基于动态NS-DE模型的利率期限结构的研究

发布时间：2018-03-25 19:48

本文选题：国债利率期限结构　切入点：差分进化算法　出处：《浙江财经大学》2014年硕士论文

【摘要】：作为金融产品定价的核心，利率期限结构一直都是金融领域的研究热点。在过去的三十几年中，利率期限结构在理论和实践应用方面都有了长足的发展，其研究范围包括了衍生品定价，资产组合配置，利率预测和模拟等领域。金融经济学家希望从理论上预测利率的变化趋势，而投资者则不断寻找一条能较好描述利率期限结构的曲线来为其投资做出参考。因此，各大机构都在不断选择、开发和改进各种不同的模型，原因就在于利率期限结构广泛的应用范围。本文就试图利用Nelson-Siegel的三因素模型来研究我国国债利率期限结构。在对我国国债做实证研究前还有不少问题需要解决。首先，我国国债有多个交易市场且交易不活跃，因此要对数据进行筛选。柜台国债市场是利用银行柜台，向中小投资者分销国债，，由于其单笔交易量较小，不能用来拟合期限结构。而银行间市场虽交易量大但报价很不活跃，也不适合用作研究利率期限结构。因此，本文只选取了交易所的价格数据作为研究对象。其次，我国发行的国债期限结构不完整，中长期国债过多而短期国债过少，因此造成样本量较少。而本文所使用的Nelson-Siegel模型对短期利率的敏感性较大，若缺乏相关数据会使模型结果不准确，缺乏稳健性。为了解决这一问题，本文选取银行间交易的质押式回购利率作为期限结构中的短期利率的替代值。在实证过程中，本文首先使用状态空间模型来构建动态Nelson-Siegel模型，将模型中的三个参数作为状态空间模型中的状态变量，并假定他们满足向量自回归，采用卡尔曼滤波算法对模型进行求解，同时将模型中的λ作为时变参数，采用最大似然法估计。最终可以得到样本期间的利率期限结构并对未来利率作预测。然后，本文又将由最大似然估计法得到的时变参数λ的最优估计作为固定值，对利率期限结构在不同时点上做静态拟合，并分别采用最小二乘法、遗传算法和差分进化算法来求解模型中的参数。差分进化算法（DE）和遗传算法（GA）都属于全局优化算法，但是他们采用了完全不同的变异和选择的策略。DE有着自适应和同等选择权等特点，相比与标准的进化算法它更易实现，且精确度和鲁棒性更好。本文将用该方法得到的结果与其他算法得到的相比，结果表明用差分进化算法得到的利率期限结构的均方根误差（RMSE）要明显小于其他方法。最后，我们基于由差分进化算法得到的利率期限结构作了利率预测，采用AR、VAR和加入了宏观变量的VAR三种方法，并与用卡尔曼滤波算法得到的预测值作对比。最终得出结论，对于构建动态Nelson-Siegel模型首先构建状态空间模型，使用最大似然估计法来求出模型中重要的时变参数λ，并将它作为固定值使用在二步法的静态拟合过程中。使用差分进化算法求各个时期NS模型的参数以得到样本期内的利率期限结构。对样本内模型的参数构建自回归模型，若预测步长较短，则建议使用AR模型，若预测步长较长，则建议使用VAR模型，从而预测出利率期限结构。本文的创新点有：采用差分进化算法（DE）估计模型参数，并对比了常用的NLLS和GA算法，得出DE算法在精确度上的优势；用状态空间模型来构建动态NS模型，用卡尔曼滤波来对参数进行求解和预测，并对比AR、VAR模型；将宏观因素加入到VAR模型中，观察其是否会加强模型的预测能力。
[Abstract]:As the core of financial product pricing, interest rate term structure has always been the research topic in the field of finance. In the past 30 years, the term structure of interest rate in theory and practical applications have been greatly developed, the scope of the study include derivatives pricing, portfolio allocation, interest rate forecasts and financial economists hope simulation and other fields. To predict the trend of interest rate in theory, and investors are constantly looking for a better description of the term structure of interest rates for the investment curve to make the reference. Therefore, the major institutions have been selected, developed and improved various models, the reason lies in the scope of application of the term structure of interest rates widely. The three factor model this paper attempts to make use of Nelson-Siegel to study the term structure of interest rates in China.
There are many problems need to be solved in doing empirical research on China's government. First, China's national debt has more than one trading market and the transaction is not active, so to filter the data. The counter bond market is the use of the bank counter, distribution of medium and small investors to bonds, because of its single transaction amount is small, can not be used to fit the term the structure of the inter-bank market. Although a large volume of transactions but the quotation is not active, is not suitable for the study on the interest rate term structure. Therefore, this paper only selects the price data exchange as the research object. Secondly, China's debt maturity structure is not complete, long-term bonds rather than short-term debt is too small, resulting in the sample is small. While the Nelson-Siegel model used in this paper to short-term interest rate sensitivity is larger, if the lack of relevant data to the model results are not accurate, lack of robustness. In order to solve this problem in this paper. The pledge rate of the interbank transaction is chosen as the replacement value of the short-term interest rate in the term structure.
In the empirical process, this paper constructs a dynamic Nelson-Siegel model using state space model, the three parameter model as state variables in the state space model, and assume that they satisfy the vector autoregression, using Calman filtering algorithm to solve the model, while the model of lambda as time-varying parameters are estimated using the maximum likelihood method. Get the term structure of interest rates during the sample period and to predict the future interest rate. Then, this paper will from maximum likelihood estimation as a fixed value method to get the optimal estimation of time-varying parameter, the term structure of interest rate in different time points and do static fitting by least squares method, genetic algorithm and the differential evolution algorithm to solve the model parameters of the differential evolution algorithm (DE) and genetic algorithm (GA) is a global optimization algorithm, but they used a completely different variable .DE strategy and selection have different adaptive and equal option characteristics, compared with the standard evolutionary algorithm which is more easily achieved, and the accuracy and better robustness. The results obtained using this method are compared with other algorithms, the results show that the root mean square error of the term structure of interest rate differential evolution algorithm to the (RMSE) is significantly less than the other methods. Finally, we term structure of interest rates by differential evolution algorithm based on the interest rate forecast by AR, VAR and VAR joined the macroscopic variables of the three methods, and compared with the predictions obtained by Calman filtering value. The final conclusion, for the construction of the dynamic Nelson-Siegel model is firstly constructed state space model, using the maximum likelihood estimation method to calculate the variable parameter in the model are important, and it is used as a fixed value used in the static fitting process of two step in. With the parameters of differential evolution algorithm for each period of the NS model to get the term structure of interest rates in the sample period. The construction of the autoregressive model parameters in sample model, if the prediction step is short, it is recommended to use the AR model, if the prediction step is longer, it is recommended to use the VAR model to predict the term structure of interest rates.
The innovations of this paper are: using differential evolution algorithm (DE) to estimate the model parameters, and compared the NLLS and GA algorithm, the advantages of DE algorithm in terms of accuracy; using the state space model to build dynamic NS model, using Calman filter to solve and prediction of parameters, and compared with AR, VAR model the macro factors; added to the VAR model, to observe whether it will strengthen the prediction ability of the model.

【学位授予单位】：浙江财经大学
【学位级别】：硕士
【学位授予年份】：2014
【分类号】：F224;F812.5;F822.0

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