Volatility relationship between crude oil and petroleum products.

Introduction

The daily price of West Texas Intermediate (WTI) crude oil has shown a six-fold variation in recent years, ranging from a low of $10.82 in December 1998 to a high of $69.91 in August 2005. During the year 2005, consumers paid the highest nominal gasoline prices ever. The high levels

and rapid fluctuations of petroleum prices have become a great concern to individual consumers, firms, policy makers and society. However, traditional price theory in economics, which determines an equilibrium price by balancing supply and demand, may not fully explain the current price behavior of crude oil and petroleum products. For example, according to the International Energy Agency (IEA), the annual growth rate of demand for petroleum products in North America has been 1.3% since the year 2000, while during the same time period, the world-wide growth rate in supply for these products was 2%, which would indicate substantial downward pressure on prices.

From the producers' point of view, volatility, whether persistent or transitory, discourages fixed capital investment due to uncertainty of the price path, and it encourages firms to hedge underlying assets against price shocks. From the traders' point of view, increasing price volatility of a commodity invites an arbitrage opportunity in the market since a volatility measure is a key determinant for derivative valuation. These various perceptions and interpretations of the price volatility by different groups lead us to review two basic questions. First, what is the volatility behavior of petroleum prices and what is its relationship in the spot and futures markets? This question will guide us in a comparative analysis of price volatility among different markets. It is well known that, because of the relatively high storage costs for crude oil and its products, inventory shocks tend to affect short-term price fluctuations in petroleum markets more than other commodity markets. Second, are these volatilities persistent or transitory, and what is the magnitude of the volatility? If the volatility is large and persistent, it may lead firms to rely more heavily on hedging operations and other types of risk management and to place more emphasis on the evaluation of investments in the context of uncertainty. Thus, it is imperative to understand the volatility behavior, its magnitude and duration, as well as its implications. This paper is unique because it compares price volatility for crude oil and petroleum products over a long period of time in both the spot and futures markets.

A volatility study of energy markets by Pindyck (2004, p. 18) concluded that changes in volatility are short-lived with a half-life of 5 to 10 weeks and that volatility has a small positive time trend, which implies little impact on firms' investment activities or on the economy. However, his model did not incorporate structural breaks that have occurred in petroleum markets. In order to shed light on the aforementioned two questions, this paper proposes three hypothesis concerning the behavior of volatility in petroleum markets:

1. Crude oil and petroleum product volatility is larger due to the new OPEC pricing regime. We suspect that higher price volatility in petroleum markets in recent years is due to the change in the Organization of Petroleum Exporting Countries' (OPEC) crude oil pricing behavior in March 1999.

2. Price volatility of petroleum products is larger than that for crude oil. We expect the gasoline and heating oil markets have higher price volatility since, in addition to price changes in conjunction with the raw material (crude oil) price, they have their own set of market factors affecting price and volatility.

3. Price volatility for near futures contracts is larger than that for more distant futures contracts. Since the spot price and near futures markets for commodities are much more affected by new information, rumors, and catastrophic events than are the more distant futures contracts, we would expect volatility to decrease as contract length increases. We would also expect the half-life of volatility shocks to decrease as contract length increases.

In order to test these hypotheses, the historical behavior of the price volatility of crude oil, motor gasoline and heating oil in U.S. markets since 1990 is examined. Similar to financial data series, price behavior in energy market is stochastic because volatilities in a period of relatively tranquility are often followed by periods of higher volatility. For that reason, an assumption of constant variance over time for the return of petroleum (crude oil and product) prices is not appropriate. Thus, to help understand certain aspects of petroleum price volatility, we utilized the generalized autoregressive conditional heteroskedasticity (GARCH) model for estimating the conditional variance of returns, which allows the conditional variance to be time-variant. We also estimated the conditional volatilities in these markets utilizing the threshold autoregressive conditional heteroskedasticity (TARCH) model where necessary. Empirical models suggest that an exogenous structural shift occurred in petroleum markets after April 1999, when OPEC changed its production behavior. (1) In all markets we studied, the estimated conditional variances after April 1999 were found to be higher than for the pre-April 1999 time period. We also found that the conditional volatility was persistent in all markets and that shocks from previous periods (ARCH terms) have a small impact on the conditional volatility.

This paper is organized as follows. The next section describes the data and discusses some descriptive statistics. The following section describes the econometric models used to estimate the conditional volatility, summarizes the estimation results, analyzes the relationship of the conditional volatility in the different commodity markets and discusses its relationship between crude oil and petroleum products. Concluding remarks are in the final section.

