Essays on Volatility in the Crude Oil and Natural Gas Markets: GARCH,

Asymmetry, Seasonality and Announcement Effects

Duong T. Le* Division of Finance

Price College of Business University of Oklahoma

Norman, OK 73019-0450 Ph: (405)325-3486

le@ou.edu

This version: 5/12/2008

Abstract

These essays examine the cause and behavior of actual and implied volatility in the US crude oil and natural gas markets. Although crude oil and natural gas prices are among the most volatile, they have received little academic scrutiny heretofore. I theorize and find that (1) the crude oil and natural gas markets are characterized by volatility persistence, (2) crude oil and natural gas implied volatilities are higher on shorter term options, (3) there is a �skew� pattern in crude oil and natural gas implied volatilities (4) negative and positive shocks have different impacts on both predicted volatility and implied volatility in these markets, (5) there are time-of-the-year and day-of-the-week effects on both actual and implied volatilities, (6) the actual volatilities increase and the implied volatilities decrease following relevant scheduled announcements and (7) these announcements have no further impact on volatility on subsequent days. I develop and employ an improved procedure to test for the determinants of volatility within GARCH type model.

* I am grateful to Louis Ederington for helpful comments and suggestions. I benefited from the comments of Duane Stock, Chitru Fernando and participants in the Finance workshop at the University of Oklahoma. I also appreciate comments received from Marian Turac and seminar participants at the 2008 Eastern Finance Association annual meeting. I thank the Price College of Business at the University of Oklahoma for financial support. All mistakes remain my own responsibility.

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This dissertation consists of two parts. The first part explores the cause and behavior of price volatility

in the crude oil and natural gas markets. The second part investigates the attributes of implied volatilities on

options traded in the crude oil and natural gas markets.

I. Introduction

Crude oil and natural gas are two of the most essential energy sources in the U.S., accounting for

about 40% and 22% of the nation�s energy consumption, respectively. Since OPEC�s 1973 decision to regulate

its oil price independently of large oil companies, crude oil prices have been subject to dramatic volatility,

especially in recent years. From less than $11 per barrel in the beginning of 1999, oil prices increased to $38

per barrel in September 2000, decreased to $18 per barrel in January 2002, going up to $77 per barrel in July

2006, sliding down to $51 per barrel in January 2007 before reaching an unprecedented level of $125 per

barrel in May 2008. Natural gas is also one of the most volatile markets, particularly since its evolution from a

highly regulated market to a largely deregulated market in which prices are driven by supply and demand. In

2007, the annualized standard deviation of the daily percentage change in prices was 31.33% for crude oil and

50.23% for natural gas. By comparison, that number was only 4.08% for the US dollar-Euro exchange rate,

16.37% for the S&P 500 and 19.10% for the 10-year T-bond interest rates1.

The high volatility in crude oil prices is likely due to supply uncertainty and the short term inelasticity

of demand. Given that crude oil is the most essential energy for both industrial and residential sectors, it is

very difficult for oil users to reduce their consumption within a short period of time. On the other hand, there is

considerable uncertainty in oil supply which depends on a variety of macroeconomic and political factors. For

example, in 1997, when the world economy was already in a recession, major oil producing countries, failing

to predict the oil demand correctly, increased their production levels which resulted in a huge decrease in oil

prices. Similarly, the high volatility in natural gas prices is likely due to the short-term inelasticity of supply

and demand. Natural gas supplies are often constrained by storage levels and thus, natural gas suppliers are

unable to increase production levels in a short period of time. Also, it is difficult for consumers to quickly

reduce their consumption even when a sharp increase in natural gas prices occurs, especially during the winter.

Since natural gas suppliers cannot rapidly adjust their production levels to match demand changes, supply and

demand imbalances may result in sharp price changes.

This high variability in crude oil and natural gas prices makes it extremely difficult for consumers to

forecast their costs and for producers to forecast their profits. The desire to protect market participants against

such price fluctuations has led to the creation of and active trading in oil and gas futures, swaps and options

where the market value of the latter depends on volatility.

