金融市场波动的多分形测度及其应用研究

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1、西南交通大学博士学位论文金融市场波动的多分形测度及其应用研究姓名：王鹏申请学位级别：博士专业：企业管理指导教师：王建琼20100501第1I页西南交通大学博士研究生学位论文检验、动态分位数回归(Dynamicquantileregression)检验、bootstrap等后验分析方法，实证比较了不同波动模型的VaR和ES测度精度。(5)MFV方法在金融衍生品定价中的应用研究。以中国股票市场中的4只认购权证(深高CWBl、上港CWBl、马钢CWBl、武钢CWBl)为例，在B．S定价模型框架下，计算了基于多分形波动率测度参数的权证价格；然后，以权证产品的市场价格为基准，与基于其它常

2、用波动率测度参数的定价精度进行了比较。关键词：多分形理论；波动率测度；ARMA模型；波动率预测；金融风险测度：衍生品定价西南交通大学博士研究生学位论文第1II页AbstractInmodernfinancialtheory,descriptionoffinancialassetvolatilityactasoneofthecorerole．Theusefulnessofvolatilitymeasurementanditsdynamicshasimportantsignificancetoacademicandpractice．Measurementsandmodelstode

3、scribeandpredictfinancialassetvolatilityaboundandmanyvolatilitymodels，suchasGARCHmodels，SVandInRV-ARFIMA，arepresentedtobeusedinfinancialtheoryandpractice．However,thesemainstreammodelsarealldefective，hencebringoninconsistencybetweentheoryinferrerandempiricalresults．Asanpowerfultooltodescribec

4、omplexityoffinancialvolatility,multifractaltheorycanfetchuplimitationsoftraditionalways．Howevermostofthesestudiesfocusonempiricaltestsofmultifractalityindifferentfinancialdatasets．Sowewonderwhethermultifractalanalysiscancontributetothemeasurementandforecastingaccuracyofvolatilityinfinancialm

5、arkets．Alongwiththisnotion，weproposeaso．calledmultifractalvolatility(MFV)measureanditsdynamicmodelbasedonthemultifractalspectrumofhigh—frequencypricemovementswithinonetradingday．WefurtherexaminedMFV’Sperformanceinvolatilityforecasting，riskmeasuringandfinancialderivativespricing．Themainresear

6、chcontentareasfollows：(1)Researchonseveralcomplexfeaturesofvolatility,suchasinspectiontodistributioncharacteristicsoffinancialreturnsbasedondifferentfrequencydataanddescriptivestatistics，QQplotandprobabilitydistributionplot；analysisofhigher-momentsvolatilitycharacteristicsbasedonG瓜SK-Mmodel；

7、researchoflong．memoryfeatureofvolatilitybasedonR／Sanalysis．(2)Constructionandmodelingofmultifractalvolatility(MFV)．Throughonegroupofmultifractallanguage，weempiricallystudiedmultifractalfeatureoffinancialvolatilityandfurtherdiscussedrelationshipbetw