The Data and Descriptive Statistics

In order to have a comprehensive understanding of volatility behavior, we obtained daily closing prices for the spot and futures markets, including 1-month, 3-month, 6-month and 12-month futures contracts, for the following petroleum commodities: West Texas Intermediate (WTI) crude oil, conventional and reformulated (RFG) gasoline, and heating oil; both New York Harbor (NYH) and U.S. Gulf Coast (USG) were included for the gasoline and heating oil spot markets. The spot price series were obtained from Reuters, while the New York Mercantile Exchange (NYMEX) prices were obtained from Reuters or Bloomberg. Weekly data were created as the end-of-week closing price. The sample period studied is from January 1, 1990 to May 20, 2005. (2) Table 1 displays full period descriptive statistics of the log difference in price (or weekly return) for the different markets. Since at least one structural break in price behavior is suspected, the weekly observations in the full sample period were divided into four sub-periods: Period 1, pre-Gulf War 1, from 1/12/1990 to 6/29/1990, this period is related to the stable market; Period 2, Gulf War I, from 7/ 6/1990 to 2/22/1991; Period 3, stable market, from 3/1/1991 to 3/26/1999; and Period 4, transitional market, from 4/2/1999 to 5/20/2005, which includes Gulf War II.

Figure 1 shows the behavior of percent returns and price movement for the nearby crude oil futures contract during the four periods; note the similarity of period 1 and period 3. The fluctuation in the percent return is relatively constant during periods 1 and 3, when crude oil prices averaged around $20 per barrel. The returns are unstable in period 2 due to the uncertainty surrounding the invasion of Kuwait and Gulf War I, while period 4 shows larger fluctuations corresponding to the transitional regime of rising prices.

Table 1 displays descriptive statistics of the calculated weekly returns for both spot and futures in all the markets, and it shows that the variation of the return for the transitional market (Period 4) is consistently higher than for the stable market (Periods 1 and 3). This suggests that a structural break should be included in the estimation for the conditional variance of the returns. For the individual commodities, variation in spot price returns is greater than the variation in 1-month futures contract in nearly all sub-sample periods, with the only exceptions occurring during Gulf War I. With respect to magnitude of a change in price, these data support hypothesis #2, that the petroleum product price variance is greater than crude oil variances. The only contrary evidence occurring during the crude oil market disruption caused by the invasion of Kuwait, when spot and near futures crude oil prices show larger variation than do gasoline and heating oil. The table also shows that the expected decrease in price variability as the futures market contract length increases; this being due to the lessening impact that current news has on the more distant contracts.

[FIGURE 1 OMITTED]

Figure 2 depicts the behavior of price volatility in the nearby contract for crude oil and petroleum products. The figure shows, (1) that although the volatility fluctuation differs in detail, the overall level for all three commodities is the same; (2) that volatility has substantial autoregressive characteristics; and (3) that volatility is mean-reverting since the base level is constant (or slightly increasing) over long periods of time. The figure also shows that the three-fold price increase during the last 15 years tended to increase volatility only slightly. Figure 3 depicts the monthly volatility behavior in recent years for crude oil contracts and shows that the base level of volatility remained relatively constant even though prices doubled during this period. The figure clearly demonstrates that the volatility of more distant futures contracts is lower than that of short-term contracts, which provides evidence for the validity of hypothesis #3. Similar behavior also occurs in petroleum product contracts.

Table 2 reports descriptive statistics for annualized volatilities by market and by year. The table shows that the overall mean volatility for spot WTI crude oil (38%) is less than that of spot market gasoline (42% for NYH, 46% for USG) or heating oil (41% for NYH, 40% for USG), which supports hypothesis #2. However, for individual years, the volatility for a product is sometimes greater than that for crude oil, especially for the Gulf War I period and for NYH heating oil. This pattern is repeated in the futures markets. An alternative examination of the volatility for the futures contracts for each individual commodity always shows that the longer term contracts have less volatility than the shorter contracts, whether on average or for an individual year. These observations demonstrate the validity of hypothesis #3.

[FIGURE 2 OMITTED]

[FIGURE 3 OMITTED]

These observations are supported by the existing asymmetric price response literature. A study by Borenstein, Cameron, and Gilbert (1997) explained that "prices are sticky because when input prices fall the old price offers a natural focal point for oligopolistic sellers." Their paper argued that a price that firms charge before a crude oil price reduction is a focal point for coordination, but it is not a unique equilibrium. This behavior can exist in both gasoline and heating oil markets and can be explained by oligopolistic coordination theory, which states that an increase in crude oil price volatility leads to a "faster" response of gasoline and heating oil prices than to a crude oil price "decline," due to lack of monitoring of competitors' prices.

In the following section, we specify a model to estimate the volatilities and offer interpretations of the empirical results.

