本文選題：國債利率期限結(jié)構(gòu)　切入點：差分進化算法　出處：《浙江財經(jīng)大學(xué)》2014年碩士論文

【摘要】：作為金融產(chǎn)品定價的核心，利率期限結(jié)構(gòu)一直都是金融領(lǐng)域的研究熱點。在過去的三十幾年中，利率期限結(jié)構(gòu)在理論和實踐應(yīng)用方面都有了長足的發(fā)展，其研究范圍包括了衍生品定價，資產(chǎn)組合配置，利率預(yù)測和模擬等領(lǐng)域。金融經(jīng)濟學(xué)家希望從理論上預(yù)測利率的變化趨勢，而投資者則不斷尋找一條能較好描述利率期限結(jié)構(gòu)的曲線來為其投資做出參考。因此，各大機構(gòu)都在不斷選擇、開發(fā)和改進各種不同的模型，原因就在于利率期限結(jié)構(gòu)廣泛的應(yīng)用范圍。本文就試圖利用Nelson-Siegel的三因素模型來研究我國國債利率期限結(jié)構(gòu)。 在對我國國債做實證研究前還有不少問題需要解決。首先，我國國債有多個交易市場且交易不活躍，因此要對數(shù)據(jù)進行篩選。柜臺國債市場是利用銀行柜臺，向中小投資者分銷國債，，由于其單筆交易量較小，不能用來擬合期限結(jié)構(gòu)。而銀行間市場雖交易量大但報價很不活躍，也不適合用作研究利率期限結(jié)構(gòu)。因此，本文只選取了交易所的價格數(shù)據(jù)作為研究對象。其次，我國發(fā)行的國債期限結(jié)構(gòu)不完整，中長期國債過多而短期國債過少，因此造成樣本量較少。而本文所使用的Nelson-Siegel模型對短期利率的敏感性較大，若缺乏相關(guān)數(shù)據(jù)會使模型結(jié)果不準(zhǔn)確，缺乏穩(wěn)健性。為了解決這一問題，本文選取銀行間交易的質(zhì)押式回購利率作為期限結(jié)構(gòu)中的短期利率的替代值。 在實證過程中，本文首先使用狀態(tài)空間模型來構(gòu)建動態(tài)Nelson-Siegel模型，將模型中的三個參數(shù)作為狀態(tài)空間模型中的狀態(tài)變量，并假定他們滿足向量自回歸，采用卡爾曼濾波算法對模型進行求解，同時將模型中的λ作為時變參數(shù)，采用最大似然法估計。最終可以得到樣本期間的利率期限結(jié)構(gòu)并對未來利率作預(yù)測。然后，本文又將由最大似然估計法得到的時變參數(shù)λ的最優(yōu)估計作為固定值，對利率期限結(jié)構(gòu)在不同時點上做靜態(tài)擬合，并分別采用最小二乘法、遺傳算法和差分進化算法來求解模型中的參數(shù)。差分進化算法（DE）和遺傳算法（GA）都屬于全局優(yōu)化算法，但是他們采用了完全不同的變異和選擇的策略。DE有著自適應(yīng)和同等選擇權(quán)等特點，相比與標(biāo)準(zhǔn)的進化算法它更易實現(xiàn)，且精確度和魯棒性更好。本文將用該方法得到的結(jié)果與其他算法得到的相比，結(jié)果表明用差分進化算法得到的利率期限結(jié)構(gòu)的均方根誤差（RMSE）要明顯小于其他方法。最后，我們基于由差分進化算法得到的利率期限結(jié)構(gòu)作了利率預(yù)測，采用AR、VAR和加入了宏觀變量的VAR三種方法，并與用卡爾曼濾波算法得到的預(yù)測值作對比。最終得出結(jié)論，對于構(gòu)建動態(tài)Nelson-Siegel模型首先構(gòu)建狀態(tài)空間模型，使用最大似然估計法來求出模型中重要的時變參數(shù)λ，并將它作為固定值使用在二步法的靜態(tài)擬合過程中。使用差分進化算法求各個時期NS模型的參數(shù)以得到樣本期內(nèi)的利率期限結(jié)構(gòu)。對樣本內(nèi)模型的參數(shù)構(gòu)建自回歸模型，若預(yù)測步長較短，則建議使用AR模型，若預(yù)測步長較長，則建議使用VAR模型，從而預(yù)測出利率期限結(jié)構(gòu)。 本文的創(chuàng)新點有：采用差分進化算法（DE）估計模型參數(shù)，并對比了常用的NLLS和GA算法，得出DE算法在精確度上的優(yōu)勢；用狀態(tài)空間模型來構(gòu)建動態(tài)NS模型，用卡爾曼濾波來對參數(shù)進行求解和預(yù)測，并對比AR、VAR模型；將宏觀因素加入到VAR模型中，觀察其是否會加強模型的預(yù)測能力。
[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.

【學(xué)位授予單位】：浙江財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2014
【分類號】：F224;F812.5;F822.0

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