Predicting Implied Volatility in the Commodity Futures Options Markets

Transcription

1 Predicing Implied Volailiy in he Commodiy Fuures Opions Markes By Sephen Ferris* Deparmen of Finance College of Business Universiy of Missouri - Columbia Columbia, MO Phone: ferris@missouri.edu Weiyu Guo Universiy of Nebraska - Omaha 6001 Dodge Sree, Omaha, NE Phone wguo@unomaha.edu Tie Su Universiy of Miami P.O. Box Coral Gables, FL, Phone ie@maimi.edu March 2003 We hank he raders a ConAgra Trade Group, Ankush Bhandri, John Harangody, and Edward Prosser for commens and suggesions. Guo hanks Carl Mammel and Bill Lapp for he faculyin-residence opporuniy a ConAgra Foods, and summer research suppor from he Universiy Commiee on Research a he Universiy of Nebraska a Omaha.

2 Predicing Implied Volailiy in he Commodiy Fuures Opions Markes Absrac Academics and praciioners have subsanial ineres in he implied volailiy paerns recovered from commodiy fuures opions. Such knowledge enhances heir abiliy o accuraely forecas volailiy embedded in hese high-risk opions. This paper reviews opion-implied volailiy in he Sepember corn fuures opion conracs for he period of I also invesigaes wheher a weekend effec exiss. We compare forecasing performance of differen hisorical volailiy measures. We furher repor average rading profis of a shor sraddle sraegy, which is moivaed by differences beween opion implied volailiy and hisorical volailiy. JEL Code: G10, G12, G13 Keywords: commodiy fuures opions, implied volailiy

3 Predicing Implied Volailiy in he Commodiy Fuures Opions Markes 1. Inroducion A call opion gives an opion holder he righ o buy an asse a a price pre-specified in he opion conrac on or before he opion s expiraion dae. The opion holder is no obligaed o exercise he opion. However, he opion holder exercises he opion only o increase his own wealh. Because he opion premium reveals he invesor's expecaion regarding fuure price movemen by he asse, observed opion prices conain informaion abou he marke s expeced price as well as he volailiy of he underlying asse. If an opion pricing model works well o price opions, hen an invesor can use he observed opion prices o inver he opion pricing model and obain he marke s esimae of he underlying asse s volailiy. This volailiy is referred o as he opion implied volailiy. The imporance and usefulness of opion implied volailiy has been exensively recognized in he academic lieraure. Canina and Figlewski (1993) and Fleming (1996, 1998) examine implied volailiies using S&P 100 sock index opions (OEX) while Beckers (1981) and Lamoureux and Lasrapes (1993) consider opions on individual socks. Day and Lewis (1993) invesigae he naure of implied volailiies on crude oil fuures while Jorion (1995) examines foreign currency fuures and Ferri (1996) analyzes foreign currency opions. Findings from Black and Scholes (1973), Meron (1973), Manaser and Rendleman (1982), Day and Lewis (1992), Ederingon and Lee (1996), and Chrisensen and Prabhala (1998) show ha implied volailiies conain informaion abou he expeced variance of sock reurns. More recen work by Mayhew and Sivers (2001) describes he properies of he forecass conained in opion 1

4 implied volailiies while Ferson, Heuson, and Su (2001) examine he relaion beween volailiy in sock reurns and implied sandard deviaions. Bu he sudy of implied volailiies has no been limied o equiy markes. Wilson and Fung (1990) examine informaion conen of volailiy implied by opions on grain fuures. Nelson (1996) sudies he relaion beween opion implied volailiy and he underlying conrac aciviy in he live cale marke. Kenyon and Beckman (1997) analyze muliple-year pricing opporuniies for corn and soybeans spo, fuures, and fuures opions markes. Opion implied volailiy is of grea imporance o raders, wheher hey are hedgers or speculaors. The absolue price level is of secondary imporance o raders. I is he change in price of a fuures conrac ha is imporan because such changes generae capial gains or losses. These, in urn, produce rading profis or losses. In addiion, fundamenal facors such as supply and demand, raders ofen look for relaions beween prices, volumes, open ineress, or volailiy. Exising opion pricing heories such as Black and Scholes (1973) or Meron (1973) sugges for insance ha here is a posiive relaion beween volailiy and opion price. When volailiy increases, opion prices increase as well and vice versa. Anicipaed changes in volailiy generae changes in opion prices. Some commodiy raders and academic researchers (Wilson and Fung, 1990; Nelson, 1996) suspec ha implied volailiy in commodiy fuures opions is seasonal because weaher and oher seasonal facors ha have he poenial o impac crop growh exhibi behaviors ha are predicable in calendar ime. If implied volailiy is seasonal, hen raders can predic volailiy changes based on seasonal paerns. Thus, he firs conribuion of his sudy is a es for seasonaliy paerns in implied volailiies in corn fuures opions. We elec o focus on corn fuures conracs since hey are he mos acively raded agriculural fuures conracs on he 2

