冪型歐式期權定價的鞅方法.pdf

1、哈爾濱理工大學碩士學位論文冪型歐式期權定價的鞅方法姓名：張淑娟申請學位級別：碩士專業(yè)：應用數學指導教師：孔繁亮20090301MartingaleMethodofPowerPayoffEuropeanOptionAbstractThefamousBlack—ScholesformulaiSabreakthroughofmodernmathematicalfinanceInrecentyears，theresearchoffinancia

2、lderivativeshasgainedrapiddevelopmentasaneffectivemeansofventureevadingandinvestment，especiallyfortheoptionTheoptionhasthefunctioninventureevading，ventureinvestmentandthepropertiesofagilityanddiversityetc，thereforetheopt

3、ionhasbeenbecomeoneofthemostenergeticfinancialderivativesThesecuritiesmarketwassetupnearlytwentyyearsinChina，howtolearnfromWesternfinancialderivativesecuritiespricingtheorytostrengthenthefinancialderivativespricingtheory

4、inChinaanditsapplicationsareofgreatsignificanceTheinternalandexternalactualityofoptionpricingandmartingaleanalysisareshowninthisthesis，meanwhile，someconceptionsandconclusionsofmartingaleanalysis，optionpricingtheoriesandt

5、heclassicalBlackScholesmodelareintroduced，theyarethebasicofthispaper’SmaincontentsInthepaperthecurrentpowerpayoffEuropeanoptionspricingmodelsareimprovedinordertobemorecoincidentwiththepracticalfinancialmarket，theproblems

6、ofpowerpayoffEuropeanoptionarestudiedandthepricingformulasaregotmakinguseofmartingaleprocesses，theyaretheextensionoftheclassicalBlackScholesmodelThemainresultsareasfollows：Assumingborrow—lendinginterestrateisdifferent，th

7、atistheborrowinginterestismorethanlendinginterest，thepricingformulasofcallandputpowerpayoffEuropeanoptionsarediscussedatthetimeofmaturityofoptionusingthemartingalemethodThentheoptionformulasofparityandBi—directionoptionp

8、ricingaregotwithexplicitexpressionmakinguseofGirsanovtheoriesThecallandputpowerpayoffEuropeanoptionspricingformulasarOgotbythematingaleanalysismethodandtheformulaofnonlinearFeynmanKacintheconditionthattheborrowlendingpro