Model Specifications and Estimation Results

Since the seminal works of Engle (1982) and Bollerslev (1986), ARCH and GARCH models in the literature have found extraordinarily wide use. The GARCH model has been very successful at modeling time-varying volatility in financial time series. In petroleum markets, Lee, Ni, and Ratti (1995), Sadorsky (1999), and Pindyck (2004) used GARCH models to estimate oil price volatility. Even though empirical findings suggest that the GARCH volatility model is parsimonious, its performance seems to be as good as that of more complex models. (3) The GARCH (p, q) model used in this study is formulated as follows:

[R.sub.t] = [micro]+ [[epsilon].sub.t] (1)

[[sigma].sup.2.sub.t] = [omega] + [p.summation over (i=1)] [[alpha].sub.i][[epsilon].sup.2.sub.t-i] + [q.summation over (j=1)] [[beta].sub.j][[sigma].sup.2.sub.t-j] + [lambda][LAPR99.sub.t] (2)

The mean equation, Eq. 1, expresses spot price returns as a random walk process with [[epsilon].sub.t] being the error term. The variance equation, Eq. 2, explains the error term, [[epsilon].sub.t], of the mean equation. In the variance equation, the conditional variance at time t, [[sigma].sup.2.sub.t], is specified as a function of three terms: the mean, [omega]; ARCH terms representing the effect of news in the previous period has on current volatility, [[epsilon].sup.2.sub.t-1]; and GARCH terms representing the effect that previous periods' forecast variance has on current volatility, [[sigma].sup.2.sub.t-1]. An April 1999 (LAPR99) level shift variable is included in order to test for a structural break in volatility (hypothesis #1). This variable indicates how OPEC's change to a new price regime in April 1999 impacts the mean of the conditional volatility. This GARCH model is utilized to estimate the conditional volatility for most of our data series in all three markets.

The asymmetric response of petroleum product prices, especially gasoline prices, to a change in crude oil price has been extensively studied utilizing various methodologies; however, there is no literature to date that studies asymmetric conditional volatility in petroleum markets. We find that data series in the heating oil market and the 1-month futures contract in gasoline seems to exhibit "leverage effects," i.e., an asymmetric tendency for volatility to decline when returns rise and to rise when returns fall; therefore we utilize the threshold-GARCH (TARCH) process to estimate the conditional variance for these cases. (4) This methodology was introduced and applied by Glosten, Jagannathan, and Runkle (1993) and Zakoian (1994). Hadsell, Marathe, and Shawky (2004) applied the model to estimate the volatility behavior of wholesale electricity spot prices in the U.S.

The TARCH variance equation is specified as:

[[sigma].sup.2.sub.t] = [omega] + [p.summation over (i=1)] [[alpha].sub.i][[epsilon].sup.2.sub.t-1] + [gamma][d.sub.t-1] + [q.summation over (j=1)] [[beta].sub.j][[sigma].sup.2.sub.t-j] + [lambda][LAPR99.sub.t] (3)

where a dummy variable, [d.sub.t-1], is equal one if [[epsilon].sub.t-1] is negative and is equal to zero if [[epsilon].sub.t-1] is positive. The rationale for a TARCH process is that "good news" and "bad news" have different impacts on the conditional variance. In empirical studies, the normal TARCH specification has positive errors referring to good news that impacts the ARCH term, [alpha], and negative errors referring to bad news that impacts both the ARCH and TARCH terms, [alpha]+[gamma]. If the coefficient is different from zero, [gamma][not equal to]0, an impact by the news is asymmetric, and if the coefficient of the TARCH term is positive, [gamma]>0, negative shocks will have larger effect on volatility than positive shocks. However, the notion of good news and bad news in petroleum markets is different from the financial market and has the opposite interpretation. In financial market, returns that are greater than the mean, [[epsilon].sub.t-1]>0, are good, but in petroleum market, they are bad. For that reason, we expect a negative coefficient for TARCH term when there is a leverage effect.

Tables 3, 4, and 5 show the estimated conditional variance of the log difference in price utilizing GARCH (p, q) and TARCH models for WTI crude oil, gasoline, and heating oil. In all estimations, the number of lags in the variance equation is chosen to minimize the Akaike Information Criteria (AIC), and the models are estimated using maximum likelihood. (5) For estimation purposes, the stable market period is assumed from 1/1/1990 to 3/31/1999, and the transitional market period from 4/1/ 1999 to 5/20/2005. (6) Figure 4 compares the estimated conditional variance with the calculated weekly historical volatility for crude oil spot price. The estimated variance is much smoother (due to the large GARCH term), but otherwise closely follows historical volatility.