5 Chicago Board of Trade (CBOT). Indeed, he average rading volume for his commodiy exceeds 50,000 conracs per day during our sample period, Our specific focus is on he Sepember fuures opion conracs ha expire in Augus. Volailiy in he Sepember fuures conracs is he hardes o predic among all such conracs because of he corn pollinaion ha occurs in July and Augus. The success of his pollinaion period is highly uncerain, hus making he size of he fuure harves difficul o assess. Consequenly, Sepember fuures conracs are perceived o have a much higher implied volailiy han any oher corn fuures opions. Traders have a subsanial ineres in he implied volailiy paerns recovered from Sepember fuures opions because such knowledge enhances heir abiliy o accuraely forecas he volailiy embedded in hese high-risk opions. Previous sudies of he equiy marke such as French (1980), Lakonishok (1982), Keim, Sambaugh, and Rogalski (1984) repor evidence of a weekly paern in index reurns. This anomaly is ermed he weekend effec. Jaffe and Weserfield (1985) and Jaffe, Weserfield, and Ma (1989) find limied evidence of his effec in inernaional sock markes while Dyl and Maberly (1986) and Chang, Jain, and Locke (1995) presen findings suggesing is presence in he marke for sock index fuures. In his sudy, we es for a weekend effec in he commodiy fuures opion marke by invesigaing wheher implied volailiy is higher on Fridays han Mondays due o added uncerainy resuling from he marke s weekend closure. Such informaion will be useful for raders seeking o find enry or exi poins o he marke, or o speculae on volailiy changes on a shor-erm basis. The final conribuion of his sudy is our analysis of forecasing performance using alernaive measures of hisorical volailiy. We repor he forecasing performance of four 3

6 commonly used hisorical volailiy measures, measured across en and weny day moving windows. In addiion, we repor he resuls from execuing a shor sraddle rading sraegy using empirical daa. We find posiive rading profis when opions are wihin four monhs o expiraion. We conclude ha differences in implied volailiies and hisorical volailiies lead o posiive rading profis. We organize he remainder of he paper in he following manner. In secion 2 we inroduce our mehodology while in secion 3 we describe our daa and sample consrucion. We presen our empirical findings in secion 4. We discuss he rading implicaions of our resuls in secion 5. We conclude wih a brief summary in secion Mehodology 2.1 Implied volailiy esimaion Given an opion pricing model and an opion conrac informaion, he implied volailiy parameer equaes he heoreical opion price o he observed marke opion price. The implied volailiy is regarded as he marke s expeced volailiy of reurns for he underlying asse over he remaining life of he opion. The Black (1976) opion pricing model for fuures opions is a varian of he Black- Scholes (1973) opion pricing model for equiy opions. Similar o he Black-Scholes model, a fuures price, a srike price, an ineres rae, ime o mauriy, and volailiy are used o compue a fuures opion price. The firs four variables are direcly observable from he marke. However, a rader has o esimae he asse reurn volailiy o use any opion pricing model. If he marke prices fuures opions according o he Black model, hen he marke observed opion price, C obs should be equal o he heoreical opion price, C Black, generaed from he Black model. 4

