[1]柳向东,郭慧.基于市道轮换模型的SHIBOR市场利率[J].深圳大学学报理工版,2015,32(3):317-323.[doi:10.3724/SP.J.1249.2015.03317]
　Liu Xiangdong and Guo Hui.Research of market interest rates of the SHIBOR based on regime switching model[J].Journal of Shenzhen University Science and Engineering,2015,32(3):317-323.[doi:10.3724/SP.J.1249.2015.03317]
点击复制

基于市道轮换模型的SHIBOR市场利率()
分享到：

《深圳大学学报理工版》[ISSN:1000-2618/CN:44-1401/N]

卷:
第32卷
期数:
2015年第3期
页码:
317-323
栏目:
数学与应用数学
出版日期:
2015-05-20

文章信息/Info

Title:
Research of market interest rates of the SHIBOR based on regime switching model
文章编号:
201503014
作者:
柳向东; 郭慧
暨南大学统计学系，广州 510632
Author(s):
Liu Xiangdong and Guo Hui
Department of Statistics, Jinan University, Guangzhou 510632, P.R.China
关键词:
应用统计数学; 马氏市道轮换; 广义自回归条件异方差; 上海银行间同业拆放利率; 利率期限结构; 固定波动率; 单机制模型
Keywords:
application of statistical mathematics;  Markov regime switching;  generalized autoregressive conditional heteroskedasticity (GARCH);  Shanghai interbank offered rate (SHIBOR);  term structure of interest rates;  fixed volatility;  single regime model
分类号:
O 211.9；F 830
DOI:
10.3724/SP.J.1249.2015.03317
文献标志码:
A
摘要:
基于固定波动率模型和广义自回归条件异方差（generalized autoregressive conditional heteroskedasticity，GARCH）模型，研究引入马氏市道轮换模型. 该模型可以将线性利率期限结构推广到非线性形式，运用到资产定价的变化中，特别是债券收益率的确定中.不同于唯一依赖利率水平的传统模型,马氏市道轮换模型能够模拟货币政策对利率的影响.利用2006-10-08至2013-03-29每周三上海银行间同业拆放利率（Shanghai interbank offered rate，SHIBOR）月度数据，用R语言实现并比较了固定波动率模型、GARCH模型以及混合GARCH马氏市道轮换模型对各参数的估计效果.结果表明，混合GARCH马氏市道轮换模型的拟合效果在各种情形下均占优.
Abstract:
In this paper, a new model, the Markov regime switching model, based on the fixed volatility model and the generalized autoregressive conditional heteroskedasticity (GARCH) model is introduced. In the Markov regime switching model, the linear term structure of interest rates can be extended to nonlinear form. The Markov regime switching model can be used to estimate the dynamics of asset prices, especially the bond yields. Different from the traditional model, which only depends on the level of interest rates, a state variable is introduced in the regime switching model, and thus the model can indicate the impact of the monetary policy on interest rates . Using the monthly Shanghai interbank offered rate (SHIBOR) data issued every Wednesday from October 8th, 2006 to March 29th, 2013, we use R implement and compare the performances of fixed volatility model, GARCH model, and the mixed GARCH Markov regime switching model in estimating the monthly SHIBOR. The results indicate that the mixed GARCH Markov regime switching model can make good estimations and can be considered as the best one under all circumstances.

参考文献/References:

［1］ Chan K, Karolyi A, Longstaff F, et al. An empirical comparison of alternative models of the short-term interest rate［ J］. Journal of Finance, 1992, 47（3）:1209-1227.
［2］ Vasicek O. An equilibrium characterization of the term structure［J］. Journal of Financial Economics, 1977, 5(2):177-188.
［3］ Cox J, Ingersoll Jr J, Ross S. A theory of the term structure of interest rates［J］. Econometrica, 1985, 53(2):385-407.
［4］ Clifford A B, Walter N T．The stochastic volatility of short-term interest rates: some international evidence［J］．The Journal of Finance, 1999, 54(6):2339-2359．
［5］ Xiong Jie，Zeng Yong. A branching particle approximation to the filtering problem with counting process observations［J］. Statistical Inference for Stochastic Processes, 2011，14(4): 111-140.
［6］ Del M P, Doucet A，Jasra A. On adaptive resampling procedures for sequential Monte Carlo methods［J］. Bernoulli, 2012，18(1): 252-278.
［7］ Lopes H F，Tsay R S. Particle filters and Bayesian inference in financial econometrics［J］. Journal of Forecasting, 2011，30(1): 169-209.
［8］ Douc R，Moulines E. Limit theorems for weighted samples with applications to sequential Monte Carlo methods［J］. The Annals of Statistics, 2008，36(2): 2344-2376.
［9］ Asparouhova E N, Bessembinder H，Kalchevab I. Liqui-dity biases in asset pricing tests［J］. Journal of Financial Economics, 2010，96(3): 215-237.
［10］ Stephen F G. Regime-switching in Australian short-term interest rates［J］.Accounting & Finance，1996，36（1）：65-88．
［11］ Liu Xiangdong, Zhong Nie. Pricing life insurance with jump Poisson-diffusion under no-arbitrage framework ［J］.International Journal of Applied Mathematics and Statistics, 2014, 52(4):53-62.
［12］ Liu Xiangdong, Shu Wu, Yong Zeng. The multifactor term structure of interest rates under regime shifts and Lévy jumps［J］.The 8th ICSA International Conferrence,2010,56(4):852-872.
［13］ Ait-Sahalia Y, Kimme R. Estimating affine multifactor term structure models using closed-form likelihood expansions ［J］. Journal of Financial Economics, 2010, 98(3): 113-144.
［14］ Xiang Ju, Zhu Xiaoneng. A regime-switching Nelson-Siegel term structure model and interest rate forecasts ［J］. Journal of Financial Econometrics,2013, 11(3):522-555.
［15］ Siu T K. Bond pricing under a Markovian regime-switching jump-augmented Vasicek model via stochastic flows［J］. Applied Mathematics and Computation, 2010, 216(3):3184-3190.
［16］ Liu Jinquan, Zheng Tingguo. The term structure of interest rates to regime-switching model and the empirical analysis［J］. Economic Research, 2006, 41(11): 82-91.(in Chinese)
刘金全，郑挺国.利率期限结构的马尔科夫机制转移模型与实证分析［J］．经济研究，2006，41（11）：82-91．
［17］ Wu Jilin, Tao Wangsheng. The research of short-term interest rates in our country based on the regime-switching and random fluctuations［J］. Chinese Management Science, 2009, 17(3): 40-46.(in Chinese)
吴吉林，陶旺升．基于机制转移与随机波动的我国短期利率研究［J］.中国管理科学，2009，17（3）：40-46．
［18］ Smith D R. Markov-switching and stochastic volatility diffusion models of short-term interest rates［J］.Journal of Business and Economic Statistics，2002，20（2）：183-197．
［19］ Tang Xiaobin. The state space model of markov regime-switching and its application research on the economic cycle［D］. Chengdu:Southwestern University of Finance and Economics, 2010.(in Chinese)
唐晓彬．Markov机制转移的状态空间模型及其在我国经济周期中的应用研究［D］．成都：西南财经大学，2010.
［20］ Wu Shu，Zeng Yong. A general equilibrium model of the term structure of interest rates under regime-switching risk［J］. International Journal of Theoretical and Applied Finance, 2005, 8(7):839-869.
［21］ Wu Shu, Zeng Yong. An econometric model of the term structure of interest rates under regime-switching risk［J］. Springer, 2013，2:53-59.
［22］ Zeng Yong, Wu Shu. The term structure of interest rates under regime shifts and jumps［J］.Economics Letters, 2006, 93(2):215-221.
［23］ Andrieu C, Doucet A, Holenstein R. Particle Markov chain Monte Carlo methods［J］. Journal of the Royal Statistical Society(Series B), 2010, 72:269-342.
［24］ Le A, Dai Qiang, Singleton K. Discrete-time dynamic term structure models with generalized market prices of risk［J］. Review of Finance Studies,2010, 32(1):2184-2227.
［25］ Futami H. Regime switching term structure model under partial information［J］. International Journal of Theoretical and Applied Finance, 2011, 14(2): 265-294.
［26］ Robert F E. Autoregressive conditional heteroscedasticity with estimates of the variance of United Kingdom inflation［J］.Econometrica, 1982,50(4):987-1007.
［27］ Tim B. Generalized autoregressive conditional heteroskedasticity［J］. Journal of Econometrics, 1986, 31(3):307-327.
［28］ James D H. A new approach to the economic analysis of nonstationary time series and the business cycle［J］. Econometrica, 1989, 57(2):357-384.
［29］ Hamilton J D, Susmel R. Autoregressive conditional heteroscedasticity and changes in regime［J］. Journal of Econometrics, 1994,64(2):307-333.
［30］ Ferland R, Gauthier G, Lalancette S. A regime-switching term structure model with observable state variables ［J］. Finance Research Letters, 2010, 7(2):103-109.
［31］ Elliott R J, Siu T K. On Markov-modulated exponential-affine bond price formulae ［J］. Applied Mathematical Finance, 2009, 16(1): 1-15.
［32］ Dai Qiang, Singleton K, Yang Wei. Regime shifts in a dynamic term structure model of the U.S. treasury bond yields ［J］. Review of Financial Studies, 2007, 20(2): 1669-1706.
［33］ Ang A, Bekaert G, Wei Min. The term structure of real rates and expected inflation ［J］. The Journal of Finance, 2008, 63(2):797-849.
［34］ Zhu Cai, Huang Jianhui. State-space models: application in economic and finance［M］. New York(USA)：Springer，2013.