1 The data for the US dollar-Euro exchange rate, S&P 500 and the 10-year T-bond interest rates were collected from http://www.oanda.com, CRSP and the Federal Reserve website (http://www.federalreserve.gov), respectively.

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While volatility in other markets has been a subject of intense research activity in recent decades, little

attention has been paid to volatility in energy prices. Despite the fact that crude oil and natural gas prices tend

to be more volatile than most other prices, research into the cause and behavior of crude oil and natural gas

volatilities is limited. For instance, in a well-known and comprehensive study of the volatility literature, Poon

and Granger (2003) surveyed 93 articles examining volatility in all sorts of markets; only three of these

include crude oil among the markets examined (Day and Lewis (1993), Szakmary, Ors and Kim (2003) and

Martens and Zein (2004)) and only Szakmary et al. (2003) included natural gas volatility.

Among the limited studies on crude oil volatility not surveyed by Poon and Granger (2003) are those

of Wilson, Aggarwal and Inclan (1996), Yang, Hwang and Huang (2002), Pindyck (2004), and Kuper and

Soest (2006) who found that volatility clustering is an attribute of the crude oil market. However, none of the

above papers examined other attributes of crude oil volatility such as asymmetric volatility, seasonality or

announcement effects. Among the few studies on natural gas volatility are those of Susmel and Thompson

(1997) who found that natural gas volatility follows an ARCH type process, of Szakmary et al. (2003) who

documented the information content of implied volatility on natural gas options and of Linn and Zhu (2004)

who documented that natural gas volatility increases on days the Weekly Natural Gas Storage Report is

announced.

An understanding of the cause and behavior of volatility in the crude oil and natural gas markets is

essential to market participants since the market value of risk management products such as options and swaps

depends mostly on volatility. Similarly, the only unknown factor in option pricing is volatility of the

underlying asset.

II. Essay 1: Volatility in the Crude oil and Natural gas markets: GARCH, Asymmetry,

Seasonality and Announcement effects

In the first part of my dissertation, I examine volatility in the crude oil and natural gas markets and

attempt to answer the following questions:

1. Are crude oil and natural gas prices characterized by volatility persistence as has been documented

in other markets? It has been observed that in many other markets volatile periods tend to follow volatile

periods whereas stable periods tend to follow stable periods. Among numerous studies documenting volatility

persistence are: Adrian, Pagan and Schwert (1990), Andersen, Bollerslev, Diebold and Ebens (2001), Wu

(2001) and Flannery and Protopapadakis (2002) for the stock market, Ederington and Lee (1993, 1995 and

2001) for interest rates, Harvey and Huang (1991), Ederington and Lee (1993, 1995 and 2001), Andersen and

Bollerslev (1998) and Low and Zhang (2005) for the foreign exchange market and Jones et al. (1998) for the

Treasury bond market. I hypothesize that similar volatility persistence exists in the crude oil and natural gas

markets.

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2. Is there volatility asymmetry in the crude oil and natural gas markets? That is, do equal positive

and negative shocks have different impacts on future volatility? This hypothesis is inspired by the generally

documented evidence of an asymmetric volatility in the stock market and, to a lesser extent, in some other

markets such as the Treasury bond and Treasury bond futures markets. French and Roll (1986), French,

Schwert and Stambaugh (1987), Campbell and Hentschel (1992), Veronesi (1999), Bekaert and Wu (2000)

and Wu (2001) found that in the stock market, an unexpected decrease in price has a bigger impact on

predicted volatility than an unexpected increase in price of equal magnitude.

Contrary to the evidence from the stock market, I think there are good reasons to expect a negative

shock in the oil and gas markets to have a smaller impact on predicted volatility than an equivalent positive

shock. My reasoning behind this hypothesis is the likely shape of the oil and gas supply and demand curves.