7 We use he Black model o recover implied volailiies. The procedure generally requires a numerical search rouine o accomplish his ask. Solving he Black model backward from he observed opion prices hus provides an esimae for he opion implied volailiy. Because he Black [1976] model is for European syle opions and he corn fuures opions are American syle, he binomial pricing model is more appropriae. Oher hings held consan, an American syle opion is always worh more han an oherwise idenical European syle opion. This is because an American syle opion can be exercised on or before he expiraion dae while a European syle opion can be exercised only on expiraion. Thus for commodiy fuures opions, he implied volailiy recovered from he Black model is upward biased. This bias however is of minor consequence because mos raders are fully aware of i. Hence, hey adjus heir esimaes accordingly. Furhermore, raders are more concerned wih changes in implied volailiy han he absolue level of implied volailiy. 2.2 Hisorical volailiy esimaions Hisorical volailiy is esimaed by wo differen procedures: a sandard procedure and a zero-mean procedure. Figlewski (1997) discusses boh procedures in deail. We summarize hese mehodologies as follows The sandard procedure We begin wih a se of hisorical fuures closing prices {S 0, S 1,...S T }. We hen esimae a se of log price relaives, i.e., R = ln (S /S -1 ) for from 1 o T. To obain hisorical volailiy on a en-day moving window basis, he log price relaive series is hen decomposed ino en-day inernals on a moving window basis. Tha is, {R 1, R 2,...R 10 }, {R 2, R 3,...R 11 }, and so on. The hisorical volailiy esimaes are he annualized sandard deviaions of reurns for hese en-day inervals. The numerical expression for he procedure is: 5

8 σ ( Rj R) j= = , = 1, 2,, T-9 (1) where 252 is he number of rading days in a year. R is he mean reurn for a 10-day inerval, which is equal o: R = Rj (2) 10 j= The zero mean procedure Figlewski (1997) repors ha he mean reurn of he series is in fac deermined only by he firs price observaion S -1, he las observaion in he price series S +9, and he lengh of he inerval: ( ln( ) ln( 1) ) ( ln( + 9) ln ( 1) ). (3) R = R = S S = S S j j j j= j= Esimaing a sample mean based on equaion (1) hence can be quie inaccurae. Since he volailiy does no depend heavily on he mean, Figlewski (1997) suggess imposing a sample mean as zero in he calculaion so ha hisorical volailiy is esimaed by: σ R j j= = , = 1, 2,, T-9 (4) Figlewski (1997) argues ha "using elaborae models for mean reurns is unlikely o be worh he effor in erms of any improvemen in accuracy". Noe ha he denominaor in equaion (4) is en insead of nine since he mean is no esimaed from he sample, so no observaions are los. 6

9 Hisorical volailiies on a 20-day moving window basis are esimaed similarly. In he sandard mean procedure, σ ( Rj R) j= = , = 1, 2,, T-19 (5) and in he zero mean procedure: σ Rj j= = , = 1, 2,, T-19 (6) To examine he forecasing performance of he above four hisorical volailiy measures, we use esimaed volailiy from a given inerval as he volailiy forecas for he nex inerval. We record he deviaions beween forecas and realized volailiies. We repea he above procedure using 10- and 20-day moving window measures. Roo-mean-squared-errors (RMSEs) summarize all corresponding recorded volailiy deviaions. 3. Daa and Sample Descripion 3.1 Daa descripion Boh fuures and fuures opion prices in our sample are from he Chicago Board of Trade (CBOT). They are for Grade No. 2 yellow corn. Pricing daa for all expiraion monhs are available a CBOT. Our sample focuses on all daily closing prices of Sepember fuures and fuures opion from January o July for he period of We exclude all opion conracs prior o January because of hin rading volume on he opion conracs. We furher remove all observaions afer July due o he shor remaining ime o expiraion. 7

10 The underlying asse of a Sepember fuures opion is Sepember fuures conrac. For he fuures opions, we have daa concerning he opion premium, srike price, mauriy monh, underlying securiy price, and T-bill raes. We recover he opion implied volailiy from a-hemoney opions. When he fuures price does no exacly equal any srike price, we use a near he money opion o approximae an a-he-money opion. The Black (1976) model requires a marke ineres rae o compue an opion price. We firs use a six percen consan risk free rae in he Black model. Some raders ofen use a consan ineres rae because he impac of ineres rae on he recovered implied volailiy is believed o be rivial and should no maerially impac rading decisions. We also use yields on 90-day Treasury bills as more elaborae proxies for marke ineres raes. Our ables presen resuls from boh ses of marke ineres rae proxies. 3.2 Naure of he conrac The Sepember corn fuures conracs are inroduced in May each year and expire in Sepember of he following year. The conrac size is 5,000 bushels and he ick size is 1/4 cen per bushel. The daily price limi is 20 cens per bushel above or below he previous day's selemen price. Limis are lifed wo business days before he spo monh begins. Opions on he Sepember fuures are inroduced in June and expire in mid-augus of he following year. Opion exercise resuls in an underlying fuures marke posiion. The ick size is 1/8 cen per bushel. The srike price inerval is five cens per bushel for he mos curren wo monhs and en cens per bushel for all oher monhs. A he commencemen of rading, five srikes above and five srikes below a he money are lised. Excep on he las rading day, opions are subjeced o a daily price limi of 20 cens per bushel above or below he previous day's selemen premium. Boh he fuures conracs and fuures opion conracs are raded 8

