跳跃CKLS模型的MCMC估计与应用

广东工业大学学报 ›› 2010, Vol. 27 ›› Issue (2): 68-70.

跳跃CKLS模型的MCMC估计与应用

广东工业大学应用数学学院，广东广州510090

出版日期:2010-06-25 发布日期:2010-06-25
作者简介:孙琳(1971-)，女，讲师，硕士，主要研究方向为金融数学

Parameter Estimation of Jump CKLS Model and Its Application

Faculty of Applied Mathematics，Guangdong University of Technology，Guangzhou 51~90，China

Online:2010-06-25 Published:2010-06-25

摘要/Abstract

摘要： 考虑金融市场的非系统风险，在传统的CKLS模型中加入随机跳跃因素，提出了一种刻画短期利率的扩展CKLS模型．采用Euler法离散化连续过程，得到离散过程的似然函数，并采用基于马尔可夫链蒙特卡洛法估计了模型的未知参数．采用上海银行间同业拆放利率数据进行实证研究．结果表明，跳跃在所选的研究期间以较高的概率发生，马尔可夫链蒙特卡洛法在参数估计中是有效的．

关键词: 马尔可夫链蒙特卡洛；跳跃CKLS模型；上海银行间同业拆放利率；利率模型

Abstract: Regarding the non-system risks in the financial market，the extended CKLS model，which describes the short-term interest rate，was proposed，based on the traditional CKLS mode1．Then，the likelihood function in discrete form was obtained by using the Euler method to approximate the continuous process．Furtherm ore，the parameters of this model were estimated by Markov Chain Monte Carlo method．Finally，based on 0／N SHIBOR，an empirical study was presented．The results indicate jumps happen with a high probability in the research time and Markov Chain Monte Carlo method is effective in parameter estimation．

Key words: Markov Chain Monte Carlo；Jump CKLS model；SHIBOR；interest rate

孙琳. 跳跃CKLS模型的MCMC估计与应用[J]. 广东工业大学学报, 2010, 27(2): 68-70.

SUN Lin. Parameter Estimation of Jump CKLS Model and Its Application[J]. Journal of Guangdong University of Technology, 2010, 27(2): 68-70.

参考文献

[1]Merton R．Option pricing ehen underlying stock returns are discontinuous[J]．Journal of Financial Economics，1976，3：125-144．

[2]Brennan M，Schwartz E．Saving bonds，retractable bonds，and callable bonds[J]．Journal of Financial Economies，1977．5：67-88．

[3]Brennan M，Schwartz E．A continuous time approach to the pricing of bonds[J]．Journal of Banking and Finance，1979，3：133-155．

[4]Brennan M，Schwartz E．Analyzing convertible bonds[J]．Journal of Financial and Quantitive Analysis，1980，15：907-929．

[5]Vasicek O．An equilibrium characterization of the term structure[J]．Journal of Financial Economics，1977，5：177-188．

[6]Cox J C，Ingersoll J E，Ross S A．A theory ofthe term strueture ofinterest rates[J]．Econometrica，1985，53：385-407．

[7]Chan K C，Karolyi G A，Longstaf F，et al．The volatility of short term interest rates：An empirical comparison of alternative models of the term structure of interest rates[J].Journal of Finance 47，1992：1209-1227．

[8]Das S．The surprise element：Jumps in interest rates[J]．Journal of Econometrics 106，2001，1943-1978．

[9]Johannes M．The statistical and economic role of jumps incontinuous-time interest rates models[J]．Journal of Finance，2004，227-260．

[10]Kutoyants Y．Parameter Estimation for Stochastic Processes [M]．Berlin：Helderman：1984．

[11]Prakasa Rao B L S．Statistical Inference for Difusion Type Processes[M]．London：Arnold，1999．

[12]Liptser R，Shiryav A．Statistics of Random Processes：Ⅱ[M]．Berlin：Applications，Springer，2001．

[13]Johannes M，Poison N．MCMC Methods for ContinuousTime Financial Econometrics[M]．New York：Handbook of Financial Econometrics，2006．

[14]胡素华，张世英，张彤．双指数跳跃扩散模型的MCMC估计[J]．系统工程学报，2006，21(2)：113-118．

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