The coefficient of the shift variable is positive and statistically significant for all estimations. This fails to reject the null of hypothesis #1, that the pricing structure in the crude oil market after April 1999 resulted in an increase of the conditional volatility. Figure 5 depicts how the mean of the conditional volatility in the spot market shifts after April 1999. This figure shows the increased mean volatility for two different market periods, a stable market and a transitional market after April 1999. In the spot markets, the increase in mean volatility is 0.011 for the spot crude oil, 0.0135 for NYH gasoline, 0.0151 for USG gasoline, 0.0129 for NYH heating oil and 0.0161 for USG heating oil. At the product level, the increased mean volatility for both USG gasoline and heating oil is higher than that in NYH. This behavior is consistent with what we found in Table 2 that, with a different weather conditions and transportation costs, USG is expected to be more volatile than NYH. (7)

Empirical Results for GARCH and TARCH Estimation

In this section, the empirical results of the volatility behavior across markets are summarized, and the results of GARCH and TARCH estimations are interpreted for the different commodities: WTI crude oil, gasoline, and heating oil. Point estimates of volatility persistence and "half life" of volatility shocks are also discussed. The half-life of volatility shock is the time that it takes for markets to return half way back to equilibrium and is defined by:

Half [life.sub.GARCH] = log (0.5)/log ([p.summation over (i=1)] [[alpha].sub.i] + [q.summation over (j=1)] [[beta].sub.j]) (4)

Half [life.sub.TARCH] = log (0.5)/log ([p.summation over (i=1)] [[alpha].sub.i] + 0.5[gamma] + [q.summation over (j=1)] [[beta].sub.j]) (5)

The conditional variance estimated using GARCH and TARCH specifications was found to exhibit larger GARCH (moving average) effects than ARCH (autoregressive) effects in all markets, which implies that previous period information about observed volatility has much less impact than estimated volatility on current period of the conditional volatility. Half-life for crude oil is about 10 weeks on average, while an average half-life for gasoline and heating oil is normally shorter. Tables 3, 4 and 5 list the estimated results for each commodity in the spot and futures markets.

Table 3 reports the results for crude oil markets of the variance equation using a GARCH (1, 1) specification. All the parameters in the model are statistically significant at the 1% level. The results demonstrate the common assumption that the GARCH term (the effect of the previous period's forecast variance on current volatility) increases as the contract length increases, while the ARCH term correspondingly tends to decrease. This shows that volatility shocks from current news are less important in the long-term futures markets than for the spot market. The half-life of volatility shocks was found to be 10 to 11 weeks in all cases.

The estimation results for the gasoline markets as shown in Table 4 do not follow a systematic pattern like crude oil. Spot reformulated (RFG) gasoline at NYH and the NYMEX 6-month futures contract have only ARCH effects on the conditional variance, and as a result, their halt-life for volatility shocks is very short (0.4 weeks). Only the NYMEX nearby contract shows an asymmetric (TARCH) effect, where the coefficient is negative and statistically significant at the 5% level; this indicates that the short-term futures market reacts strongly to negative news, i.e., [[epsilon].sub.t-1] >0, and that longer contracts show a more muted response. The results for the spot prices indicate that different forces may be at work in the NYH and USG markets. Conventional gasoline at both NYH and USG are similar, whereas RFG appears to behave differently in these two markets. RFG is different from conventional in both markets. The halt-life of RFG volatility shocks is less than 4 weeks, which is substantially shorter than for conventional and the shorter contracts; this result is somewhat surprising because the NYMEX contracts arc written for RFG. These results may be partly explained by the more limited RFG sample size. (8) The large GARCH terms (around 0.8) indicate substantial persistence in most markets.

The behavior of the price volatility in the heating oil is different from that in crude oil and gasoline markets in that that most price series exhibit asymmetric (TARCH) effects. The results are summarized in Table 5, which shows the summation of ARCH and GARCH parameters range from 0.83 to 0.87 for the spot and nearby contracts to about 0.93 in the longer contracts, indicating that the degree of persistence increases from the spot market to longer futures contracts. This increasing persistence is especially evident from the half-life calculations for volatility shocks which range from 3.6 to 5 weeks for the short contract (and spot market) to 8.7 to 11.4 weeks for the longer contracts. These results differ from the crude oil and gasoline markets, where the half-life is similar in both spot and futures markets.

To summarize, a total of 18 conditional variance equations with weekly returns for the spot and futures markets for all three commodities are estimated, and all estimated parameters are statistically significant at least at the 10% level (with the vast majority significant at the 1% level). Two common factors appear in all of the estimation results. The first factor is that there is a definite structural shift in April 1999 that is supported by a statistically significant coefficient for the shift variable, LAPR99. This implies that the mean of the conditional variance increased after April 1999, when OPEC changed its production behavior; thus hypothesis #1 is verified. The second factor is that the persistence of volatility in all commodity markets is transitory, which is supported by the halt-life of volatility shocks that from about 3.5 to 11.5 weeks. The crude oil market reveals the higher persistence of volatility behavior than in both the gasoline and heating oil markets. In heating oil markets, the price volatility behavior is quite transitory. Figure 5 illustrates the conditional variance for different commodities in the spot markets, and the level shift is clearly visible in these figures.