11 simulaneously in open oucry from 9:30 a.m. o 1:15 p.m. This characerisic reduces poenial noise ha could resul from non-synchronous rading, as occurs in index and index opions. 4. Empirical resuls 4.1 Implied volailiy We use he Black (1976) model o esimae opion implied volailiy of Sepember corn fuures opions. Firs, for each rading day, our sample provides us wih a se of inpu variables. They include he Sepember corn fuures closing price, opion ime o mauriy, opion srike price, marke ineres rae, and opion premium. Second, we program a numerical search rouine o compue an asse reurn volailiy ha equaes he Black fuures price o he observed marke price. Since he opion price is monoonic in volailiy, he search rouine quickly converges o a unique soluion. We repea he procedure for each rading day in our sample and documen all daily implied volailiies in our en-year sample period for furher analysis. 4.2 Paerns in annual implied volailiies Table 1 repors he average implied volailiy over each monh during our sample period. Figure 1 is a graphical presenaion of hose resuls. Over our en-year sample period, we observe a rising rend in volailiy from January o July. Implied volailiies are he lowes in January and increase seadily from January o May. They coninue o increase from he planing season in May and remain high going ino he July pollinaion season. The mean opion implied volailiy increases by more han 25% from January (23.00%) o May (29.15%). The resuls are robus wih respec o he selecion of an ineres rae proxy. <Figure 1 abou here> 9

12 <Table 1 abou here> We plo annual implied volailiy paerns in Figure 1. In 1991, implied volailiy sared a around 20% and gradually rose o over 30% in mid-july during he pollinaion period. In 1993, implied volailiy remained a he 20% level for he beginning of he year, increased in March, declined and hen emporarily jumped o slighly over 30% going ino July and finally fell o below 30% during pollinaion. The implied volailiy paerns are somewha similar for 1992 and In boh years, implied volailiy dramaically rose in May and remained high unil he end of June before declining o around 20% in July. This suggess ha he marke expeced high uncerainy in corn yield in May, bu he uncerainy was reduced during pollinaion. In 1995, volailiy sared o increase in mid-march and remained high as pollinaion approached. The year 1996 experienced a high level of volailiy. Volailiy rose dramaically in mid-april and sayed high as pollinaion approached, bu fell slighly during he acual pollinaion season. In 1997, higher uncerainy occurred during pollinaion period. In 1998, he marke sared on he high end of he volailiy range from he beginning and ended lower in lae July. In 1999, volailiy consisenly increased hroughou he firs half of he year wih high volailiy enering July. The paern in year 2000 is differen from ha of he oher years. Marke implied volailiy sared from above 30% a he beginning of he year. I wen up o as high as over 40% in May, and remained above 30% before finally dropping below 30% in lae July. Our findings sugges ha i is difficul o find evidence of seasonal paerns ha apply o even a majoriy of our sample years. Weaher, price sagnaion, and he pace of planing are all facors ha significanly impac corn yield. While curren producion plus ending sock from prior year esablish he supply side of he equaion, domesic usage and global demand deermine 10

13 demand. The imbalance beween supply and demand resul in changes in marke price as well as marke implied volailiy. Kluis (1998) noes ha echnological changes, he impac of commodiy funds, and inernaional rade combine o make he commodiy marke more sensiive and responsive o new, economically relevan informaion. These changes resul in higher shor-erm marke volailiy. These marke volailiy changes are hen capured in he annual volailiy paerns discussed above. 4.2 Weekend effec Anoher quesion ha puzzles commodiy raders is wheher implied volailiy is higher on Fridays han on Mondays due o he uncerainy resuling from a marke ha has been closed over he weekend. In shor, is here a weekend effec in implied volailiies? Insighs on his quesion are useful as raders seek o find marke enry or exi poins or o speculae on shorerm volailiy changes. Table 2 repors he means in weekday volailiy. We find ha he mean volailiy on Friday (27.49%) is slighly higher han ha on Monday (27.21%). This resul is consisen wih Chang, Jain, and Locke (1995) who find ha Friday's close is he period of highes volailiy in he S&P 500 fuures marke. However, he differences beween he Friday and Monday means are small and saisically insignifican. Alhough economically relevan aciviy migh occur during he weekend, he mean opion implied volailiy does no appear o be affeced. We conclude ha here is no a weekend effec in opion implied volailiies. <Table 2 abou here> 4.3 Hisorical volailiy Hisorical volailiy in general begins a a lower level during he early par of he year, rises a a faser pace han opion implied volailiy does during mid-year, bu approaches implied 11

