利率期限结构的随机多项式模型

发布时间：2018-06-27 00:08

本文选题：利率期限结构 + 随机微分方程　；参考：《华中科技大学》2012年硕士论文

【摘要】：在全球金融市场不断创新发展，金融理论研究不断深化，同时伴随着利率市场化的深入和多层次资本市场的逐步建立等一系列的背景下，利率期限结构理论研究日益成为金融界研究的热点内容。本文是按照定性的思维模式对期限结构的随机多项式模型进行深入研究。在本文中，作者首先对利率期限结构研究的背景和意义加以评述，其次，分别介绍了两种阶段理论模型的发展及研究现状，并对涉及的每一种理论进行展开说明。最后简要概况了两个典型的期限结构模型，并在此基础上对这些模型进行了扩展，提出了本文要点。本文首先分四个方面进行简要地分析和评价传统的期限结构理论。接着，分别从静态和动态，单因素和多因素，国内国外，理论和实证等方面进行评述现代的利率期限结构模型。本文主要研究利率期限结构的随机多项式模型，在进行研究之前，作者首先简要介绍了非参数的Ait-Sahalia模型和一般的参数模型，并且基于这两种模型提出了本文的主要内容。但是并不是每一个模型都能够很好的拟合利率，并对利率进行分析和预测，因此选择一个“良好”的模型至关重要。一个好的模型应该表现出如下特质，比如非负的全局解的存在唯一性，有界特性，数值解的收敛性，数值解逼近显示解等。一般情况下，方程没有复杂的解，，因此，需要用数值解逼近真实解。本文通过随机微分方程理论建立的这种新的模型，证明了依概率1存在唯一的非负全局解和矩的有界性。最后文章也证明了数值解能够为债权定价。
[Abstract]:With the continuous innovation and development of global financial market, the deepening of financial theory research, the deepening of interest rate marketization and the gradual establishment of multi-level capital market, The theory of term structure of interest rate has become a hot topic in the field of finance. In this paper, the stochastic polynomial model of term structure is studied according to the qualitative thinking mode. In this paper, the author first reviews the background and significance of the study on term structure of interest rate. Secondly, the author introduces the development and research status of the two stages of theoretical models, and explains each of the theories involved. In the end, two typical term structure models are briefly summarized, and on the basis of these models, the main points of this paper are put forward. Firstly, this paper briefly analyzes and evaluates the traditional term structure theory in four aspects. Then, the paper reviews the modern term structure model of interest rate from static and dynamic aspects, single factor and multiple factors, domestic and foreign, theoretical and empirical. In this paper, the stochastic polynomial model of term structure of interest rate is studied. Before the study, the non-parametric Ait-Sahalia model and the general parametric model are briefly introduced, and the main contents of this paper are presented based on these two models. However, not every model can fit the interest rate well, and analyze and predict the interest rate, so it is very important to choose a "good" model. A good model should show the following characteristics, such as the existence and uniqueness of the non-negative global solution, the boundedness, the convergence of the numerical solution, the approximation of the numerical solution to show the solution, and so on. In general, the equation has no complex solution, so it is necessary to approximate the real solution with numerical solution. In this paper, we prove the boundedness of the unique nonnegative global solutions and moments according to probability 1 by using this new model of stochastic differential equation theory. Finally, the paper also proves that the numerical solution can price the claims.
【学位授予单位】：华中科技大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：F224;F820

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