At low volume and prices, oil and gas supply is highly elastic, but once storage limits are reached, supply

becomes quite inelastic as oil and gas producers, due to infrastructure constraints, cannot increase their

production levels within a short period of time. The demand curve for oil and gas also consists of an elastic

portion when prices are low and an inelastic portion when prices are high. Given the hypothesized shape of the

supply and demand curves, the same fluctuation in demand when prices are low should cause a smaller change

in prices than when prices are high. Thus, a positive price shock which moves the oil and gas markets up the

supply and demand curves is likely to presage higher future volatility than a negative shock moving the

markets down the curves.

3. Does volatility differ by day of the week? Some academic studies found that volatility of asset

returns varies across days of the week2 and that Monday volatility (including weekend) is higher than volatility

of a normal one-day period but not as high as that of a three-weekday period presumably because there is not

much information coming out during the weekend. Consistent with the evidence from other markets, I expect

that crude oil and natural gas volatilities differ across days of the week and increase over the weekend.

Furthermore, I hypothesize that the higher weekend volatility is particularly likely for natural gas since natural

gas price fluctuations supposedly depend on weather conditions which are just as likely to change on weekend

days as on weekdays. To my knowledge, no one has looked at these questions.

4. Is there seasonality in crude oil and natural gas volatilities? A winter effect is likely unique in the

natural gas market due to the dependence of natural gas prices on weather conditions. Natural gas prices are

among the most sensitive to weather conditions as the U.S. typically consumes twice as much natural gas in

the winter as in the summer (due to space heating). At the same time, as the U.S. natural gas production is

relatively constant throughout the year (due to storage capacity) and overseas imports are very limited, the

supply of natural gas in the winter is essentially fixed. Therefore, supply and demand imbalances in the natural 2The literature on day-of-the-week effect on volatility includes French and Roll (1986), Berument and Kiymaz (2001) for the stock market, Harvey and Huang (1991), Ederington and Lee (1993) for interest rates and the foreign exchange futures market and Jones et al. (1998) for the Treasury bond market.

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gas market during the winter may cause large price swings. This observation motivates my hypothesis that

natural gas volatility is higher in winter. To my knowledge, this hypothesis has not been tested heretofore.

While it is expected that natural gas volatility increases in the winter months, the answer is less

obvious for crude oil volatility. On one hand, since part of U.S. oil consumption is for transportation, oil

volatility supposedly increases in the summer when travel demand varies. On the other hand, the demand for

heating oil, a product distilled from crude oil, may increase sharply in the winter3, and thus, crude oil volatility

should increase in the winter months. Therefore, whether there is seasonality in crude oil volatility is subject to

empirical evidence.

5. Do the Weekly Petroleum Status Report and the Weekly Natural Gas Storage Report releases cause

increased crude oil and natural gas volatilities on announcement days? It has been documented that prices in

other markets are generally more volatile when lots of new information is coming to the market. Ederington

and Lee (1993, 1995) found that following the releases of scheduled macroeconomic news such as the

employment report, the consumer price index (CPI) and the producer price index (PPI), interest rate and

exchange rate volatilities are considerably higher than normal. Jones et al. (1998) found that the releases of

employment and PPI data are responsible for an increase in volatility in the Treasury bond market on

announcement days. Flannery and Protopapadakis (2002) found that 3 macroeconomic announcements

significantly increase volatility in the stock market when they are released.

I expect that consistent with the evidence from other markets, volatilities increase on days the Weekly

Petroleum Status Report and the Weekly Natural Gas Storage Report4, which are reportedly among the most

important news influencing the crude oil and natural gas markets, are released. To my knowledge no previous

study has examined the possible impact of any scheduled announcement on oil volatility. The impact of the

Storage Report announcement on natural gas volatility was first documented in Linn and Zhu (2004) but they

use a Generalized Method of Moments (GMM) framework whereas I employ a GARCH (1,1) type model.