[FIGURE 4 OMITTED]

[FIGURE 5 OMITTED]

Table 6 summarizes the level of volatility for all contracts for the two periods as determined from the estimated constants in the volatility equation. The first thing to note is that the base level of volatility is lower for crude oil than for the products in each individual market. This seems to verify hypothesis #2. The second thing to note is that for each commodity, the volatility decreases as contract length increases. This seems to verify hypothesis #3. These observations are valid for both time periods. The only abnormality occurs with RFG; the abnormally large volatility values may be due to the estimation having no GARCH terms.

Conclusion

This study of petroleum commodity markets reached three major conclusions: (1) there is a higher level of volatility due to OPEC's new pricing behavior; (2) GARCH effects are larger than ARCH effects in all markets and commodities; and (3) price volatility behavior is quite transitory. This study also provided substantiation for the validity of our three hypotheses. First, there was a volatility increase corresponding to the structural price shift after April 1999, which is supported by a positive and statistically significant coefficient for the shift variable in the estimations. This implies that the mean of the conditional variance increased after April 1999, when OPEC changed its production behavior. Second, GARCH effects dominate ARCH effects in the conditional variance for all estimations across markets. This indicates that the information about volatility observed from the previous period has a small impact on the conditional volatility. Also, in most markets, the empirical evidence shows a steady decline in the ARCH effect as contract length increases, which implies that volatility shocks from current news is not as important for the long-term contracts in the futures markets than that of spot markets. Volatility behavior in most heating oil markets estimations was found to exhibit leverage effects. Since the notion of good news and bad news has opposite interpretations from the financial market, negative TARCH coefficients appropriately capture the leverage effect. However, the crude oil or gasoline markets do not show this asymmetric volatility response to news. Third, persistence of volatility in all commodity markets is quite transitory, which is supported by the half-life of volatility shocks that ranging from 1 Springer

In addition to these results, neither historical volatilities nor the estimated conditional variance (GARCH process) show rapidly increasing patterns or persistence of volatility, so that the current transitional (high price) petroleum markets should have minimal impacts on firms' business investment decisions, society and the economy as a whole. While this paper examines and comprehensively compares the historical behavior of the price volatility in petroleum markets, two important task remain within the GARCH family specification: possible nonlinear response and the power of forecasting. Even though a GARCH process is useful to approximate short-term volatilities in a forecast, it may be less useful with longer forecasting horizons, especially when considering the behavior of an Integrated GARCH (IGARCH) process (Morana, 2002). Whether the presence of the high degree of persistence volatilities results in IGARCH effects, structural breaks or non-linear responses is an empirical question and is an important task for future research.

Published online: 17 January 2007

References

Bollerslev, T. (1986). Generalized autoregressive conditional heteroskedasticity. Journal of Econometrics, 31, 307-327.

Borenstein, S., Cameron, A. C., & Gilbert, R. (1997). Do gasoline prices respond asymmetrically to crude oil changes? The Quarterly Journal of Economics, 112, 305 339.

Engle, R. F. (1982). Autoregressive conditional and threshold adjustment. Journal of Business and Economic Statistics, 19, 166-176.

Glosten, L. R., Jagannathan, R., & Runkle, D. E. (1993). On the relation between expected value and the volatility of the nominal excess returns on stocks. Journal of Finance, 48, 1779-1801.

Hadsell, L., Marathe, A., & Shawky, H. A. (2004). Estimating the volatility of wholesale electricity spot prices in the US. The Energy Journal, 25, 23-40.

Hansen, P. R., & Lunde, A. (2001). A Comparison of Volatility Models: Does Anything Beat a GARCH (1, 1) Model? Brown University Working Paper.

Lee, K., Ni, S., & Ratti, R. A. (1995). Oil shocks and the macroeconomy: The role of price variability. Energy Journal, 16, 39-56.

Morana, C. (2002). IGARCH effects: An interpretation. Applied Economics, 9, 745-748.

Pindyck, R. S. (2004). Volatility in natural gas and oil markets. Journal of Energy and Development, Atttumn, 1-19.

Poon, S.-H., & Granger, C. W. J. (2003). Forecasting volatility in finance markets: A review. Journal of Economic Literature, 41, 478-539.

Sadorsky, P. (1999). Oil price shocks and stock market activity. Energy Economics, 21, 449-469.

Zakoian, J. (1994). Threshold heteroskedastic models. Journal of Economic Dynamic and Control, 18, 931-995.

(1) In 1998, world crude oil production consistently exceeded demand, and inventories grew to unusually high levels. WTI spot prices fell to near $10 per barrel by the end of 1998 due to this excess of production and the resulting inventory build. In 1999, OPEC cut back production to a level well below demand, while the demand for crude oil increased as the Asian economies recovered. The excess inventories which had built up fell rapidly to below normal levels, and WTI spot prices rose rapidly to over $30 per barrel by the early March 2000.

