跳-擴(kuò)散模型下未定權(quán)益定價問題的研究.pdf

1、西北工業(yè)大學(xué)碩士學(xué)位論文跳擴(kuò)散模型下未定權(quán)益定價問題的研究姓名：蘇軍申請學(xué)位級別：碩士專業(yè)：統(tǒng)計學(xué)指導(dǎo)教師：趙選民20050301AbstractContingentclaimsvaluationisoneofthekernelproblemsonfinancialmathematicsAmassoffinancepracticehasindicatedthatthereisaseriouswarpbetweenthehypothesi

2、sofBlackScholesmodelabouttheunderlyingassetpriceandtherealisticmarkets.Thesolutionstocontingentclaimsaredeterminedbythealterationlawoftheunderlyingassetprices.SotheimprovementonBlackScholesmodelatractswideatentionandmany

3、newmodelsareproposed.Thisdissertationcontributestooptionpricingprobleminjumpdifusionmodelsandproposesanewassetpricesmodel.Thisthesishasthefollowingcontents:l.Completesecuritymarketswithdiscontinuoussecuritypricearestudie

4、d.UsingmartingalemethodgeneralpricingformulaofEuropeancontingentclaimsisderivedandEuropeanoptionandputcallparityisanalyzed.Theseresultsaregainedunderunderlyingassetpricebeingdrivenbyajumpdifusionprocess.2.Anewmethodo#opt

5、ionpricing(i.e.insuranceactuarypricing)isintroduced.ItisprovedthatmartingalepricingisconsistentwithinsuranceactuarypricinginaPoissonjumpdifusionmodel.PricingwarpsonBlackScholesmodelareanalyzed.3.Anewmodelisproposedwherea

6、ssetpricesaregivenbythecombinationoffinitestateQprocessstochasticvolatilityandacompoundPoissonprocess.ThegeneralformulaofEuropeancalloptionpricinghasbeenderivedandtheresultsofHullandWhitearegeneralized.Atlastananalysisan

7、dnumericalsimulationsforjumpdifusionmodelwithQprocessvolatilityaregiven.4.Theproblemofcontingentclaimsvaluationisdiscussedwhentheunderlyingassetpriceisajumpdifusionprocessunderstochasticinterestrates.Usingmartingalemetho

8、dpricingformulaofEuropeancontingentclaimsisderivedandputcallparityisanalyzed.PricingformulaofEuropeanoptionisalsogivenwhenriskassetpayscontinuousdividends.Keywords:BlackScholesmodelcontingentclaimsjumpdifusionprocessputc