6. If there is evidence that crude oil and natural gas volatilities increase on scheduled announcement

days, does the high volatility persist on days following the announcements? In other words, is public

information in the reports immediately incorporated in oil and gas prices or does the announcement impact

persist on subsequent days? If oil and gas market participants finish adjusting prices according to the new

information within the announcement day, volatility should fall back to normal levels on the following day. On

the other hand, GARCH type models consistently find evidence of volatility persistence, implying that if an

announcement creates high volatility one day, that high volatility will tend to linger.

3Heating oil can be used as a substitute for natural gas. Of the 107 million households in the United States, approximately 8.1 million use heating oil as their main heating fuel. Source: Energy Information Administration. 4 The Weekly Petroleum Status Report and the Weekly Natural Gas Storage Report are both compiled and issued by the U.S. Energy Information Administration.

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The data in this study are the daily closing prices for the nearby crude oil and natural gas futures

contracts traded on the New York Mercantile Exchange (NYMEX) from January 1, 1997 to July 31, 2007

totaling 2,645 daily observations.

In order to explore the above questions (1-5), I estimate a model in which the conditional variance

follows a regime-switching GJR type process which is similar to the model outlined in Jones et al. (1998):

Rt = µ + Φ1Rt-1 + st1/2εt, (1)

ht = ω+ αεt-12+βht-1+ γεt-1

2It-1, (2)

st = {Π(1+ δD,iDi,t)}(1+δWWINt)(1+δSSUMt)(1+δADAt), (3)

where Rt is the log percentage change in price of the nearby futures contract on day t, εt is presumed to be an

independent random variable which is normally distributed with conditional mean zero and conditional

variance ht. It-1=1 if εt-1 <0 and 0 otherwise. st is the transitory effects equation in which Di,t are the weekday

dummies, WINt =1 in the winter months (from November through March) and 0 otherwise, SUMt =1 in the

summer months (from June through August) and 0 otherwise. DAt is the announcement dummy =1 on days the

reports are released. δD,i, δW, δS and δA measure day-of-the-week, seasonality and announcement effects on the

conditional volatility

This model, which separates conditional volatility into a persistent part (equation 2) and a transitory

part (equation 3), allows conditional volatility to differ on each day of the week, in different times of the year

and on announcement days. Furthermore, the st equation allows weekday and announcement effects impact

that day�s volatility only. The above model is a methodological improvement over a number of studies on

volatility in other markets5. In previous studies, the dummies are in the conditional variance equation (equation

2) and thus, weekday or announcement effect is forced to have persistent impact on conditional volatility on

the following day6. In my study, the separation of conditional volatility into persistent and transitory parts

allows me to implement a much cleaner study of the determinants of volatility.

My estimation results from the specification (1-3) show that α and β are significantly positive,

implying that volatility persistence is an attribute of the crude oil and natural gas markets. For the crude oil

market, γ is significantly positive, indicating that a negative oil shock has more impact on predicted volatility

than an equivalent positive shock. For the natural gas market, γ is significantly negative, indicating that a 5 See, for example, Hsieh (1989), Berument and Kiymaz (2001) and Ederington and Lee (2001) 6 In previous studies, there is no st equation (equation 3) and weekday and/or announcement dummies are in the ht equation (equation 2): ht+1 = ω + αεt2 + βht + γεt

2It+ λMDWM,t+1 + λWDWW,t+1 + λRDWR,t+1 + λFDWF,t+1, (4). In equation (4), the dummy for any day of the week impacts volatilities on all days of the week through the ht-1 term on the right hand side of the equation. Suppose, for instance, that day t is Monday. ∂ht/∂DWM,t = λM. Now consider the impact of the Monday dummy on the Tuesday�s (day t+1) volatility. From equation (4), ∂ht+1/∂DWM,t = βλM. Likewise, the Monday dummy impact on the Wednesday�s volatility is ∂ht+2/∂DWM,t = β2λM. Thus, when weekday dummies are in the ht equation, as in equation (4), λM does not measure how much higher volatility is on Monday than on the omitted day (Tuesday). Indeed, depending on the coefficient pattern, day X which has the highest λX coefficient may not be the day with the highest volatility.