(2) The data period was extended to September 30, 2005 for historical volatility calculations, including those in Table 2 and Fig. 2.

(3) Hansen and Lunde (2001) argue that the best volatility models do not provide a significantly better forecast than the GARCH model. See Poon and Granger (2003) for a comprehensive review of alternative methods for estimating and forecasting volatility.

(4) Since the majority of our estimations, especially crude oil, showed statistically insignificant coefficients for the TARCH terms in the variance equation, we only utilized a TARCH model when the correlogram of squared residuals of the data did not indicate randomness.

(5) Lagged values of moving average (MA) were added, if necessary, to the mean equation in order to correct for autocorrelation and to satisfy Q-statistics. This correction has virtually no effect on estimated parameters in the variance equation.

(6) Since there are only 34 observations in period 2, Gulf-War 1, this period is included in the stable market period. The estimation results without these observation did not change significantly.

(7) Graphs fur the futures markets are similar and available upon request.

(8) Contrary to other commodities, RFG began listing on NYMEX in November 1994. Also, the sample size for the 6-month contract is shorter because of a three-week gap in trading while the older contract convened to RFG; the estimation results correspond to the RFG regime. to 11 weeks. Also, this study found empirical evidence that volatility in petroleum products is greater than that in crude oil, and evidence that the volatility of long contracts is less than that for short contracts.

The views expressed are those of the authors and do not necessarily reflect those of the Energy Information Administration. The authors would like to thank Yavuz Koruk for his research assistance.

T. K. Lee ([mail envelop])

School of Business Administration, Marymount University, 2807 North Glebe Road, Arlington,

VA 22207-4299, USA

e-mail: thomas.lee@marymount.edu

Table 1 Descriptive statistics for weekly returns January 1990 through
May 2005

                     Spot

                     Cushing    NYH        USG
Crude Oil       n
  Std. Dev.
    Period 1    25    0.04901
    Period 2    34    0.10923
    Period 3   422    0.04385
    Period 4   321    0.05571
    All        802    0.05313
  Median       802    0.00371
  Max.         802    0.20561
  Min.         802   -0.31341
Gasoline        n
  Std. Dev.                     Conv.      Conv.
    Period 1    25               0.04894    0.05158
    Period 2    34               0.08813    0.09282
    Period 3   422               0.05002    0.04958
    Period 4   321               0.06485    0.06706
    All        802               0.05823    0.05939
  Median       802               0.00263    0.00328
  Max.         802               0.16446    0.18523
  Min.         802              -0.22781   -0.24937
Heating Oil     n
  Std. Dev.
    Period 1    25               0.05098    0.04382
    Period 2    34               0.09690    0.10050
    Period 3   422               0.04617    0.04334
    Period 4   321               0.08302    0.06211
    All        802               0.06607    0.05500
  Median       802               0.00175    0.00130
  Max.         802               0.50714    0.20744
  Min.         802              -0.79756   -0.26016

               Futures Contract by Month

               1          3          6          12
Crude Oil
  Std. Dev.
    Period 1    0.03530    0.02271    0.01789    0.01810
    Period 2    0.10714    0.08695    0.06955    0.05416
    Period 3    0.04046    0.03167    0.02510    0.01933
    Period 4    0.05320    0.04568    0.03749    0.02805
    All         0.05010    0.04115    0.03326    0.02541
  Median        0.00330    0.00315    0.00229    0.00118
  Max.          0.20054    0.14127    0.12783    0.09486
  Min.         -0.34901   -0.29564   -0.21759   -0.13706
Gasoline
  Std. Dev.
    Period 1    0.04249    0.03521    0.02628
    Period 2    0.08949    0.07860    0.07594
    Period 3    0.04296    0.03185    0.02580
    Period 4    0.06091    0.04745    0.03864
    All         0.05329    0.04158    0.03492
  Median        0.00294    0.00121    0.00283
  Max.          0.18891    0.14838    0.13157
  Min.         -0.23801   -0.20746   -0.15326
Heating Oil
  Std. Dev.
    Period 1    0.03705    0.02169    0.01955    0.01975
    Period 2    0.09995    0.09116    0.06938    0.06270
    Period 3    0.03970    0.03140    0.02550    0.02056
    Period 4    0.05965    0.04810    0.03946    0.03055
    All         0.05210    0.04248    0.03432    0.02785
  Median        0.00232    0.00042    0.00105    0.00169
  Max.          0.23647    0.14199    0.10487    0.10043
  Min.         -0.22911   -0.20955   -0.16877   -0.16191

Weekly returns refers to the standard deviation of the log difference
in (weekly) prices. Four distinct subperiods can be recognized:

Period 1: 1/12/1990-6/29/1990 (Pre-Gulf War 1)

Period 2: 7/06/1990-2/22/1991 (Gulf War 1)

Period 3: 3/01/1991-3/26/1999 (Stable Market)

Period 4: 4/02/1999-5/20/2005 (OPEC Regime Change & Transitional
Market)

All: 1/12/1990 5/20/2005 (Full Period)

The gasoline data refer to conventional grade. Results for RFG
(which began in 1995) are similar.

