欧式看涨期权定价微分方程非标准有限差分数值解法

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1、哈尔滨工业大学理学硕士学位论文AbstractInthe1970s,BlackandScholesonthebasisoftheresearchonfinancialmarkets,pioneeringforoptionpricing,presentstherelevanttheoriesandmodels.OptionpricingresearchofBlackandScholeshadalsopromotedthedevelopmentofmathematicalfinance.Innovationistheuseofnon-standardfinitedif

2、ferencemethodforsolvingtheBlack-ScholesEuropeancalloptionpricingdifferentialequation.Theadvantageofnon-standardfinitedifferenceschemeistokeeppositiveandboundedofthesolutions,whichistheoptionpricerequirements.Theconvergenceandstabilityofdifferenceschemecanbeholdinthecaseofpositivecondi

3、tions.Andtimestepcanbedeterminedbythespatialsteplength.InfactBlack-Scholesoptionpricingmodelwiththeanalyticalsolutionundercertaininitialandboundaryconditions,buttheformoftheanalyticalsolutionistoocomplex.Andtheanalyticalsolutiondoesnotnecessarilyexistundercertaininitialandboundarycond

4、itions,ResearchofusingofnumericalmethodtosolveBlack-Scholesoptionpricingmodelisclearlynecessary.Firstdescriptdevelopmentandperfectingprocessoptionpricing.Wesupposemorepressclosetothepriceofoptionsandstockoftheoperationmechanismofthefinancialmarkets.WededucedifferentialequationofBlack-

5、Scholesoptionpricingusingtherandomprocessandtectonicportfolioskills,combinedwiththebasictheorysuchasdifferentialequation.Andweexplainhowtoaffectthepriceoftheoption,accordingtotheanalysisoffactorsinfluencingtheoptionpriceinthedifferentialequation.Weraiseprinciplesofestablishingthenonst

6、andardfinitedifferencescheme,wehowtoselectthedenominatorfunctionintheprocessofconstructing.Accordingprinciplesofestablishingthenonstandardfinitedifferencescheme,firstweapplysub-equationmethodtoestablishnonstandardfinitedifferenceschemeoftheBlack-ScholesEuropeancalloptionpricingdiffere

7、ntialequation.Theconvergenceandstabilityofdifferenceschemecanbeholdinthecaseofpositiveconditions.Itisconcludedthatthecorrespondingtheorem.Themethodofcorrectionequationanalysisisusedtoanalyzethedifferencescheme.Thedifferenceschemeisgoodreactionrateinfluenceonnumericalsolution.Thentrans

8、forma