相似文献/References:

[1]柳向东,杨飞.基于期权价格的Lévy过程参数估计研究[J].深圳大学学报理工版,2014,31(3):325.[doi:10.3724/SP.J.1249.2014.03325]
　Liu Xiangdong and Yang Fei.The research of parameter estimation under the Lévy process based on option pricing[J].Journal of Shenzhen University Science and Engineering,2014,31(3):325.[doi:10.3724/SP.J.1249.2014.03325]
[2]李松臣,李育鹏,陈迎运,等.随机和非随机部件组成的串并联系统寿命比较[J].深圳大学学报理工版,2014,31(3):312.[doi:10.3724/SP.J.1249.2014.03312]
　Li Songchen,Li Yupeng,Chen Yingyun,et al.Comparisons of series and parallel systems with random and non-random dependent components[J].Journal of Shenzhen University Science and Engineering,2014,31(3):312.[doi:10.3724/SP.J.1249.2014.03312]
[3]柳向东,王星蕊.最小熵鞅测度下的半马氏市道轮换利率模型[J].深圳大学学报理工版,2016,33(2):154.[doi:10.3724/SP.J.1249.2016.02154]
　Liu Xiangdong and Wang Xingrui.Semi-Markov regime switching interest rate models under minimal entropy martingale measure[J].Journal of Shenzhen University Science and Engineering,2016,33(3):154.[doi:10.3724/SP.J.1249.2016.02154]
[4]柳向东,靳晓洁.市道轮换下的高频数据参数估计[J].深圳大学学报理工版,2018,35(4):432.[doi:10.3724/SP.J.1249.2018.04432]
　LIU Xiangdong and JIN Xiaojie.Parameter estimation via regime switching model for high frequency data[J].Journal of Shenzhen University Science and Engineering,2018,35(3):432.[doi:10.3724/SP.J.1249.2018.04432]

备注/Memo

备注/Memo:
Received：2014-12-17；Accepted：2015-01-26
Foundation：National Natural Science Foundation of China (71471075); Humanities and Social Science Foundation of Ministry of Education（14YJAZH052）
Corresponding author：Associate professor Liu Xiangdong. E-mail: tliuxd@jnu.edu.cn
Citation：Liu Xiangdong，Guo Hui. Research of market interest rates of the SHIBOR based on regime switching model［J］. Journal of Shenzhen University Science and Engineering, 2015, 32(3): 317-323.（in Chinese）
基金项目：国家自然科学基金资助项目（71471075）;教育部人文社会科学研究资助项目（14YJAZH052）
作者简介：柳向东（1973—），男（汉族），湖南省浏阳市人，暨南大学副教授、博士. E-mail: tliuxd@jnu.edu.cn
引文：柳向东，郭慧. 基于市道轮换模型的SHIBOR市场利率［J］. 深圳大学学报理工版，2015，32（3）：317-323.
更新日期/Last Update: 2015-05-09