Table 2 Descriptive statistics for annualized historical volatility
January 1990 through September 2005

Year      Spot Market                          Futures Market

          WTI      Gasoline      Heating Oil   Crude Oil

          Crush.   NYH    USG    NYH    USG    1      3      6

1990        63.1   53.6   58.3   58.2   56.6   60.5   41.9   38.5
1991        57.9   47.2   48.1   57.6   57.7   56.7   43.6   33.1
1992        20.3   27.4   27.3   25.8   25.5   19.9   17.8   15.5
1993        23.8   27.5   31.5   22.7   24.5   24.8   20.3   17.3
1994        29.5   39.5   39.0   33.0   36.6   28.9   23.4   19.8
1995        23.0   30.5   36.5   20.9   21.8   20.3   15.3   12.2
1996        40.4   36.5   41.2   44.9   45.9   39.5   26.8   22.2
1997        28.4   31.0   34.8   27.5   29.1   28.7   23.1   19.4
1998        52.6   45.7   49.5   39.0   40_3   46.8   35.1   28.0
1999        35.7   41.9   44.9   35.4   37.7   35.3   30.2   26.2
2000        46.3   50.2   52.2   91.5   51.6   43.5   34.9   30.0
2001        46.6   49.4   60.9   44.1   51.0   43.5   36.7   31.5
2002        33.3   45.0   49.5   32.9   35.9   34.8   30.0   25.9
2003        44.8   50.5   52.0   45.4   45.1   39.4   31.6   25.3
2004        36.2   45.4   48.2   40.9   45.0   36.4   33.8   30.8
2005        31.9   54.8   67.0   35.7   40.5   29.0   25.3   23.3
Median      36.0   45.2   48.2   37.4   40.4   35.9   30.1   25.6
Mean        38.4   42.3   46.3   41.0   40.3   36.8   29.4   24.9
St. Dev.    12.7    9.2   10.9   17.3   11.1   11.7    8.2    7.0
Max         63.1   54.8   67.0   91.5   57.7   60.5   43.6   38.5
Min         20.3   27.4   27.3   20.9   21.8   19.9   15.3   12.2

Year       Futures Market

           Crude Oil   Gasoline             Heating Oil

           12          1      3      6      1      3      6      12

1990       36.1        54.8   39.2   37.0   54.4   40.7   37.6   36.4
1991       23.9        48.1   36.5   33.5   59.0   43.2   34.6   31.8
1992       13.4        26.4   20.8   17.8   24.8   19.6   17.0   15.5
1993       15.0        25.7   20.5   18.3   42.1   19.2   16.3   14.9
1994       17.3        33.4   27.5   21.7   30.7   23.7   21.3   18.2
1995       10.1        29.1   17.7   14.9   20.6   17.0   14.3   13.4
1996       20.4        31.7   24.7   20.9   39.9   25.8   21.3   19.7
1997       16.6        29.8   21.4   20.0   28.0   23.1   18.7   16.5
1998       20.9        37.6   29.1   23.8   35.2   31.9   26.3   21.9
1999       21.8        35.7   30.2   24.4   34.6   31.7   27.8   23.9
2000       26.1        43.4   34.5   29.6   52.8   35.8   31.6   27.4
2001       26.3        45.8   35.7   31.8   43.2   35.5   31.2   27.4
2002       21.4        45.6   34.0   26.8   34.3   31.1   28.7   24.2
2003       18.9        50.8   35.6   31.5   47.8   36.8   30.0   24.6
2004       26.3        41.2   36.0   32.5   40.4   36.6   32.3   27.5
2005       21.6        44.7   29.4   26.0   34.7   32.6   28.0   24.8
Median     21.2        39.4   29.8   25.2   37.6   31.8   27.9   24.1
Mean       21.0        39.0   29.6   25.7   38.9   30.3   26.1   23.0
St. Dev.    6.2         9.1    6.8    6.5   10.8    8.0    7.1    6.4
Max        36.1        54.8   39.2   37.0   59.0   43.2   37.6   36.4
Min        10.1        25.7   17.7   14.9   20.6   17.0   14.3   13.4

All values are in percent.

