【作者】 魏法明；

【导师】 陈伟忠；

【作者基本信息】 同济大学 ， 技术经济及管理， 2008， 博士

【摘要】 随机规划模型作为一个强大的工具被广泛地应用到资产配置、资产负债管理以及投资组合管理等金融领域。随机规划需要生成大量的情景元素来模拟未来的不确定性,以此构建情景树作为随机优化模型的输入,得到出模型的全局最优解,并据此给金融规划提供决策建议。因此,不确定性的准确刻画非常重要,其决定了多阶段投资组合决策成败。本文就随机规划中情景生成模型进行了深入研究,主要研究工作及结论如下:1、构建了基于GARCH的情景生成模型。GARCH族模型能很好地刻画金融资产收益的“波动率聚从”,“尖峰厚尾”及“不对称效应”现象。本文利用GARCH模型的突出优点,针对不同类别的资产,建立了相应的AR模型及GARCH模型用于情景生成。主要的研究工作包括四个方面:一元GARCH情景生成模型的研究;多元GARCH情景生成模型的研究;对一元GARCH和多元GARCH模型生成的随机情景质量进行了比较;构建了一个2阶段情景树。数值研究发现:一元和多元GARCH模型生成情景的累计概率分布与历史数据较为接近,这表明GARCH模型用于情景生成是可取的。其次,多元GARCH模型生成的情景的累计概率分布要比一元模型更接近历史分布,这反映了多元GARCH模型更适合于资产组合时情景生成,原因是多元GARCH模型由于能把资产收益之间的相关性纳入考虑范围,更符合实际情形。不足之处是,多元GARCH模型结构复杂,参数估计困难,当组合资产间的相关性较低时,可考虑一元GARCH模型作为其替代。2、单变量的矩匹配情景模型生成研究。Hoyland和Wallace最初提出了矩匹配法生成情景的一般框架,但存在许多缺陷,如局部最优解,存在套利等。本研究改进了其模型,主要做了三方面的工作:单变量的矩匹配情景生成模型研究;套利机会的排除方法研究;历史情景描述性特征的反映;给出了另一种矩匹配情景生成的思路。单变量的矩匹配模型,以情景的概率作为优化模型的决策变量,通过逼近历史收益序列的各阶中心矩,生成单阶段情景树,然后进一步结合向量自回归模型生成多阶段情景生成。优化模型中增加了一个约束可以有效解决生成情景的描述性特征问题。此外,把收益区间适当剖分一般可避免套利的发生。第二种方法的思路是每次只产生一个随机变量的离散边际分布,然后在所有离散边际分布的基础上生成联合分布的结果。然后运用各种变换迭代逼近目标矩和相关矩阵。实证研究表明,该方法不仅可以避免大量的数值计算,而且得到的情景取得和历史数据较为吻合的统计特征。3、基于聚类情景生成的研究及应用K-均值聚类法可以对大量的数据进行剖分,建立一个单水平的类集,可以将样本数据集剖分成K个互相独立的类,可以被用来构建资产收益情景。本部分研究应用此算法,进行情景生成的尝试,并与矩匹配法生成的情景进行统计意义上的对比。研究表明,K均值聚类法尽量从历史数据的角度出发,挖掘不同资产的收益之间的相关关系;并且给出了只要增加一个情景就可以避免套利的简便易行的线性规划方法。该情景生成方法除了具有矩匹配情景生成方法的优点外,还在对统计特征的刻画上有所改进,能以更少的情景更精确地刻画统计特征。这为选取少量的情景以降低问题的规模奠定了基础,更重要的是为多阶段情景生成引入了一种全新的思路。4、向量自回归(VAR)模型的情景生成研究及应用向量自回归模型是金融数据分析中一种常用的模型,常用于预测相互联系的时间序列系统及分析随机扰动对变量系统的动态冲击。本文做了利用VAR模型生成情景的尝试,主要工作如下:构建了包含四个股指收益的VAR模型;基于蒙塔卡罗模拟的情景生成生;多元GARCH模型与VAR模型所生成情景在统计意义上比较;应用VAR建立了一个2阶段的情景树。研究表明:VAR生成情景在统计意义上较多元GARCH更为可靠,其情景的累计概率分布更接近于历史数据。此外,VAR模型结构较多元GARCH简单,除了体现变量间的相关性,还能很好地反映不同决策阶段的相关性,是一种更优良的情景生成技术。5、基于Copula函数的情景生成。Copula函数有三个优点:多元随机变量的联合分布灵活构造,非线性相关性的准确描述及收益非正态分布的支持,这些优点利于构建更准确的情景生成模型。本部分做的工作:给出一个基于Copula函数,GARCH模型及极值理论的一个多资产收益情景生成步骤。将此方法得到情景与VAR,聚类法进行统计意义上的比较工作。研究表明,此方法所生成情景的在统计特征上最接近历史数据,是最为可靠的情景生成方法。更多还原

