paul wilmott on quantitative finance energy derivatives

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1、CHAPTER72energyderivativesInthisChapter...•whytheenergymarketsarespecial•theconvenienceyield•thePilopovictwo-factormodel´72.1INTRODUCTIONThischaptercanonlybeaverybriefintroductiontotheenergymarkets.Theissuesinvolvedcanbequitecomplexandwouldrequireawholebooktocaptureallofthesubtleties.A

2、nd,tobehonest,Idon’tbelievemuchofwhatI’mwriting,andbytheendofthechapterIhopeyou’llseewhy.72.2THEENERGYMARKETTheenergymarketconsistsofcommoditiessuchas•Naturalgas•Oil,ofvarioustypes•ElectricityThesemarketssharesomeofthecharacteristicsofothercommoditymarkets,suchasthatforporkbellies.Ther

3、eisaspotmarketforimmediatedeliveryandafuturesmarketfordeliveryatsomespecifiedtimeinthefuture.Spotpricesaretypicallyveryvolatile.Aswithothercommoditiesthereisacostassociatedwiththestorageoftheenergyforfutureuseordelivery.Sometimesthisstorageissimplyamatterofphysicallyholdingontothecommod

4、ityinspeciallocations,suchaswithoil.Sometimes,aswithelectricity,morecomplexstoragearrangementsmustbemade,andoftenaren’tpossibleatall.Forexample,usetheelectricitytopumpwaterintoareservoir,storetheenergyaspotentialenergyforlaterreleaseashydroelectricenergy.Generallyspeakingthough,theoppo

5、rtunitiesforarbitragebyexploitingapparentmispricingsarenegligible;andbecauseofstoragedifficulties,oneday’sdeliveryofelectricityisacompletelydifferentproductfromthefollowingday’s.Therearetwoformsofdelivery,physicalandcash.Asitsnamesuggests,physicaldeliveryiswhentheactualcommodityisgivent

6、othebuyer.Thecontractusuallyspecifiesthelocation1142PartFiveadvancedtopics161412108p/Therm6420Aug-99Mar-00Oct-00Apr-01Nov-01May-02Dec-02Figure72.1Futurenaturalgasprices.atwhichdeliverywillbemade.Differentcommoditieshavedifferentdeliverylocationsorhubs,andtherewillbeseveralsuchlocationsa

7、roundthecountry.Cashdeliveryiswhentheequivalentamountisgiveninmoney.Averyimportanteffectthatisseeninenergypricesistheseasonalityeffect.Priceshaveastrongseasonalitycomponentthatisseeninthefuturepricecurve.Figure72.1showsfuturepricesofnaturalgas.IntheUS,heatingoilismoreexpensiveinthewi