14 volailiy near he opion expiraion dae. Figure 2 illusraes monhly averages of en and weny day moving window hisorical sandard volailiy measures and he mean opion implied volailiy. Since hisorical volailiy measures are esimaed from hisorical fuures prices, a possible explanaion for lower hisorical volailiy in he early par of a year is he non-rading effec" (Figlewski, 1997). When he fuures markes are relaively less acive a he beginning of he year, he full impac of a large informaion even ends o spread over wo or more days' recorded closing prices, which would resul in posiive auocorrelaion in reurns. The auocorrelaion in reurn reduces esimaed volailiy. When he fuures markes become more acive, fuures prices become more volaile and we observe higher hisorical volailiies. <Figure 2 abou here> Table 3 repors he average hisorical volailiies by monh for each year. We also observe an increasing rend in he realized hisorical volailiies from January o July. The resuls are consisen wih hose presened in Table 1. Table 4 repors he forecasing performance of he four differen hisorical volailiy measures. The roo-mean-squared-errors (RMSEs) measure he forecasing performance. The smaller he RMSE, he beer he forecas. RMSE indicae ha he 20-day zero mean hisorical volailiy gives bes forecasing resuls among all four hisorical volailiy measures. The 20-day sandard hisorical volailiy performs he second bes. <Table 4 abou here> 5. Trading implicaions While some corn raders suspec ha corn fuures opion implied volailiy migh be seasonal due o he fac ha corn growh is affeced by many seasonal facors, a close 12

15 examinaion of he volailiy paern for he decade of he 1990s reveals ha volailiy is no as seasonal as suspeced. The volailiy is largely affeced by he impac of weaher on he planing, pollinaion, and growh of he corn crop. Alhough a general rising rend of implied volailiy from January o July is observed, ime decay may offse he gains in opion prices ha resul from higher volailiy. Traders frequenly compare implied volailiy wih hisorical volailiy from he same period from prior years o predic shor-erm implied volailiy changes. Hisorical volailiy ends o be lower han implied volailiy in he early par of a year. This paern, however, does no necessarily imply a rading opporuniy. Sill, we are curious abou he poenial for profi resuling from he difference in implied and realized volailiies. If implied volailiy is consisenly larger han realized volailiy in fuures conracs, hen he fuures opions will end o be over-priced. A shor opions sraddle, which involves a shor call opion and a shor pu opion on he same underlying asse, wih he same ime o mauriy and exercise price, should generae a profi. These shor sraddles are also called volailiy sraegies, or volailiy plays. Holders of shor sraddles gain if he marke price a mauriy says wihin a narrow range around he sraddle s srike price. This assumes ha he posiions are held o mauriy wihou dela neural hedging 1. We simulae his rading sraegy wih empirical fuures and fuures opions daa. On each rading day in our sample, we consruc a shor sraddle by using an a-he-money call and a pu opion pair. The call and he pu share he same a-he-money srike price and he same mauriy 1 Traders are likely o creae a dela neural hedge o proec agains losses from an adverse movemen in fuures prices. A dela-neural hedge involves a long posiion in a fracion of a uni of he underlying asse and a shor call conrac. For small changes in he underlying asse, he overall porfolio value is unchanged. Consequenly, he porfolio is called a hedged porfolio. Dela refers o he hedge raio, i.e., he fracion of shares ha needs o hedge a shor call. 13