【Abstract】 Stochastic Programming Model (SPM), as a powerful tool, has been widely used to such financial fields as asset allocation, Asset and liability management (ALM), and securities’ portfolio management and so on. SPM need generate many scenarios simulating future uncertainty of which scenario tree acted as input to stochastic optimization is constructed on basis. The global optimal solution of model is the basis of decision-making advices for financial programming. So, the description of uncertain economic scenario plays a great role in the success of the decision-making in multistage investment portfolio. This paper focuses on study of several models for scenario generation. The main research work and conclusions is as following:1、building the scenario generation model based on GARCH model.GARCH family models can depicts the following phenomena of asset return in financial market: volatility clustering, non-asymmetric, leptokurtic features. The paper utilizes these advantages to build the corresponding AR and GARCH models according to the respective asset kinds’ features. The main work done here includes four aspects: scenario generation model based on univariate GARCH model. Scenario generation model based on multivariate GARCH model. Comparison of the two kinds of models in statistics. Construction of two-period scenario tree.The numerical result shows that the two kinds of GARCH models can produce scenarios with similar statistical attributes to historical data which tells us that the GARCH family model is sufficient to scenario generation. Secondly, the multivariate GARCH model has a better performance than the univariate one maybe for the reason that it can take the correlation among the assets into consideration. However, multivariate GARCH model also has a disadvantage, much too complex model structure and difficult parameter estimation. Univariate GARCH model can replace multivariate one when the correlation among assets are small.2. Single variable moment-matching scenario generation model.Hoyland and Wallace firstly give a common framework to generate scenario based on moment-matching which builds a scenario tree by solving a non-linear optimization model and getting the value and probability of scenario. It has some pitfalls such as local optimal solution and arbitrage opportunity existence and so on. The work here improves the above model which includes three aspects: study of Single variable moment-matching scenario generation model; how to avoid the arbitrage opportunity; how to depict the descriptive features and another idea of scenario generation based on moment-matching.Single variable moment-matching scenario generation model takes the probability of the scenario’s value as the variable decided and construct the single-period scenario tree by approaching the four center moment of historical return data and then generate multistage tree with the help of VAR model. The article adds a constraint to solve the problem of ’descriptive feature’ ignored in scenario generation in the long term. Besides the above, the idea of ’partition of return interzone’ assures that it can avoid arbitrage opportunity.The second way is to produce one random variable’s discrete marginal distribution once and then produce a joint distribution on the basis of all the produced discrete marginal distribution, finally, approaches the aimed moment and correlation matrix by all kinds of transforms. Empirical study shows that this way avoid vast numerical computation and can get the scenario with much similar statistical feature of the historical return.3. Research on generating scenario by clustering and application.K-means clustering can partition large set of data and build a single-level class, dividing the sample data into K independent clusters as the asset return scenario. The research work here tries this way to generate scenarios and compare it with the way of moment-matching statistically. The result here shows that this method tries not to rely on model to produce scenario but to find the correlation between asset returns from historical data. At the same time, the article gives a linear programming method that adding a scenario in order to avoid arbitrage. The empirical study shows that the way not only has the advantage of moment-matching way, but also has improved in depicting statistical features, which can much more accurately depict statistical features through much less scenarios. The methods lay the foundation for decreasing the size of problems by much less scenario, especially introduces a new idea for multistage scenario generation.4、Research on scenario generation based on VAR and its applicationVAR model is a usual way for financial data analyzing and often used to forecast connected time serials system and analyzes dynamic impulsion to variable system by random disturbance. The research work here includes construction of proper VAR model of four indexes’ return; Production a lot of scenarios by Monte Carlo simulation, Comparison of the effect between VAR and multivariate GARCH model; Constructing a 2-period scenario tree.The research result shows that VAR models performs better than multivariate GARCH model for its CDF is nearer to historical data than the multivariate GARCH model. Besides that, VAR models are simpler. It not only demonstrates the correlation among variables and periods. So it is a excellent way for scenario generation.5. Scenario generation based on Copula function.Copula function mainly has three advantages as follows: it can flexibly construct multi-dimension random variable joint distribution; it can accurately depict nonlinear correlation; It can can overcome the limitation of the normal distribution hypothesis of assets return. Here this article does the following research work: Bring forward a comprehensive way to generate scenarios based on Copula function, GARCH model and extreme value theory; Compare its scenario effect with VAR and clustering. The numerical test shows that the way proposal by us is a more reliable method than the other two ones.更多还原