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1、AppliedMathematicalFinance9,21–43(2002)Energyfuturesprices:termstructuremodelswithKalmanlterestimation12MIHAELAMANOLIUandSTATHISTOMPAIDIS1Caminus,Zai*NetAnalytics,747ThirdAvenue,NewYork,NY10017,USA.email:Mihaela.Manoliu@caminus.com2MSISDepartmentandCenterf

2、orComputationalFinance,UniversityofTexasatAustin,Austin,TX78712,USA.email:Stathis.Tompaidis@bus.utexas.eduReceived10October1998andinrevisedform9November2000Wepresentaclassofmulti-factorstochasticmodelsforenergyfuturesprices,similartotheinterestratefuturesm

3、odelsrecentlyformulatedbyHeath.Wedonotpostulatedirectlytherisk-neutralprocessesfollowedbyfuturesprices,butdeneenergyfuturespricesintermsofaspotprice,notdirectlyobservable,drivenbyseveralstochasticfactors.Ourformulationleadstoanexpressionforfuturespriceswhi

4、chiswellsuitedtotheapplicationofKalmanlteringtechniquestogetherwithmaximumlikelihoodestimationmethods.Basedonthesetechniques,weperformanempiricalstudyofaone-andatwo-factormodelforfuturespricesfornaturalgas.Keywords:multi-factortermstructuremodels,Kalmanlte

5、restimation1.IntroductionPricesofenergycommodities,likeelectricityandnaturalgas,havetraditionallybeenregulated,withthenancialrisksassociatedwiththecostsofrunningautilitycompanycollectivelybornebytheusers.AstheUSAandEuropearemovingtowardsaderegulatedenviron

6、mentandasnewnancialinstrumentstailoredtoindividualdemandprolesarebeingdeveloped,itisimportanttointroducemodelsthataccountfortherisksthatthesellersandbuyersofsuchenergyinstrumentswouldface.Inthispaper,weofferageneralmulti-factormodeldesignedtoaccountfortheo

7、bservedstochasticbehaviourofenergyfuturesprices,inthespiritoftheinterestratemodelproposedbyHeath(1998)forbondfutures.Likeothermodelsofthetermstructureofcommodityfuturesprices,suchasCortazarandSchwartz(1994),andMiltersenandSchwartz(1998),ourmodeltswithinthe

8、generalHeath,JarrowandMorton(1992)no-arbitrageframework.Additionally,similartotheworkofSchwartzandSmith(1997),weofferaconnectionbetweenthemodelforthefuturespricesandamodelforanunderlyingspotprice.Thespotprice