Valuing of American Option by simulation A simple Least-Squares Approach The Review of Financial Studies

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1、ValuingAmericanOptionsbySimulation:ASimpleLeast-SquaresApproachFrancisA.LongstaffUCLAEduardoS.SchwartzUCLAThisarticlepresentsasimpleyetpowerfulnewapproachforapproximatingthevalueofAmericanoptionsbysimulation.Thekeytothisapproachistheuseofleastsquarestoestimateth

2、econditionalexpectedpayofftotheoptionholderfromcontinuation.Thismakesthisapproachreadilyapplicableinpath-dependentandmultifactorsituationswheretraditionalfinitedifferencetechniquescannotbeused.Weillustratethistech-niquewithseveralrealisticexamplesincludingvaluing

3、anoptionwhentheunderlyingassetfollowsajump-diffusionprocessandvaluinganAmericanswaptionina20-factorstringmodelofthetermstructure.OneofthemostimportantproblemsinoptionpricingtheoryisthevaluationandoptimalexerciseofderivativeswithAmerican-styleexercisefeatures.The

4、setypesofderivativesarefoundinallmajorfinancialmarketsinclud-ingtheequity,commodity,foreignexchange,insurance,energy,sovereign,agency,municipal,mortgage,credit,realestate,convertible,swap,andemerg-ingmarkets.Despiterecentadvances,however,thevaluationandoptimalexe

5、rciseofAmericanoptionsremainsoneofthemostchallengingproblemsinderivativesfinance,particularlywhenmorethanonefactoraffectsthevalueoftheoption.Thisisprimarilybecausefinitedifferenceandbinomial1techniquesbecomeimpracticalinsituationswheretherearemultiplefactors.Weare

6、gratefulforthecommentsofYaserAbu-Mostafa,GiovanniBarone-Adesi,MarcoAvellaneda,PeterBossaerts,PeterCarr,PeterDeCrem,CraigFithian,BjornFlesaker,JamesGammill,GordonGemmill,RobertGeske,EricGhysels,RavitEfratyMandell,SoetojoTanudjaja,JohnThornley,BruceTuckman,PedroSa

7、nta-Clara,PratapSondhi,RossValkanov,andseminarparticipantsatBearStearns,theUniversityofBritishColumbia,theCaliforniaInstituteofTechnology,ChaseManhattanBank,Citibank,theCourantInstituteatNewYorkUniversity,CreditSuisseFirstBoston,DaiwaSecurities,FujiBank,GoldmanS

8、achs,GreenwichCapital,MorganStanleyDeanWitter,theNorinchukinBank,NikkoSecurities,theMathWeekRiskMagazineConferencesinLondonandNewYork,SalomonSmithBarneyinLondonandNew