卢策-毕业论文-反常扩散模型在风险管理中的应用

毕业设计（论文）题目反常扩散模型在风险管理中的应用姓名卢策学号3090411021专业班级09信计1班指导教师吕龙进学院信息科学与工程学院完成日期2013年6月1日宁波理工学院I摘要随着世界经济和中国金融市场的不断发展，各种行业尤其是金融行业的投资风险日益成为了各种机构无可避免的重要问题，所以风险管理愈发显得重要，也成为了日益紧迫的任务。在各种投资风险管理手段中，VaR方法以其精密的科学性和广泛的实用性脱颖而出，成为了风险管理的重要方法。但是随着市场的不断发展，各种不可预知的因素导致市场走向千变万化，这样一来就暴露出了经典风险计算模型的不足。首先，本文讨论反常扩散的特征，以及反常扩散下的概率密度函数的特征，结合大数定律运用蒙特卡洛模拟法，模拟出反常扩散下市场利率分布呈尖峰厚尾性质的图像。其次，本文将反常扩散模型应用到风险管理中去，并计算此时的VaR值。最后我们得出结果，并希望此模型能对现今的风险管理模型的发展起到推动的作用。关键词：风险管理；VaR；反常扩散模型；蒙特卡洛模拟法IIAbstractWiththecontinuousdevelopmentofworldeconomyandChina'sfinancialmarket,allkindsofindustries,especiallytheinvestmentriskofthefinancialindustryhasincreasinglybecomeanimportantandinevitableproblemofvariousinstitutions.Therefore,riskmanagementhasbecomeevenmoreimportantaswellasapressingtask.Amongallkindsofmanagementmethodsofinvestmentrisk,VaRmethodmakesitselfstandoutwithitsprecisescientificityandextensivepracticality,andhasbecomeanimportantmethodofriskmanagement.However,withthedevelopmentofthemarket,allsortsofunpredictablefactorsmakethepresentmarketever-changing.Asaresult,itgraduallyrevealsthedisadvantagesoftraditionalRiskcalculationmodel.Inthispaper,wefirstdiscussthefeaturesofanomalousdiffusionanditstheprobabilitydensityfunctionundertheanomalousdiffusion.Then,usingtheMonteCarlosimulationmethodbasedonthelawoflargenumberstosimulatethedistributionofmarketinterestrates,weobtainthedistributionfollowsheavytailundertheanomalousdiffusionmodel.Secondly,weshowhowtoapplytheanomalousdiffusiontotheriskmanagement,andcalculatetheVaR.Finally,wegetthecalculationformulaofVaRunderanomalousdiffusion,andhopethismodelcanhelpthedevelopmentofmodernriskmanagementmodel.Keywords:Riskmanagement；VaR；Anomalousdiffusionmodel;MonteCarloSimulation，MCSIII目录摘要错误!未定义书签。Abstract............................................................II目录III第1章概述.........................................................11.1引言.................................................................................................................11.2风险的类型.....................................................................................................21.2.1市场风险........................................................................................21.2.2信用风险........................................................................................21.2.3流动性风险....................................................................................31.2.4操作性风险....................................................................................31.2.5法律风险........................................................................................41.3风险管理的意义与应用背景.........................................................................41.3.1风险管理的定义............................................................................41.3.2风险管理的意义............................................................................51.3.3风险管理的概念............................................................................51.3.4风险管理的发展历史....................................................................51.4本文工作.........................................................................................................7第2章风险管理的VaR方法...........................................92.1风险管理的VaR方法介绍............................................................................92.1.1VaR方法的出现.............................................................................92.1.2VaR方法的作用.............................................................................92.1.3VaR方法的表达...........................................................................102.2计算VaR值的方法......................................................................................102.2.1历史模拟法..................................................................................102.2.2方差——协方差法......................................................................112.2.3蒙特卡洛模拟法..........................................................................122.3三种VaR值计算方法应用的范围以及缺陷分析.......................................12IV2.3.1历史模拟法应用范围及缺陷......................................................122.3.2方差——协方差法应用范围及缺陷..........................................132.3.3蒙特卡洛模拟法应用范围及缺陷..............................................132.3.4三种VaR计算方法的直观比较.................................................142.4我国VaR风险度量方法应用存在的问题讨论..........................................152.4.1市场缺陷......................................................................................152.4.2操作缺陷......................................................................................152.5反常扩散应用于VaR的优点.......................................................................15第3章反常扩散模型的模拟..........................................173.1反常扩散模型的概念...................................................................................173.2反常扩散模型的提出...................................................................................173.3反常扩散模型的模拟...................................................................................19第4章反常扩散模型在VaR方法中应用................................234.1正态分布下VaR的具体计算.