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1、THEUNIVERSITYOFCHICAGOIMPLIEDVOLATILITYASYMPTOTICSADISSERTATIONSUBMITTEDTOTHEFACULTYOFTHEDIVISIONOFTHEPHYSICALSCIENCESINCANDIDACYFORTHEDEGREEOFDOCTOROFPHILOSOPHYDEPARTMENTOFMATHEMATICSBYKUNGAOCHICAGO,ILLINOISAUGUST2012UMINumber:3526300AllrightsreservedINFORMATIONTOALLUSERSThequality
2、ofthisreproductionisdependentonthequalityofthecopysubmitted.Intheunlikelyeventthattheauthordidnotsendacompletemanuscriptandtherearemissingpages,thesewillbenoted.Also,ifmaterialhadtoberemoved,anotewillindicatethedeletion.UMI3526300Copyright2012byProQuestLLC.Allrightsreserved.Thisedit
3、ionoftheworkisprotectedagainstunauthorizedcopyingunderTitle17,UnitedStatesCode.ProQuestLLC.789EastEisenhowerParkwayP.O.Box1346AnnArbor,MI48106-1346Copyrightc2012byKunGaoAllRightsReservedDedicatedtomyparentsandmywifeXiaoyu.TABLEOFCONTENTSLISTOFFIGURES.................................
4、...viACKNOWLEDGMENTS.................................viiABSTRACT........................................viii1INTRODUCTION...................................12ITERATIONSCHEMESANDFULLASYMPTOTICTHEOREM........82.1NotationsandAuxiliaryFunctions.......................82.2OptionPricingFor
5、mulas.............................112.3AsymptoticRegimes...............................142.4FullAsymptoticSolutionbyIteration......................162.5Substitutions...................................272.6Corollaries.....................................313APPLICATIONS...............
6、.....................473.1Large-strikeHeston................................473.2Short-expiryL′evy.................................493.3Long-expiryand/orLarge-strikeL′evy......................513.4PositivityandNo-ArbitrageCondition.....................594QUADRATICDRIFT3/2MODEL:MOMEN
7、TEXPLOSIONANDLARGEDEVI-ATIONS.........................................704.1AnalyticContinuationofFourierTransform..................704.2MomentExplosion................................794.3LargeDeviationsandImpliedVolatilityAsymptotics.............864.4Appendices.....................
8、...............90iv
