指數(shù)Ornstein-Uhlenbeck模型下的期權(quán)定價(jià).pdf

1、湖南師范大學(xué)碩士學(xué)位論文指數(shù)nsteinUhlenbeck模型下的期權(quán)定價(jià)姓名：陳琪瓊申請(qǐng)學(xué)位級(jí)別：碩士專業(yè)：概率論與數(shù)理統(tǒng)計(jì)指導(dǎo)教師：楊向群20050301ABS鬻RACTOptionpricingtheoryisanimportantpartofmodernfitlanceTogetherwithtileportfolioselectiontheoDjthecapitalassetpricingtbeol’ytheeffective

2、nesstheoryofmarketandactingissueitisregardedasone《thefivetheorymodulesinmodernfinanceManyscholarshavedoneagreatdealofresearches0nBl地SchelesmodelandobtainedalotofresultswhichisinstrnctivetofinancialpracticeHowewrtsupposin

3、gthattheprocessofstoc蠡priceisoflognormaldistribution，invariableexpectantyieldsnleansmovementofstockpricetowardsjustonedireetionalongwiththechmlgeoftime，Demonstrations弧nlieshaveindicatedthattheexpectmltyiehtsofstockprices

4、arealwayslluctuant，andluaybefunctionsdependingoutimegildstockpricesTherefore，manyscholarspntforwardallkindsofoptionpricingmodelsbyrelaxingseinea8sumingconditionsofBlack—Schol∞modelInthisdissertation，Weconsiderexponential

5、OrnsteinUhlenbeekmodel，whichcorrespondtotheactualeharacteristicsofstockpricemovementbetterThatisparameterelcausedown。trendofstockpricewhilerisingtoSo／hedegreeThisdissertationstudyoptionpricingproblemsunderexponential0rns

6、teinUhlenbeckmodelbyIneansofmathematicaltoolssuchastnartin，galetheoryandstochasticanalysisprovidethepricingformulaoflookbackoptions、makepricesofexponentialOrnsteinUhlenbeckmodelnnderthehypothesisofstochasticinterestratea

7、ndestablishangeneralizedexponentialOrnsteinUhlenbeckmodelwith‘]ump”，todeducetheoptionvalueequationandtheoptionpricingformulatndetailwehavemademainconclusionsasfoltows：(1)Underthehypothesisofexponential0一Umodelandconstant

8、interestrate，usingriskneutralpricingprincipleweobtainthepricingformulasoflookbackoptionintwocasesoffixedstrikepriceandfloatingstrikeprice，andthepatcallparityrelationisdeduced；(2)Underthehypothesisofexponential0一Uprocessm

9、odelandeontinaousstochasticin—terestrate，weobtaintheoptionvalueequationmidthepricingformulaofEuropeancalloption：f3)UnderthehypothesisofexponentialOUprocessmodelm—ineontinuousstochKstieinterestrate，weobtaintheoptionvaluee

10、quationandthepricingformulaofEuropeancalloption；(4)WeestablishangeneralizedexponentialOUmodelwith‘jump“andtheoptionvalneequationandthepricingformulaofEuropeancalloptionarededucedunderincontimmusstochasticinterestratemode