16 monh (Sepember). We collec opions premiums (C 0 + P 0 ) for he call and he pu on he se up day. We hold he shor sraddle unil he opions maures and hen compue he payoff, which is F T X. This sraegy generaes a dollar profi/loss of W and a percen reurn of R: W = C 0 + P 0 - F T X (7) R = W / (C 0 + P 0 ) (8) We define C 0 as he call opion premium on he se up day, P 0 as he pu opion premium on he se up day, F T as he fuures price on he expiraion day, and X as he srike price of he call and pu. Table 5 conains he average dollar and percen reurns across each of he monhs during our sample period. We repor he resuls by monh. Average dollar profis are quoed on a cens per bushel basis while percen reurn is quoed as a percen of he iniial call and pu premiums colleced, as defined in equaion (8). In he firs hree monhs of each year, he average dollar profis are negaive, suggesing ha he shor sraddles lose money on average. The resuls are no surprising because of he long holding period. There is a lo of risk in he underlying fuures conrac. Holding a shor sraddle on hese conracs involves is risky. Our empirical resuls show ha here is no benefi, on average, in a shor sraddle sraegy during he monhs of January, February, and March. However, average rading profis for he monhs beween April and July are significanly posiive. The highes average rading profi occurs in he monh of April. The mean is 6.87 cens per bushel, which corresponds o a reurn of 16.32%. These saisics are boh saisically and economically significan. Consider a six-cen per bushel profi. Since he conrac size of corn fuures is 5,000 bushels, he profi direcly ranslaes o $300 per conrac ($0.06 5,000 = $300). <Table 5 abou here> 14

17 We argue ha he posiive rading profis are closely relaed o he fac ha opion implied volailiies are visibly larger han realized volailiies as presened in Figure 2. High implied volailiy leads o high opion prices, which lead o profis on shor opions sraddles. Since realized volailiies are lower han implied volailiies, he underlying fuures conracs do no generae he degree of movemen anicipaed by opion raders. Consequenly, shor sraddles produce posiive profis. However, we mus inerpre he resuls wih cauion. Firs, in our compuaion, we ignored marke fricions, including bu no limied o, bid/ask spread and ransacion coss. Including such facors will clearly reduce profis and increase losses. Traders face hese coss. Spread and ransacion adjused profis and losses are more meaningful in such a calculaion. Second, opions on fuures are highly risky securiies. Shor fuures opion sraddles are highly risky speculaive posiions. A close examinaion of Table 5 reveals he sandard deviaions of he rading reurns are in he neighborhood of 60%, and he maximum loss can go well beyond -100% ( % in he monh of July). I is rue ha he average rading profis are posiive. However, i is no clear ha he average risk-adjused reurns on he shor sraddles are sill posiive. 6. Conclusion This paper examines volailiy embedded in he Sepember corn fuures opion markes for he sample period, Our analysis focuses on he corn fuures conracs since hey are he mos acively raded agriculural fuures conrac on he CBOT. We find an increase rend in boh he implied volailiy and hisorical volailiy in Sepember corn fuures conrac over January o July period. However, i is difficul o find any oher genuine annual seasonal paern 15

18 ha fis all he years. Weaher, price sagnaion and he pace of planing all exer an influence on marke price and volailiy. Implied volailiy on Fridays, in general, is higher han ha on Mondays. However, he differences are small and saisically insignifican. Hisorical volailiy in general is lower han opion implied volailiy in he earlier par of he year. However, hisorical volailiy rises a a faser pace han implied volailiy during mid-year and approaches implied volailiy near he opion expiraion dae. Shor sraddle posiions generae posiive profis only when fuures opions are wihin four monhs o expiraion. The average reurns are posiive wih a large variance. The roo-mean-squared-errors (RMSEs) indicae ha 20-day moving window zero mean hisorical volailiy measures gives he bes forecasing resuls among all four candidaes we consider in his sudy. 16

19 References Beckers, S., Sandard deviaions implied in opion prices as predicors of fuure sock price variabiliy. Journal of Banking and Finance 5, Black, F., The pricing of commodiy conracs. Journal of Financial Economics 3, Black, F., and Scholes, M., The pricing of opions and corporae liabiliies. Journal of Poliical Economy 81, Canina, L., and Figlewski, S., The informaional conen of implied volailiy. Review of Financial Sudies 6, Chang, E., Jain, P., and Locke, P., Sandard & Poor's 500 index fuures volailiy and price changes around he New York Sock Exchange close. The Journal of Business 68(1), Chrisensen, B., and Prabhala, N., The Relaion beween implied and realized volailiy. Journal of Financial Economics 50, Day, T., and Lewis, C., Sock marke volailiy and he informaion conen of sock index opions. Journal of Economerics 52, Day, T., and Lewis, C., Forecasing fuures marke volailiy. Journal of Derivaives 1, Dyl, E., and Maberly, E., The weekly paern in sock index fuures: A furher noe. The Journal of Finance 41(5), Ederingon, L., and Lee, J., The creaion and resoluion of marke uncerainy: The impac of informaion releases on implied volailiy. Journal of Financial and Quaniaive Analysis 31, Ferri, A., Unpublished Disseraion Research. New York Universiy Sern School of Business. Ferson, W., Heuson, A., and Su, T., How much do expeced sock reurns vary over ime? Answers from he opions marke. Working paper. Universiy of Miami. Figlewski, S., Forecasing volailiy. In: Financial Markes, Insiuions, and Insrumens. Boson MA: Blackwell Publishers, Vol.6, No.1. Fleming, J., The qualiy of marke volailiy forecass implied by S & P 100 index opions prices. Working paper. Jones Graduae School, Rice Universiy. Fleming, J., The qualiy of marke volailiy forecass implied by he S&P 100 index opions. Journal of Empirical Finance 5, French, K., Sock reurns and he weekend effec. Journal of Financial Economics 8(1), Jaffe, J., Weserfield, R., The week-end effec in common sock reurns: The inernaional evidence. The Journal of Finance 40(2),