Table 3 Crude oil--weekly volatility estimation results January 1990
through May 2005

            Spot       Futures contract

            Cushing    1          3          6          12

N           803        803        803        803        803
Constant    0.000149   0.000136   0.000085   0.000048   0.000028
            (2.85)     (3.09)     (3.28)     (3.59)     (3.01)
ARCH(1)     0.113052   0.099417   0.092446   0.078942   0.085757
            (3.80)     (4.29)     (4.24)     (4.13)     (4.11)
GARCH(1)    0.820165   0.834538   0.840111   0.859145   0.854969
            (17.85)    (22.43)    (22.55)    (27.13)    (23.62)
LAPR99      0.000124   0.000100   0.000094   0.000059   0.000025
            (2.63)     (3.07)     (3.09)     (3.25)     (2.62)
Sum         0.9332     0.9340     0.9326     0.9381     0.9407
Half-life   10.0       10.1       9.9        10.8       11.3

t-statistics are in parentheses.

Table 4 Gasoline weekly volatility estimation results January 1990
through May 2005

            Spot

            Conventional          Reformulated

            NYH        USG        NYH        USG

N           803        1103       551        544
Constant    0.000258   0.000172   0.002447   0.000488
            (1.83)     (1.79)     (8.48)     (1.26)
ARCH([)     0.070459   0.070930   0.149784   0.090534
            (2.71)     (2.85)     (2.25)     (2.01)
GARCH(I)    0.831514   0.863586              0.740187
            (11.31)    (15.29)               (4.44)
TARCH

LAPR99      0.000189   0.000160   0.000865   0.000322
            (1.69)     (1.57)     (2.33)     (1.15)
Sum         0.9020     0.9345     0.1498     0.8307
Halt-life   6.7        10.2       0.4        3.7

            Futures Contract

            1           2          3

N           803         803        514
Constant    0.000239    0.000136   0.000680
            (2.52)      (3.05)     (9.83)
ARCH([)     0.098421    0.081545   0.141221
            (3.28)      (3.74)     (2.99)
GARCH(I)    0.833462    0.808788
            (14.32)     (16.01)
TARCH       -0.083195
            (-2.29)
LAPR99      0.000210    0.000145   0.000550
            (2.11)      (2.90)     (4.33)
Sum         0.8903      0.8903     0.1412
Half-life   6.0         6.0        0.4

t-statistics are in parentheses.

Table 5 Heating oil--weekly volatility estimation results January 1990
through May 2005

            Spot                   Futures Contract

            NYH        USG         1           2           6

N           803        803         803         803         803
Constant    0.000394   0.000290    0.000288    0.000077    0.000059
            (3.07)     (3.03)      (3.34)      (3.24)      (3.03)
ARCH(1)     0.107645   0.160977    0.145450    0.091738    0.064813
            (2.85)     (3.44)      (3.13)      (3.86)      (3.77)
ARCH(2)     0.101142               0.074321
            (1.90)                 (1.86)
GARCH(1)    0.616323   0.754609    0.697982    0.878237    0.858522
            (6.48)     (12.13)     (10.13)     (27.90)     (22.71)
GARCH(2)
TARCH                  -0.091049   -0.124651   -0.061157
                       (-1.89)     (-2.52)     (-2.45)
LAPR99      0.000322   0.000259    0.000242    0.000087    0.000074
            (2.49)     (2.52)      (2.19)      (2.86)      (2.80)
Sum         0.8251     0.8701      0.8554      0.9394      0.9233
Half-life   3.6        5.0         4.4         11.1        8.7

            Futures Contract

            12

N           800
Constant    0.000031
            (2.86)
ARCH(1)     0.130472
            (4.65)
ARCH(2)
GARCH(1)    0.130237
            (1.17)
GARCH(2)    0.745492
            (6.79)
TARCH       -0.130441
            (-4.10)
LAPR99      0.000031
            (2.46)
Sum         0.9410
Half-life   11.4

t-statistics are in parentheses.

Table 6 Volatility level comparison using the estimated constant
stable market vs. transitional market

             Crude Oil            Gasoline

             Stable *   Transit   Stable *   Transit

Crude oil
  Spot       1.49       2.73
    Conv.                         2.58        4.47
    RFG                           2.45       11.1
Futures
  1 month    1.36       2.36      2.39        4.49
  3 month    0.85       1.79      1.36        2.81
  6 month    0.48       1.07      6.8        12.3
  12 month   0.28       0.53

             Heating Oil

             Stable    Transit

Crude oil
  Spot       3.94       7.16
    Conv.
    RFG
Futures
  l month    2.88       5.30
  3 month    0.77       1.64
  6 month    0.59       1.33
  12 month   0.31       0.61

The stable market represents sample periods 1, 2 and 3 (January
1990 to March 1999), while the transitional market represents period
4 (April 1999 to May 2005). All values in table are multiplied by
10-4.