本文選題：利率期限結(jié)構(gòu) + 卡爾曼濾波　； 參考：《安徽財經(jīng)大學(xué)》2013年碩士論文

【摘要】：近年來,隨著我國金融市場的不斷發(fā)展和完善以及利率市場化改革的持續(xù)深入,我國國債的期限結(jié)構(gòu)日趨合理,國債交易規(guī)模不斷增大。這方面要求我們對利率期限結(jié)構(gòu)進行更加深入的研究,為投資者進行投資決策和國家制定貨幣政策提供依據(jù),另一方面豐富的國債交易數(shù)據(jù)也為我們對利率期限結(jié)構(gòu)進行進一步的研究提供了數(shù)據(jù)基礎(chǔ)。 本文首先對幾種經(jīng)典的靜態(tài)利率期限結(jié)構(gòu)模型進行了介紹,并分析了各模型在擬合收益率曲線時的優(yōu)缺點。在對比各模型的擬合效果后,筆者認為N-S模型較為適宜用來估計我國利率期限結(jié)構(gòu),因此,本文選擇使用N-S模型來對上交所國債所隱含的利率期限結(jié)構(gòu)進行估計。從文中的實際估計結(jié)果來看,N-S模型對上交所國債所隱含的利率曲線結(jié)構(gòu)擬合效果出色,這同時也說明了我國國債市場相對有效,且投資者較為理性。 基于N-S模型估計出的每一日的利率期限結(jié)構(gòu),通過計算可以獲得當(dāng)日的任意到期期限國債的到期收益率,根據(jù)本文研究需要,本文求出了到期期限分別為1、2、3、4、5、7、10年的即期收益率。在對不同到期期限的即期收益率序列進行相關(guān)性檢驗后發(fā)現(xiàn),所有相關(guān)系數(shù)均不為1,這說明單個因子不足以刻畫瞬時利率的動態(tài)特性,瞬時利率的動態(tài)特性需要由多個因子來刻畫,從而說明了建立多因子模型的必要性。隨后,本文對不同到期期限的即期利率序列進行了主成分分析,主成分分分析結(jié)果顯示,前四個因子的解釋能力較高,總解釋能力達到99.941%,因此本文認為使用四個因子來刻畫瞬時利率的動態(tài)特性較為合適。 鑒于單因子模型與事實不太相符,于是本文在單因子CIR模型的基礎(chǔ)上對其進行了擴展,將因子個數(shù)從一個增加到四個,從而建立了四因子CIR模型。在四因子CIR模型的估計方面,本文首先使用回歸法估計出各參數(shù)的初始值,進而使用卡爾曼濾波方法來求得模型參數(shù)的最優(yōu)估計。隨后,本文選擇誤差均分方跟作為評價模型擬合優(yōu)度的指標并計算得出了各期限利率序列的誤差均方根,計算結(jié)果表明,四因子模型對樣本的擬合效果優(yōu)良。
[Abstract]:In recent years, with the continuous development and perfection of our financial market and the continuous deepening of the reform of market-oriented interest rate, the term structure of national debt is becoming more and more reasonable, and the scale of national debt trading is increasing. In this regard, we are required to conduct a more in-depth study of the term structure of interest rates to provide a basis for investors to make investment decisions and countries to formulate monetary policies. On the other hand, the abundant data of bond trading also provide the data basis for our further study on the term structure of interest rate. In this paper, several classical term structure models of static interest rate are introduced, and the advantages and disadvantages of these models in fitting the yield curve are analyzed. After comparing the fitting results of each model, the author thinks that N-S model is more suitable to estimate the term structure of interest rate in China. Therefore, this paper chooses N-S model to estimate the term structure of interest rate implied by Shanghai Stock Exchange. From the actual estimation results in this paper, we can see that the N-S model fits well the interest rate curve structure implied by Shanghai Stock Exchange, which also shows that the bond market in China is relatively effective and the investors are more rational. Based on the N-S model, the term structure of interest rate per day can be calculated to obtain the maturity yield of the bond with arbitrary maturity on the same day. According to the need of this study, this paper calculates the spot yield of 10 years, and the maturity period is 1 / 2 / 3 / 4 / 4 / 5 / 7 and 10 years respectively. It is found that all the correlation coefficients are not 1, which indicates that a single factor is not enough to describe the dynamic characteristics of instantaneous interest rate. The dynamic characteristics of the instantaneous interest rate need to be characterized by multiple factors, so it is necessary to establish a multi-factor model. Then, the paper makes principal component analysis on the sequence of spot interest rates with different maturities. The results of principal component analysis show that the first four factors have higher explanatory ability. The total explanatory ability is 99.941, so it is more appropriate to use four factors to describe the dynamic characteristics of instantaneous interest rate. In view of the fact that the single factor model is not quite consistent with the facts, this paper extends the single factor CIR model, and increases the number of factors from one to four, thus establishing a four-factor CIR model. In the estimation of four-factor CIR model, the initial value of each parameter is estimated by regression method, and then the optimal estimation of model parameters is obtained by using Kalman filter method. Then, this paper selects the error mean square followed as the index to evaluate the goodness of fit of the model and calculates the root of the error mean square of the interest rate sequence of each term. The results show that the four-factor model has a good fitting effect on the sample.
【學(xué)位授予單位】：安徽財經(jīng)大學(xué)
【學(xué)位級別】：碩士
【學(xué)位授予年份】：2013
【分類號】：F832.51;F224

【參考文獻】

相關(guān)期刊論文 前10條

1 陳典發(fā);利率期限結(jié)構(gòu)的一致性[J];系統(tǒng)工程;2002年01期

2 周榮喜,邱菀華;基于多項式樣條函數(shù)的利率期限結(jié)構(gòu)模型實證比較[J];系統(tǒng)工程;2004年06期

3 傅曼麗,董榮杰,屠梅曾;國債利率期限結(jié)構(gòu)模型的實證比較[J];系統(tǒng)工程;2005年08期

4 范龍振,王曉麗;上交所國債市場利率期限結(jié)構(gòu)及其信息價值[J];管理工程學(xué)報;2004年01期

5 梅山佳;;基于我國債券市場的二因素Vasicek模型研究[J];金融經(jīng)濟;2010年20期

6 朱世武,陳健恒;交易所國債利率期限結(jié)構(gòu)實證研究[J];金融研究;2003年10期

7 趙宇齡;中國國債收益率曲線構(gòu)造的比較分析[J];上海金融;2003年09期

8 張玉桂;蘇云鵬;楊寶臣;;基于Vasicek和CIR模型的SHIBOR期限結(jié)構(gòu)實證分析[J];統(tǒng)計與信息論壇;2009年06期

9 劉湘云;;基于CIR模型的利率風(fēng)險計量及實證——以我國國債市場為例[J];武漢大學(xué)學(xué)報(哲學(xué)社會科學(xué)版);2007年06期

10 范龍振,張國慶;兩因子CIR模型對上交所利率期限結(jié)構(gòu)的實證研究[J];系統(tǒng)工程學(xué)報;2005年05期

，

本文編號：1844012