000  0.00001  1.64079  0.1008 
AR(1) = 1 1 - D t P b   1.23618  0.51536  2.39868  0.0165 
AR(2) = 2 2 - D t P b   -1.91887  0.95016  -2.01952  0.0434 
MA(1) = 1 1 - C t le   -1.28359  0.51899  -2.47324  0.0134 
MA(2) = 2 2 - C t le   1.97088  0.97966  2.01180  0.0442 
  Variance Equation 
0 w   0.00000  0.00000  3.468757  0.0005 
ARCH(1) 
2
1 1 - t e w   0.34590  0.05110  6.769711  0.0000 
GARCH(1)
2
1 2 - t s w   0.46017  0.05335  8.625466  0.0000 
         
R-squared  -0.00541       
Adjusted R-squared  -0.00574       
 
 
 
Figure 1. Plot of 10-minute interval Gold volume (Tick-Count) across the trading day 
 
0
20
40
60
80
100
120
140
160
08:30 09:30 10:30 11:30 12:30 13:30 14:30 15:30
 
   8 
Figure 2. Plot of the change in 10-minute gold price, January 1999 to December 2005 
  
Time Measured in 10-minute Intervals
L
o
g
 
O
p
e
n
 
P
r
i
c
e
 
C
h
a
n
g
e
￿￿￿￿￿ ￿ ￿￿￿￿ ￿ ￿￿￿￿ ￿ ￿￿￿￿ ￿￿￿￿￿ ￿
￿￿ ￿￿ ￿
￿￿ ￿￿￿
￿￿ ￿￿ ￿
￿￿ ￿￿￿
￿ ￿￿ ￿￿ ￿
￿ ￿￿ ￿￿￿
  
 
 
 
Figure 3. Plot of 10-minute gold volatility (Gke), January 1999 to December 2005    9 
Figure 4. Plot of 10-minute gold volatility (Gke) across the trading day 
 
0
0.00001
0.00002
0.00003
0.00004
0.00005
0.00006
0.00007
0.00008
08:30 09:30 10:30 11:30 12:30 13:30 14:30 15:30
 
 
 
 
Figure 5. The correlation between 10-minute volatility (GKe) and volume (tick-count) 
across the trading week 
 
 
Correlation between GK Estimator and Total Vol
0
0.1
0.2
0.3
0.4
0.5
0.6
8 9 10 11 12 13 8 9 10 11 12 13 8 9 10 11 12 13 8 9 10 11 12 13 8 9 10 11 12 13
Monday Tuesday Wednesday Thursday Friday
 
 Institute for International Integration Studies
The Sutherland Centre, Trinity College Dublin, Dublin 2, Ireland

An examination of stock market return volatility during overnight and intraday periods, 1964–1989,

An intraday examination of the federal funds market: implications for the theories of the reverse-J pattern,

Gold as a hedge against the dollar,

On the estimation of security price volatilities from historical data,

Price discovery in strategicallylinked markets: the case of the gold-silver spread,

The determinates of bid-ask spreads in the foreign exchange futures market: a microstructure analysis,

The relation between price changes and trading volume: a survey,

Trading volume and price reactions to public announcements,

Volatility in the Gold Futures Market

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Volatility in the Gold Futures Market

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