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negative gas shock has less impact on the predicted volatility than a positive shock of the same magnitude. In

both markets, the Friday-close-to-Monday-close volatility, which incorporates volatility over the weekend, is

higher than any normal weekday volatility. The standard deviations of the Friday-close-to-Monday-close oil

and gas returns increase by 20.08% and 39.39%, respectively. There is significant evidence that crude oil and

natural gas volatilities increase in the winter months, confirming the seasonality effects in both markets. Crude

oil and natural gas volatility significantly increases on days the Petroleum Report (for crude oil market) and

the Storage Report (for natural gas market) releases are announced. In a separate test I find no significant

evidence that the increase in oil and gas volatility due to announcement effects persists on the following days.

III. Essay 2: Implied Volatility in the Crude oil and Natural gas Markets

In the second part of my dissertation, I examine the attributes of crude oil and natural gas implied

volatilities calculated from daily closing prices of futures and futures options traded on the NYME from

September 01, 1999 through June 30, 2006. The samples are broken into four time-to-maturity groups

according to option expiry: near-, second-, third- and fourth- month. Each of the maturity group is then divided

into ten �moneyness� subsamples corresponding to the amount the options are in- or out- of the money.

In this essay, I attempt to answer the following questions:

1. Is there a term structure in crude oil and natural gas implied volatility? It has been

documented that in the stock index option market, implied volatilities are lower for options at shorter

maturities.7 To my knowledge, no previous study explored the term structure of implied volatility in any

futures option market, including energy market. Contrary to the evidence in the stock index option market, I

find that implied volatilities are higher on near term oil and gas options than on longer term ones. Thus,

average implied volatility on nearby options is higher than average implied volatility on second-month options

which is, in turn, higher than that on third-month options, etc.

The term structure of implied volatilities on crude oil and natural gas options may possibly be

explained by the pattern of actual volatilities in oil and gas futures markets. Summary statistics of returns in oil

and gas futures markets indicate that returns on nearby contracts are more volatile than those on second-month

which are, in turn, more volatile than those on third-month, etc. This may be due to the fact that news such as

OPEC policy changes, refinery outages (for crude oil) or storage shortage, unfavorable weather forecasts (for

natural gas) seem to have more impact on near term contracts than on longer term ones, causing larger price

changes for the former. As implied volatility supposedly represents the market�s expectation of actual

volatility, the term structure of implied volatility should be consistent with the pattern of the actual volatility

and thus, implied volatilities on near term oil and gas options should be higher than those on longer term ones.

7Park and Sears (1985), Becker and Tucker (1991), Dumas, Fleming and Whaley (1998)

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2. Is there a �smile� in crude oil and natural gas implied volatilities? Since implied volatilities

calculated from different strike options with the same expiration date represent the market�s expectation of

volatility over the same period, there should be no significant difference in those implied volatilities. However,

contrary to this theory, previous studies document sizable and persistent cross-sectional differences in implied

volatilities in other markets. Implied volatilities on stock and stock index options, for example, form a �smile�

pattern8 prior to the October 1987 market crash and a �smirk� pattern9 after the crash10. Although the literature

is replete with studies on the implied volatility smile in various financial markets, none of the previous studies,

to the best of my knowledge, explores the possible smile pattern in any futures options, including crude oil and

natural gas options. My study aims to fill this gap in our understanding.

I find evidence of a �skew� pattern in crude oil and natural gas implied volatilities where implied

volatilities are generally lowest when options� strikes are low and increase monotonically with strikes.

Interestingly this �skew� pattern is opposite to the �sneer�, or �smirk� pattern in the post-1987 stock and stock

index option markets where implied volatilities monotonically decrease with strikes. One possible explanation

for the �skew� pattern in crude oil and natural gas options is the hedging pressure in the oil and gas markets

similarly to the argument in Bollen and Whaley (2004) for stock indices. Given that crude oil and natural gas

are two of the most essential energy sources, it is extremely difficult for consumers to quickly reduce their oil

and gas consumption, even when a sharp increase in price occurs. Consequently, there may be more oil and

gas users hedging against a price increase than there are sellers hedging against a price decrease, pushing

upward prices and implied volatilities on options with high strikes. If much trading in the oil and gas options is

due to hedging, I expect to find that call volume would be higher at the high strike options and put volume

would be higher at the low strikes, especially the former. Also, if the hedging pressure hypothesis holds, I

expect implied volatilities at the high strikes to be higher on calls than on puts (although they should be close

according to put-call parity).