20 Jaffe, J., Weserfield, R., and Ma, C., A wis on he Monday effec in sock prices: Evidence from he U.S. and foreign sock markes. Journal of Banking & Finance 13(4,5), Jorion, P., Predicing volailiy in he foreign exchange marke. Journal of Finance 50, Keim, D., Sambaugh, R., and Rogalski, R., A furher invesigaion of he weekend effec in sock reurns/discussion. The Journal of Finance 39(3), Kenyon, D., and Beckman, C., Muliple-year pricing sraegies for corn and soybeans. Journal of Fuures Markes 17(8) Kluis, A., Markeing paerns have changed. Soybean Diges Augus/Sepember. Lakonishok, J., and Maurice L., Weekend effecs on sock reurns: A noe. The Journal of Finance 37(3), Lamoureux, C., and Lasrapes, W., Forecasing sock-reurn variance: Toward an undersanding of sochasic implied volailiies. Review of Financial Sudies 6(2), Manaser, S., and Rendleman, Jr., R., Opion prices as predicors of equilibrium sock prices. Journal of Finance 37, Mayhew, S., and Sivers, C., Esimaing sock reurn dynamics using implied volailiies. Working paper. Universiy of Georgia. Meron, R., The heory of raional opion pricing. Bell Journal of Economics and Managemen Science 4, Nelson, J., The oher live cale marke: Implied volailiy. Fuures 25(10), Wilson, W., and Fung, H., Informaion conen of volailiies implied by opion premiums in grain fuures. Journal of Fuures Markes 10(1),

21 Figure 1 Opion implied volailiy for Sepember corn fuures, We use he Black[1976] model o esimae he opion implied volailiy. Specifically, we program a numerical search rouine o compue an asse reurn volailiy ha equaes a Black fuures price o an observed marke price. The procedure is repeaed for each rading day in our sample. Daily ATM opion implied volailiy (IV) is repored below wih IV on he verical axis, and year and monhs on he horizonal axis. Yields on 90-day T-bill are used as marke ineres rae proxies. IV 60% 50% 40% 30% 20% 10% 0% IV 60% 50% 40% 30% 20% 10% 0% 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 1-Feb 2-Jan 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 31-Jan 1-Jan IV 60% 50% 40% 30% 20% 10% 0% IV 60% 50% 40% 30% 20% 10% 0% 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 31-Jan 1-Jan 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 31-Jan 1-Jan IV 60% 50% 40% 30% 20% 10% 0% IV 60% 50% 40% 30% 20% 10% 0% 29-Jul 29-Jun 30-May 30-Apr 31-Mar 1-Mar 31-Jan 1-Jan 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 31-Jan 1-Jan IV 60% 50% 40% 30% 20% 10% 0% IV 60% 50% 40% 30% 20% 10% 0% 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 31-Jan 1-Jan 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 31-Jan 1-Jan IV 60% 50% 40% 30% 20% 10% 0% IV 60% 50% 40% 30% 20% 10% 0% 29-Jul 29-Jun 30-May 30-Apr 31-Mar 1-Mar 31-Jan 1-Jan 30-Jul 30-Jun 31-May 1-May 1-Apr 2-Mar 31-Jan 1-Jan

