MCMC方法在利率期限结构模型中的应用

发布时间：2018-05-31 00:43

本文选题：MCMC方法 + 利率期限结构模型　；参考：《暨南大学》2012年硕士论文

【摘要】：动态资产定价理论运用套汇和平衡理论来得到资产价格和经济基础之间的关系，其中包括：状态变量，结构参数和市场价格风险。连续时间模型是这种方法的核心，因为它具有易处理性。在大多数情况下，这些模型能够得到封闭形式的解或者容易计算各种我们感兴趣对象的方程，例如，各种价格或最佳的投资组合加权。动态资产定价模型的经验分析解决了一些方面的问题，从观察到得价格上提取了一些关于潜在状态变量，，结构参数和市场价格风险的信息。而利用贝叶斯推断是要得到参数，状态变量X，在观察价格Y上的条件分布。这个后验分布p，，结合了模型和观察价格两方面的信息，是在参数和状态变量的基础上进行推断的关键。这篇文章主要讨论了利用Markov Chain Monte Carlo(MCMC)方法在连续时间资产定价模型中得到后验分布。本文讨论的连续时间定价模型主要是利率期限结构模型，利用MCMC方法从这些复杂的高维分布中抽样，并在空间，X上产生一条马尔可夫链它的目标分布是p θ，X Y。这种蒙特卡洛方法利用这些样本进行积分，并最终进行参数估计，状态估计和模型比较。在连续时间定资产定价模型中确定p θ，X Y是比较困难的。原因如下：第一，观察到的价格是离散的而这个模型在理论上要求价格和状态变量在时间上是连续的。第二，从研究者的角度来看，状态变量是潜伏的。第三，p θ，X Y是很高维的分布，普通的抽样方法行不通的。第四：特别是对于利率期限结构模型来说，参数是非线性的甚至是非解析形式的。在这篇文章中我们将说明MCMC方法能解决上述问题。在文章的第二，三部分，我们将给出贝叶斯推断和MCMC方法的简要综述。在第四部分，我们将着重讨论MCMC方法在利率期限结构模型中的的具体应用。
[Abstract]:Dynamic asset pricing theory uses arbitrage and equilibrium theory to obtain the relationship between asset price and economic base, including: state variables, structural parameters and market price risk. Continuous time model is the core of this method because it is easy to deal with. In most cases, these models can obtain closed form solutions or can easily calculate the equations of various objects of interest, for example, various prices or optimal portfolio weights. The empirical analysis of dynamic asset pricing model solves some problems, and extracts some information about potential state variables, structural parameters and market price risks from observed prices. By using Bayesian inference, the conditional distribution of the parameter, the state variable X, and the observed price Y is obtained. This posterior distribution, which combines the information of model and observed price, is the key to infer on the basis of parameters and state variables. In this paper, we mainly discuss the posteriori distribution in the continuous time asset pricing model by using the Markov Chain Monte Carlogne MCMC method. The continuous time pricing model discussed in this paper is mainly the term structure model of interest rate. The MCMC method is used to sample these complex high-dimensional distributions, and a Markov chain is generated on space X, the target distribution of which is p 胃 X Y. The Monte Carlo method uses these samples to integrate, and finally carries out parameter estimation, state estimation and model comparison. It is difficult to determine p 胃 X Y in the continuous time fixed asset pricing model. The reasons are as follows: first, the observed price is discrete and the model theoretically requires price and state variables to be continuous in time. Second, from the perspective of researchers, state variables are latent. The third p 胃 X Y is a very high dimensional distribution, and the ordinary sampling method is not feasible. Fourth, especially for the term structure model of interest rate, the parameters are nonlinear and even non-analytical. In this article we will show that the MCMC method can solve these problems. In the second and third parts, we give a brief overview of Bayesian inference and MCMC methods. In the fourth part, we will discuss the application of MCMC method in the term structure model of interest rate.
【学位授予单位】：暨南大学
【学位级别】：硕士
【学位授予年份】：2012
【分类号】：O212.8;F820

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