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1、SIAMREVIEWc2003SocietyforIndustrialandAppliedMathematicsVol.45,No.4,pp.627–685PricingandHedgingSpreadOptions∗ReneCarmona´†ValdoDurrleman†Abstract.Wesurveytheoreticalandcomputationalproblemsassociatedwiththepricingandhedgingofspreadoptions.Theseoptionsareubiq
2、uitousinthefinancialmarkets,whethertheybeequity,fixedincome,foreignexchange,commodities,orenergymarkets.Asamatterofintroduction,wepresentageneraloverviewofthecommonfeaturesofallspreadoptionsbydiscussingindetailtheirrolesasspeculationdevicesandriskmanagementtool
3、s.Wedescribethemathematicalframeworkusedtomodelthem,andwereviewthenumericalalgorithmsactuallyusedtopriceandhedgethem.Thereisalreadyextensiveliteratureonthepricingofspreadoptionsintheequityandfixedincomemarkets,andourcontributionismostlytoputtogethermaterialsca
4、tteredacrossawidespectrumofrecenttextbooksandjournalarticles.Ontheotherhand,informationaboutthevariousnumericalproceduresthatcanbeusedtopriceandhedgespreadoptionsonphysicalcommoditiesismoredifficulttofind.Forthisreason,wemakeasystematicefforttochooseexamplesfromt
5、heenergymarketsinordertoillustratethenumericalchallengesassociatedwiththeseinstruments.Thisgivesusachancetodiscussaninterestingapplicationofspreadoptionstoanassetvaluationproblemafteritisrecastintheframeworkofrealoptions.Thisapproachiscurrentlytheobjectofinte
6、nsemathematicalresearch.Inthisspirit,wereviewthetwomajoravenuestomodelingenergypricedynamics.Weexplainhowthepricingandhedgingalgorithmscanbeimplementedintheframeworkofmodelsforboththespotpricedynamicsandtheforwardcurvedynamics.Keywords.spreadoptions,energymar
7、kets,derivativepricingtheory,closedformapproximationsAMSsubjectclassifications.60H10,91B28DOI.10.1137/S00361445034247981.Introduction.Themaingoalofthissurveyistoaddressoneofthemostfun-damentalchallengesfacingappliedmathematiciansinthefinancialarena:pricingandhe
8、dgingfinancialinstrumentsforwhichclosedformformulaecannotbederived.Fol-lowingthepioneeringworkofBlack,ScholesandMerton,pricingandhedgingschemeshavebeendevelopedforallsortsoffinancialderivat