3. How well do crude oil and natural gas implied volatilities predict future volatility? In other

words, I examine whether implied volatility on crude oil and natural gas options is an unbiased and efficient

forecast of actual volatility.

The volatility implied in an option�s price is widely regarded as the market�s forecast of future returns

volatility over the remaining life of the option. If option markets are efficient, implied volatility should be an

efficient forecast of future volatility, i.e., implied volatility should subsume all other information in explaining

future volatility. The literature is replete with studies on whether implied volatility predicts future volatility

8In a volatility �smile�, options that are deep in-the-money or out-of-the-money have higher implied volatilities than at-the-money options. 9In a volatility �smirk�, implied volatilities decrease monotonically as the exercise price increases. 10 See, for example, Canina and Figlewski (1993), Rubinstein (1994), Dumas, Fleming and Whaley (1998), Das and Sundaram (1999), Ederington and Guan (2005)

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and whether it does so efficiently in various markets, including the stock and stock index options market11,

foreign exchange options market12, futures options markets13, Eurodollar options market14, etc.

Day and Lewis (1993), Martens and Zein (2004) and Szakmary et al. (2003) examine the information

content of crude oil and natural gas implied volatilities but their data are limited to implied volatilities

calculated from nearby at-the-money options. In contrast, the large data set in this study enables me to further

explore whether implied volatility calculated from any specific maturity and moneyness group is the best

forecast of future volatility15. I expect implied volatilities on near term options to be the best forecast of future

volatility. Furthermore, I expect that implied volatilities of high strike options whose prices are supposedly

impacted heavily by hedging pressures should be less representative of the market�s volatility expectation than

implied volatilities calculated from options with lower strikes whose prices should be less subject to hedging

pressures.

I estimate the following specification on each maturity and moneyness subsample:

1 , , , ,( ) ,t i j t i j tISD uσ τ α β= + ⋅ + (1) and

(2)

where , ,i j tISD is the implied volatility (measured as the implied standard deviation) computed on day t from

the option in maturity group i and �moneyness� group j , and , ,i j tu represents the regression error. ( )tσ τ is

the realized volatility of log returns over the period between t and t τ+ , the option�s expiration date,

annualized by multiplying the standard deviation calculated per day by 252. Log return is defined as:

1

tt

t

FR LnF −

=

where Ft and Ft-1 are the underlying futures prices on day t and day t-1, respectively.

I then employ Hansen (1982) procedure to correct for serial correlation caused by overlapping

observations.

Results from specification (1) and (2) show that implied volatilities calculated from near-the-money

and slightly out-of-the-money call options in the nearby and second-month groups are unbiased and efficient

predictors of future volatility in the crude oil and natural gas markets.

11See, for example, Day and Lewis (1992), Lamoureux and Lastrapes (1993). Canina and Figlewski (1993), Christensen and Prabhala (1998), etc. 12Jorion (1995) 13See, Day and Lewis (1993), Martens and Zein (2004), Szakmary, Ors and Kim (2003) 14Amin and Ng (1997) 15 This question is inspired by the findings in Ederington and Guan (2005) that implied volatilities calculated from moderately high strike options are both unbiased and efficient whereas those on at-the-money options are biased and less efficient.

