Cox-Ingersoll-Ross模型的推廣及其Euler-Maruyama方法近似研究.pdf

1、華中科技大學碩士學位論文CoxIngersollRoss模型的推廣及其EulerMaruyama方法近似研究姓名：王曉娟申請學位級別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計指導教師：殷寶健20110515IIABSTRACTStochasticdifferentialequationsarememeapplicableinfinancialeconomicstheyareoftenusedtodescribethedynamicsofasset’s

2、price.Howevermostofstochasticdifferentialequationsinfinancedonothaveexplicitsolutions.Hencenumericalmethodsisaveryusefulmethodifwecancontroltheerrboundofitsnumericalsimulationsthenthismethodcandescribesomefinancialquanti

3、ties.AsoneofthemostimptantnumericalmethodsMonteCarlosimulationshavereceivedmemeattentiononthevaluationoffinancialquantities.InthispaperwemainlyconsidertheEulerMaruyamamethodofMonteCarlosimulations.AitSahaliainhisseminalp

4、aperproposedahighlynonlinearmodelinfinancewhichisanonlinearstochasticdifferentialequationwhereboththedriftdiffusioncoefficientsdonotobeytheclassicallineargrowthcondition.Ofcoursethisnonlinearstochasticdifferentialequatio

5、ndonothaveexplicitsolutioneither.Inadditiontotheusualexternaldisturbancefinancialassetsarealsooftensubjecttotheimpactofunexpectedeventsmemeempiricalevidenceshowsthatthejumpdiffusionprocessismeidealthanthegeneralstochasti

6、cdifferentialequationstomodelanasset’spricetheinterestratestochasticvolatility.ConsequentlybytheAitSahaliasmodelweinthispaperconcentrateoninvestigatingtheEulerMaruyamamethodfahighlynonlinearmodelwithjumpderivingexplicitl

7、ycomparableerrboundsoverfinitetimeintervals.Theseerrboundsimplystrongconvergenceasthetimesteptendstozero.Fconsideringthestochasticvolatilitymanypapersintroducejumpintotheunderlyingpriceprocess.Inthispaperwealsoconsiderth

8、ehighlynonlinearmodelwithjumpasstochasticvolatilitythenstudytheEulerMaruyamamethodthestrongconvergenceoferrboundsunderstochasticvolatilitywithcrelatedjumps.FinallyfromthoseconvergenceresultsweshowthattheEulerMaruyamameth