拟蒙特卡洛方法下Heston模型的离散化.pdf

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1、AbstractAbstractBlack-Scholesmodelisoneofthemostfamousandusefulmodelforoptionpricing.UnderBlack-Scholesmodel,volatilityofunderlyingassetisconstant.IfBlack-Scholesmodelwereabsolutelytruetopriceoptions,theimpliedvolatilitywouldbeonlyonevalueregardlessoftheas

2、setpriceoftheoption.Butactually,thesmileandskewofimpliedvolatilityshowthatmarketoptionpricesarenotpricedunderBlack-ScholesmodelalthoughithasbeenproventhatBlack-Scholesmodelisthebestwaytoestimatethevolatility.Thusthequestionis,whattherelationshipbetweenthei

3、mpliedvolatilityandthetruevolatilityis.HestonmodelisoneofthemostfamousstochasticvolatilitymodelswhichwasproposedbyHestonin1993.Thereislotsofevidencesshowthatthevolatilityisstochasticandthedistributionofthereturnsofriskassethaslongertailsthannormaldistribut

4、ion.ItalsoshowsthatBlack-Scholesmodelhastoostrictassumptionsforassetpricessothatstochasticvolatilitymodelisabletoreflectthetruemarketmoreappropriately.ButHestonmodelisverycomplex,especiallyoncalculatingexactsolutionsofoptionseveniftheoptionisEuropean.After

5、Hestonproposedtheclosed-formsolution,moreandmoreresearchersturntothediscretizationnumericalsolutionsofthemodel.Thepaperdoessomeresearchinquasi-MonteCarlomethodfordiscretizationsofHestonmodel.WechooseEulerSchemeandMilsteinSchemeforthediscretizationsandEurop

6、eancalloption,AsiancalloptionandLookbackcalloptionfortheoptionschoices.Weusequasi-MonteCarlomethodinsteadofMonteCarlomethod,whichwaswidelyusedbefore,togeneratemoreuniformlypoints.Inwhich,weuseSobol’sequenceandrandomizedquasi-MonteCarlomethodsinceSobol’sequ

7、enceismuchbetterthanHaltonsequenceandFauresequencecannotdobetterthanit.Whereasrandomizedquasi-MonteCarlomethodcanimprovetheefficiencyofsimulationanddoesgoodhelpoftheresults.Intheendofthepaper,weprovethatquasi-MonteCarlomethodhashigherefficiencythanMonteCar

8、lomethodusingdiscretizationswhichmeansthevarianceisreducedunderquasi-MonteCarlomethod.Keywords:Hestonmodel;quasi-MonteCarlomethod;Eulerscheme;MilsteinschemeII目录目录第1章绪论.........................................