本文選題：跳躍CKLS模型　切入點(diǎn)：Euler法　出處：《浙江工商大學(xué)》2014年碩士論文　論文類型：學(xué)位論文

【摘要】：利率作為金融市場(chǎng)中資產(chǎn)定價(jià)、金融產(chǎn)品設(shè)計(jì)、利率風(fēng)險(xiǎn)管理等研究的重要理論基礎(chǔ),其在金融市場(chǎng)中占著非常重要的地位。近年來(lái),國(guó)際金融市場(chǎng)中對(duì)利率期限結(jié)構(gòu)模型的研究亦是愈演愈烈,因此本文對(duì)利率期限結(jié)構(gòu)模型理論進(jìn)行了擴(kuò)展分析及實(shí)證估計(jì)。 本文以CKLS模型作為研究對(duì)象,考慮了市場(chǎng)中一些突發(fā)狀況的發(fā)生對(duì)利率產(chǎn)生的影響以及實(shí)際利率具有尖峰厚尾性等特征,從而在CKLS模型中引入跳躍項(xiàng),并且分別估算出不同情形下跳躍CKLS模型的轉(zhuǎn)移密度函數(shù),最后則用MCMC參數(shù)估計(jì)方法進(jìn)行了實(shí)證分析,并得到各個(gè)參數(shù)序列的統(tǒng)計(jì)值以及參數(shù)估計(jì)過(guò)程中的核密度圖等,以便分析中國(guó)利率市場(chǎng)的基本特征,具體如下。 首先,建立利率期限結(jié)構(gòu)模型。文章先后對(duì)比了目前理論上幾種重要的利率期限結(jié)構(gòu)模型,最終選擇了CKLS模型作為本文的研究對(duì)象,并結(jié)合中國(guó)利率市場(chǎng)的特點(diǎn),在模型中加入了跳躍因子。關(guān)于跳躍部分,本文分兩種情形進(jìn)行了分析,一是在規(guī)定時(shí)間間隔內(nèi)至多發(fā)生一次跳；二是在規(guī)定時(shí)間間隔內(nèi)可能發(fā)生多次跳躍,且假設(shè)發(fā)生跳躍的次數(shù)服從泊松過(guò)程。 其次,求解模型轉(zhuǎn)移密度。由于本文中所用模型比較復(fù)雜,無(wú)法求出模型轉(zhuǎn)移密度函數(shù)的數(shù)值解,因此本文采用離散化的方法估算出了模型的轉(zhuǎn)移密度函數(shù),也可理解為條件密度函數(shù)。在離散化方法的選擇中,本文選用了既簡(jiǎn)單又容易實(shí)施的Euler離散化方法。這一部分所求得的密度函數(shù)則為接下來(lái)的MCMC參數(shù)估計(jì)中似然函數(shù)的求解打下了重要的基礎(chǔ)。 最后,參數(shù)估計(jì)及實(shí)證分析。在參數(shù)估計(jì)的方法選擇方面,本文采用的是基于貝葉斯原理的MCMC方法,利用MCMC方法經(jīng)過(guò)多次模擬得到各項(xiàng)參數(shù)的基本統(tǒng)計(jì)特征值、核密度圖形以及分位數(shù)圖形等,最終選取多次模擬結(jié)果的均值作為參數(shù)的估計(jì)值。在數(shù)據(jù)選擇方面,本文結(jié)合了中國(guó)利率市場(chǎng)的特點(diǎn),分析了上海銀行間同業(yè)拆放利率各個(gè)品種的交易量及相互之間的相關(guān)性等特征,最終選取了上海銀行間同業(yè)拆放隔夜利率作為金融市場(chǎng)利率的一個(gè)替代。在參數(shù)估計(jì)過(guò)程中,本文對(duì)基于Euler離散化方法下求出的似然函數(shù)運(yùn)用MCMC方法做出了模擬,并利用所得到的結(jié)果作為分析對(duì)象,對(duì)實(shí)證結(jié)果進(jìn)行了分析。
[Abstract]:Interest rate, as an important theoretical basis of asset pricing, financial product design and interest rate risk management in financial market, occupies a very important position in financial market in recent years. The research on term structure model of interest rate in international financial market is becoming more and more serious, so this paper makes an extended analysis and empirical estimation on the theory of term structure model of interest rate. In this paper, the CKLS model is taken as the research object, considering the influence of some unexpected situations on the interest rate in the market, and the real interest rate has the characteristics of peak and thick tail, so the jump term is introduced into the CKLS model. The transfer density function of the hopping CKLS model is estimated in different cases. Finally, the empirical analysis is carried out by using the MCMC parameter estimation method, and the statistical values of each parameter sequence and the kernel density graph in the process of parameter estimation are obtained. In order to analyze the basic characteristics of China's interest rate market, as follows. First of all, the paper establishes the term structure model of interest rate. This paper compares several important term structure models of interest rate in theory, and finally chooses CKLS model as the research object of this paper, and combines the characteristics of interest rate market in China. The jump factor is added to the model. As for the jump part, this paper analyzes it in two cases: one is that there is at most one jump within the specified time interval, the other is that multiple jumps may occur in the specified time interval. And assume that the number of jumps occurs from the Poisson process. Secondly, the transfer density of the model is solved. Because the model used in this paper is very complicated, the numerical solution of the transfer density function of the model can not be obtained, so the transfer density function of the model is estimated by the discrete method. It can also be understood as conditional density function. In the selection of discretization methods, In this paper, the Euler discretization method, which is simple and easy to implement, is chosen. The density function obtained in this part lays an important foundation for the solution of the likelihood function in the next MCMC parameter estimation. Finally, the parameter estimation and empirical analysis. In the method selection of parameter estimation, this paper adopts the MCMC method based on Bayesian principle, and obtains the basic statistical characteristic value of each parameter by MCMC method after many times simulation. The kernel density graph and the quantile graph are used to select the mean value of multiple simulation results as the estimated value of the parameters. In terms of data selection, this paper combines the characteristics of the interest rate market in China. Based on the analysis of the transaction volume and the correlation among the various kinds of Shanghai interbank offered rate, the overnight interest rate of Shanghai interbank offered rate is selected as an alternative to the interest rate in the financial market. In the process of parameter estimation, In this paper, the likelihood function based on Euler discretization method is simulated by MCMC method, and the empirical results are analyzed by using the obtained results as the object of analysis.
【學(xué)位授予單位】：浙江工商大學(xué)
【學(xué)位級(jí)別】：碩士
【學(xué)位授予年份】：2014
【分類號(hào)】：F832.5;F224

【參考文獻(xiàn)】

相關(guān)期刊論文 前4條

1 潘冠中,邵斌;單因子利率模型的極大似然估計(jì)——對(duì)中國(guó)利率的實(shí)證分析[J];財(cái)經(jīng)研究;2004年10期

2 劉金全;鄭挺國(guó);;利率期限結(jié)構(gòu)的馬爾科夫區(qū)制轉(zhuǎn)移模型與實(shí)證分析[J];經(jīng)濟(jì)研究;2006年11期

3 謝赤,鄧藝穎;描述利率動(dòng)態(tài)行為的GARCH-JUMP模型[J];數(shù)量經(jīng)濟(jì)技術(shù)經(jīng)濟(jì)研究;2003年03期

4 謝赤,吳雄偉;基于Vasicek和CIR模型中的中國(guó)貨幣市場(chǎng)利率行為實(shí)證分析[J];中國(guó)管理科學(xué);2002年03期

，

本文編號(hào)：1569582