风险价值计算的蒙特卡洛模拟法及其改进

风险价值计算的蒙特卡洛模拟法及其改进二O一O年四月二十日1摘要金融市场的主要功能之一就是对经济活动中的金融风险进行有效分配。风险管理的技术和方法可以使风险承担者更准确地识别、量化和分解其面临的金融市场风险，并根据自己的风险承受能力和风险偏好更有效地选择、剥离和转移风险，从而提高金融市场风险分配的效率，增强金融市场运行的稳定性，最终促进金融市场的健康发展。随着金融市场的发展、金融工具的变革，金融管理的法规越来越健全，方式越来越创新，效率也越来越高，风险管理已成为金融管理的一项重要内容，特别是其在放松管制、全球化和交叉经营的背景下形成的发展趋势，使得风险管理成为金融公司基本的战略性活动。而风险管理的基础与核心是对风险的定量分析和评估，即风险价值VaR的度量和检验。在经济、金融高度一体化、全球化的今天，市场不稳定因素在增加，单个地区单个部门出现的小问题可能会引发区域性或全球性的危机。鉴于此，1988年《巴塞尔协议》对银行最低核心资本充足率作出了不得低于8%的定性要求。该协议随着时间的推移得到了多次修改与完善。其中，三十国集团（groupofthirty）在1993年推出的市场风险信工具——风险价值VaR（Value-at-Risk）模型的计量方法是一项重大的创新，作为一种能全面量化复杂投资组合风险的方法，引起了银行界的广泛关注。并被广泛应用于金融监管部门和金融机构，得到了迅速发展。近几年来，VaR已成为金融界和金融数学界研究的热点课题。本论文将基于蒙特卡洛模拟法的不同分布假设以及波动性的估计方法运用到风险价值VaR的度量和检验中。首先在第一章导论中概述选题的背景和意义、国内外文献综述、研究的内容、方法和创新之处。接着在第二章风险价值VaR的理论、度量和检验中，简介VaR模型、VaR的几种度量方法和几种估计VaR准确性的检验方法。随后在第三章基于资产收益率的统计分析中，介绍了金融资产收益率的统计学特征、资产收益率的统计估计方法和资产收益率的统计学检验等。在第四章风险价值计算的蒙特卡洛模拟法及其改进和检验中，对蒙特卡洛模拟方法做了简单介绍，并介绍了基于蒙特卡洛模拟法的风险价值VaR的计算问题，并讨论了蒙特卡洛模拟法的缺陷与改进问题——即设想将基于条件异方差GARCH模型和t分布的蒙特卡洛模拟法运用到风险价值VaR的度量和检验中，针对金融时间序列往往存在尖峰厚尾的特征和集群波动的现象加以改进，增进风险价值估计的效率，提高估计精度。在第五章基于中国证券市场风险价值VaR的度量和检验的实证分析中，运用了中国证券市场上证指数及其收益率的数据，分别讨论基于GARCH族模型的蒙特卡洛模拟法的VaR度量和检验，基于EGARCH族模型的蒙特卡洛模拟法的VaR度量和检验，以及基于t分布和GARCH模型的蒙特卡2洛模拟法的VaR度量和检验，通过对上述改进过程的实证分析，以及对各种VaR的度量和检验的比较，对基于扩展蒙特卡洛模拟法的各种改进模型的风险度量和检验有更全面的了解，为模型的选择提供依据。最后第六章是本论文的结论。本论文得出的结论是：基于t分布和GARCH族模型的蒙特卡洛模拟法对上证指数日收盘价格的VaR进行计算，效果较好。关键词：VaR；蒙特卡洛模拟法；GARCH模型IAbstractOneoftheimportantfunctionsofthefinancialmarketistoallocatetheriskthatwearefacinginoureconomics.Technologyandmethodsinriskmanagementcanhelptheriskundertakerstodiscern,quantifyandbreakdowntherisktheyarefacinginthefinancialmarket.Besides,theycanchoose,keepawayfromortransfertherisktoothersaccordingtotheirrisktoleranceandpreference.Thus,theefficiencyoftheriskallocationinthefinancialmarketcanbeimproved,thestabilityofthefinancialmarketcanbeenforced,whichwouldhelpthefinancialmarketdevelophealthilyeventually.Asthedevelopingpaceofthefinancemarketquickensandthefinancialinstrumentsevolve,therulesandregulationsofthefinancialmanagementbecomemoreandmoreperfect.Riskmanagementhasbecomeanimportantitemofthefinancialmanagement,especiallyintheatmosphereofderegulation,globalizationandfinancialmixedoperation.Alloftheabovemaketheriskmanagementbecomethebasicstrategicincorporationstoday.Intherecentyears,theglobalfinancialmarketisfullofcrisisandthreatens.Therearemanyexamplesforthetopic:France’sCreditLyonnaisincurredanenormouslosswhentheyspeculatedinrealestateandotherbusiness.TheactsofarecklessanddishonestemployeefinallycausedthedemiseofBaringsbank;oneoftheoldestandvenerablebanksofU.K.Thailand’scurrentaccountdeficitwas6.5%ofGDPwhenitwasforcedtodevalueitsbahtcurrencyin1997,triggeringtheAsianfinancialcrisis.TheUnitedStates’subprimecrisishastremendousnegativeeffectsonAmerica'seconomy,financeandinternationaltransmission.Alloftheselessonsaretellingustheimportanceofstrictlycontrollingandmanagingtheriskoftheassets.Whilethebaseandthecoreoftheriskcontrollingandmanagementarethequantitativeanalysisandestimation,orinotherwords,quantificationfortherisk.Withtheunificationoftheworldeconomyandfinance,unstablefactorsinthemarketareincreasing.Trivialprobleminasingleareaordepartmentmaycauseaworld-widecrisis.So,TheBaselAccord(edition1988)isthefirstonetonormthecapitalofbankinganddrawuptheuniteruleforthecompetitioninallovertheworldbanking.Thisaccordgotsomeamendmentandperfectionastimepassby.Amongallthoseamendmentandperfection,theVaR(Value-at-Risk)methodwhichwasbroughtoutbyGroupofThirtyin1993hasbeenregardedasthegreatinnovation.AsamethodwhichcansystematicallyquantifycomplicatedportfolioithasgivenrisetoawideIIpublicconcernanddiscussionandhasbeenwidelyusedinfinancialsupervisiondepartmentandfinancialinstitutions.Recently,ithasobtainedrapiddevelopmentandbecomethehottopicinfinancialfield.ThispaperistryingtouseadifferentdistributionalhypothesisanddifferentevaluatingmethodsinvolatilitytogetherwithMonteCarlosimulationapproachtocalculateVaR.Inthebeginning,theconceptoftheVaRandtheMonteCarlosimulationapproachwillbeintroduced.Then,itwillcometothedefectsofthegeneralMonteCarlosimulationapproachandimproveitgradually,thatis,usingtheGARCHmodelandtdistributionalhypothesistogetherwiththeMonteCarlosimulationapproach,soastodealwiththe“leptokurtosisandfat-tail”probleminthefinancialtimeseries.Itcouldincreasetheefficiencyoftheevaluationforthemodelandalsoimproveitsprecision.Atlast,anempiricalanalysisbasedonShanghaiStockIndexanditsrateofreturnwillbegiven.Inthecourseoftherevolution,Ihopethatthecomprehensiveknowledgeandthecomputingmethodforthismodelcanbeclearlyilluminated.Keywords：VaR;MonteCarlosimulationapproach;GARCHmodel1目录第一章导论··················································································1第一节选题背景和意义············································································1第二节国内外文献综述············································································3一、国外部分·····················································································3二、国内部分················································································