Options,Futures,andOtherDerivativesEleventhEditionChapter35EnergyandCommodityDerivativesCopyright?2022,2018,2012PearsonEducation,Inc.AllRightsReservedAgriculturalCommoditiesCorn,wheat,soybeans,cocoa,coffee,sugar,cotton,frozenorangejuice,cattle,hogs,porkbellies,etcSupply-demandmeasuredbystocks-to-useratioSeasonalityandmeanreversioninprices(farmershaveachoiceaboutwhattheyproduce)WeatherimportantMetalsGold,silver,platinum,palladium,copper,tin,lead,zinc,nickel,aluminium,etcNoseasonality;weatherunimportantInvestmentversusconsumptionmetalsSomemeanreversion(Itcanbecomeuneconomictoextractametal.)RecyclingEnergyCommoditiesMainenergysourcesOilGasElectricityAllhavemeanrevertingpricesGasandelectricityexhibitjumpsCrudeOilLargestcommoditymarketintheworldManygrades.Forexample:Brentcrudeoil(sourcedfromNorthSea)WestTexasIntermediate(W

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I)crudeRefinedproducts,forexample:GasolineHeatingoilKeroseneOilDerivativesVirtuallyallderivativesavailableonstocksandstockindicesarealsoavailableintheO

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CmarketwithoilastheunderlyingassetFuturesandfuturesoptionstradedontheNewYorkMercantileExchange(N

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X)andtheInternationalPetroleumExchange(I

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E)arealsopopularNaturalGasandElectricityDeregulatedEliminationofgovernmentmonopoliesProducerandsuppliernotnecessarilythesameNaturalGasDerivativesAtypicalO

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Ccontractisforthedeliveryofaspecifiedamountofnaturalgasataroughlyuniformratetospecifiedlocationduringamonth.N

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XandI

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Etradecontractsthatrequiredeliveryof10,000millionBritishthermalunitsofnaturalgastoaspecifiedlocationElectricityDerivatives(1of2)ElectricityisanunusualcommodityinthatitcannotbestoredTheU.Sisdividedintoabout140controlareasandamarketforelectricityiscreatedbytradingbetweencontrolareas.ElectricityDerivatives(2of2)Atypicalcontractallowsonesidetoreceiveaspecifiednumberofmegawatthoursforaspecifiedpriceataspecifiedlocationduringaparticularmonth.Typesofcontracts:dailyormonthlyexercise,swingoptionsCommodityPricesFuturespricescanbeusedtodefinetheprocessfollowedbyacommoditypriceinarisk-neutralworld.WecanbuildinmeanreversionanduseaprocessforconstructingtrinomialtreesthatisanalogoustothatusedforinterestratesinChapter32.TheProcessfortheCommodityPriceAsimplemeanrevertingprocessisCanalsobewrittenAssumeTreeforNaturalLogofSAssumingThetaLeftParenthesistRightParenthesis=0

(Figure35.1)NodeABCDEFGHIpsubu0.16670.12170.16670.22170.88670.12170.16670.22170.0867psubm0.66660.65660.66660.65660.02660.65660.66660.65660.0266psubd0.16670.22170.16670.12170.08670.22170.16670.12170.8867DeterminingThetaLeftParenthesistRightParenthesisThenodesonthetreearemovedsothattheexpectedcommoditypriceequalsthefuturespriceAssumethattheone-year,two-yearandthree-yearsfuturespriceforthecommodityare$22,$23,and$24,respectivelyFinalTree(Figure35.2)NodeABCDEFGHIpsubu0.16670.12170.16670.22170.88670.12170.16670.22170.0867psubm0.66660.65660.66660.65660.02660.65660.66660.65660.0266psubd0.16670.22170.16670.12170.08670.22170.16670.12170.8867InterpolationandSeasonalityAsimpleapproachUsea12monthmovingaverageofspotpricestodetermineapercentageseasonalityfactorforeachmonthDe-seasonalizethefuturespricesthatareknownInterpolatetodetermineotherde-seasonalizedfuturespricesRe-seasonalizeallfuturespricesandconstructtreeJumpsSomecommoditypricessuchasgasandelectricityexhibitjumpsAprocessthatcanbeassumedisthenwhered

pisaPoissonprocessgeneratingjumpsIfPoissonprocessisknown,wecanusetreetomodelprocesswithoutjumpsandtherebydetermineCanbeimplementedwithMonteCarlosimulationOtherModelsConvenienceyieldfollowsameanrevertingprocess(GibsonandSchwartz)Volatilitystochastic(EydelandandGeman)Reversionlevelstochastic(Geman)WeatherDerivatives(Section35.5)Heatingdegreedays(H

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D):ForeachdaythisiswhereAistheaverageofthehighestandlowesttemperatureinCoolingDegreeDays(C

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D):ForeachdaythisisContractsspecifytheweatherstationtobeusedWeatherDerivatives:ProductsAtypicalproductisaforwardcontractoranoptiononthecumulativeC

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DorH

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Dduringamonth.Weatherderivativesareoftenusedbyenergycompaniestohedgethevolumeofenergyrequiredforheatingorcoolingduringaparticularmonth.HowwouldyouvalueanoptiononAugustC

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Dataparticularweatherstation?HowanEnergyProducerHedgesRisks(Section35.8)EstimatearelationshipoftheformwhereYisthemonthlyprofit,Pistheaverageenergyprices,Tistemperature,andisanerrortermTakeapositionofinenergyforwardsandinweatherforwards.InsuranceDerivatives(Section35.6)C

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TbondsareanalternativetotraditionalreinsuranceThisisabondissuedbyasubsidiaryofaninsurancecompanythatpaysahigher-than-normalinterestrate.Ifclaimsofacertaintypeareinacertainrange,theinterestandpossiblytheprincipalonthebondareusedtomeetclaims.PricingIssues(Section35.7)Toagoodapproximationmanyunderlyingvariablesininsurance,weather,andenergyderivativescontractscanbeassumedtohavezerosystematicrisk.Thismeansthatwecancalculateexpectedpayoffintherealworldanddiscountattherisk-freera