' '1 , , 2 , , , ,( ) ' ,t i j t i j t i j tISD HIS uσ τ α β β= + ⋅ + ⋅ +

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4. Is there a seasonality pattern in crude oil and natural gas implied volatilities? As analyzed in

the first essay, a winter effect is an attribute of the natural gas market due to the dependence of natural gas

prices on weather conditions, and to a lesser extent, there is also evidence of higher crude oil volatility in

winter. In this essay, I hypothesize that implied volatilities are higher on oil and gas options expiring in the

winter months than on options expiring in other months. This hypothesis is likely due to two reasons. First, as

the market participants forecast actual volatilities to increase in winter, this forecast is incorporated in options

prices and thus, implied volatilities are higher on options expiring in the winter months. Second, as oil and gas

volatilities tend to increase in winter, there may be more oil and gas users buying options to hedge against

price increases, pushing upward prices and implied volatilities on options expiring in the winter months. To

my knowledge, none of the previous studies examined seasonality pattern for any option market.

I find evidence of a seasonality pattern in crude oil and natural gas option markets in that average

implied volatilities on options expiring in the winter months are higher than those on options expiring in other

months. In the natural gas option market, the average implied volatility (as measured by implied standard

deviation) calculated from options expiring in the winter peak is approximately 60% higher than those

expiring in the summer trough whereas in the crude oil option market, the peak is 22% higher than the trough.

This month-of-the-year pattern is consistent across all maturity groups in both markets.

5. Is there a day-of-the-week pattern in crude oil and natural gas implied volatilities? A day-of-

the-week effect on implied volatility has been documented for several markets16. However, no previous study

explored weekday pattern in any futures option market, including crude oil and natural gas. I find that implied

volatilities in crude oil and natural gas option markets significantly increase on Friday and decrease on

Monday. As the forecast of Monday actual volatility is included in Friday implied volatility (which represents

the market�s expectation of future volatility from the following Monday to the option expiration) and dropped

from Monday implied volatility (which represents the market�s expectation of future volatility from Tuesday

to the option expiration), evidence of a higher Friday implied volatility and a lower Monday implied volatility

indicates that Monday is a high volatile day in both markets.

6. Do the crude oil and natural gas implied volatilities tend to fall following important scheduled

announcements? In the first essay, I find that crude oil and natural gas actual volatilities increase on days the

Weekly Petroleum Status Report and the Weekly Natural Gas Storage Report are announced. Consistent with

this finding, I expect that crude oil and natural gas implied volatilities tend to fall following these

announcements. Since market participants know that important scheduled releases tend to impact the

underlying prices, uncertainty, as measured by implied volatility, should be high prior to the release.

Following the announcement release, the actual volatility should increase but the implied volatility should fall

as this source of uncertainty is resolved. (Ederington and Lee (1996)). 16 See, for example, Becker and Tucker (1991), Harvey and Whaley (1992) and Ederington and Lee (1996)

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7. Do positive and negative shocks in crude oil and natural gas returns have different impact on

the subsequent implied volatility? In the first essay, I find that a negative shock in the crude oil and natural gas

futures markets has a different impact on predicted volatility than a positive shock of the same magnitude.

Consequently, in this essay, I investigate whether a negative shock in these markets has more or less impact on

the implied volatility than an equal positive shock. The main difference between this part and the previous part

is that the predicted volatility in the futures markets is forecast from a GJR type model17 whereas in this part,

implied volatility is the forecast of future volatility. This is the first time the impact of underlying returns

shocks on the subsequent implied volatility is explored in the literature.

To test the impact of positive and negative returns shocks on implied volatility, I use the following

specification: 0 1 1 2 1 3 1 1 (3)t t t t t tISD ISDα α α ε α η ε υ− − − −= + + + + where tISD is the implied standard

deviation on day t, 260t tε ζ= and tζ is the residual from the following equation: 1 (4)t t tR Rµ φ ζ−= + + ;

1ln( / )t t tR F F −= where tF is the futures price on day t, tη =1 if tε <0 and 0 otherwise.

To the best of my knowledge, my second essay will be the first full study of the attributes of implied

volatility such as the term structure and the smile in implied volatility, information content, seasonality, day-

of-the-week and announcement effects and the impact of previous returns shocks on implied volatility.

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17 The GJR model is named after Glosten, Jagannathan and Runkle (1993)

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