22 Figure 2 Mean monhly volailiies, We used he Black[1976] model o esimae opion implied volailiy of Sepember corn fuures opions. In he sandard procedure, we esimae hisorical volailiy by σ + N 1 2 ( Rj R) j= = 252 N 1 10 (20) - day moving average procedure; 252 is he number of rading day in a year; 0.5 R, where N = 10 (20) in he N = N j= R j is he mean reurn for a N-day inerval. In he zero mean procedure, sample mean is assumed o be zero and hisorical volailiy is esimaed by σ + N 1 2 R j j= = 252 N Implied volailiy Monh ATM implied volailiy 10-day hisorical volailiy (sample mean) 10-day hisorical volailiy (zero mean) 20-day hisorical volailiy (sample mean) 20-day hisorical volailiy (zero mean) 20

23 Table 1 Mean implied volailiy based on a-he-money calls by monh for The Black (1976) model is used o esimae he opion implied volailiy of Sepember corn fuures opions. For each rading day, our sample provides us wih a se of inpu variables including fuures closing price, opion ime o mauriy, opion srike price, marke ineres rae, and opion premium. We program a numerical search rouine o compue an asse reurn volailiy ha equaes he Black fuures price o he observed marke price. We repea he procedure for each rading day in our sample and documen all daily implied volailiies in our en-year sample period. Panel A: The ineres rae is derived from yields on 90-day T-bills Year January February March April May June July average Panel B: The ineres rae is se a six percen Year January February March April May June July average

24 Table 2 Mean implied volailiy based on a-he-money calls by day of week, The Black (1976) model is used o recover implied volailiies. Solving he Black model backward from he observed opion prices provides an esimae for he opion implied volailiy. Panel A: The ineres rae is derived from yields on 90-day T-bills Monday Tuesday Wednesday Thursday Friday Mean Sandard Dev Panel B: The ineres rae is se a six percen Monday Tuesday Wednesday Thursday Friday Mean Sandard Dev

25 Table 3 Mean hisorical volailiy by monh, N 1 2 ( Rj R) In he sandard procedure, we esimae hisorical volailiy by j= σ = 252, where N 1 N = 10 (20) in he 10 (20) - day moving average procedure; 252 is he number of rading day in a year; R N = N j= R j is he mean reurn for a N-day inerval. In he zero mean procedure, sample mean is assumed o be zero and hisorical volailiy is esimaed by σ + N 1 2 R j j= = 252 N Sandard procedure 10-day hisorical volailiy Zero mean procedure 10-day hisorical volailiy (zero mean) Monh Max Min Mean Sd. Max Min Mean Sd. Jan Feb Mar Apr May Jun Jul day hisorical volailiy 20-day hisorical volailiy (zero mean) Monh Max Min Mean Sd. Max Min Mean Sd. Jan Feb Mar Apr May Jun Jul

26 Table 4 Forecasing performance of hisorical volailiy esimaes for We use esimaed volailiy from a given inerval as he volailiy forecas for he nex inerval. We record he deviaions beween forecas and realized volailiies. We repea he above procedure using 10- and 20-day moving window measures. Roo-meansquared-errors (RMSEs) summarize all corresponding recorded volailiy deviaions. In he zero mean procedure, we compue boh realized and forecas volailiy in he forecasing period assuming a zero-mean. 10-day 20-day 10-day 20-day Realized volailiy (acual mean) (acual mean) (zero mean) (zero mean) (January July) Year RMSE RMSE RMSE RMSE MEAN Averages:

27 Table 5 Average rading profis of a shor sraddle sraegy across calendar monhs We se up shor sraddle posiions using a-he-money opions for each rading day. We hold he shor sraddles unil he opions mauriy day and compue gains or losses. The able repors he average rading profis/losses and reurns during each monh in our sample period beween 1991 and Profis are quoed on a cens per bushel basis. Reurn is measured as he percen of iniial call and pu opion premiums colleced when we se up he shor sraddle. ** indicaes ha he average is significan differen from zero a he 0.01 significance level. Panel A: Dollar rading profis Monh Profi S. dev. Min Max January February March April 6.87 ** May 4.29 ** June 2.55 ** July 2.90 ** Overall 2.09 ** Panel B: Percenage rading reurns Monh Reurn S. dev. Min Max January 1.25% 63.03% % 98.58% February 3.05% 63.21% % 98.51% March -0.10% 57.82% % 98.43% April 16.32% ** 61.01% % 98.39% May 16.08% ** 60.81% % 99.03% June 8.08% ** 56.21% % 98.89% July 14.69% ** 65.19% % 98.99% Overall 10.49% ** 60.32% % 99.03% 25