中国货币市场短期利率的CIR模型及其参数估计的期望方差法
CIR Model for Short-Term Interest Rates in the Chinese Money Market and Parameter Estimation Using the Expectation-Variance Method
摘要: 为了研究中国货币市场短期利率的动态规律，本文用CIR模型对瞬时利率的演化过程建模。对于模型中存在的未知参数，采用期望方差法建立估计量；并进一步选取银行间质押式7天回购利率(R007)数据作为瞬时利率的近似替代，得到CIR模型中参数的估计值；最终借助CIR模型给出中国货币市场短期利率的动态变化规律。
Abstract: This paper presents the CIR model for the evolution of instantaneous interest rates to investigate the dynamic patterns of short-term interest rates in the Chinese money market. For unknown pa-rameters in the model, the expectation-variance method is applied to give their estimators. Fur-thermore, we select the interbank pledge 7-day repo rate (R007) data as an approximate substitute for instantaneous interest rates, obtaining estimates for the parameters in the CIR model. Ulti-mately, with the assistance of the CIR model, we elucidate the dynamic change rule of short-term interest rates in the Chinese money market.
文章引用：李文利, 王岩, 于慧. 中国货币市场短期利率的CIR模型及其参数估计的期望方差法[J]. 统计学与应用, 2023, 12(6): 1598-1605. https://doi.org/10.12677/SA.2023.126163

参考文献

[1] Feng, X. and Xie, D. (2011) Application of MCMC Algorithm in Interest Rate Modeling.
http://www.researchgate.net/publication/50864448_ Application_of_MCMC_Algorithm_in_Interest_Rate_Modeling
[2] Feng, X. and Xie, D. (2012) Bayesian Estimation of CIR Model. Journal of Data Science, 10, 271-280.
[3] 高利翠. CIR模型的模拟及参数估计分析研究[D]: [硕士学位论文]. 上海: 上海交通大学, 2015.
[4] 马笑天. 短期利率扩散模型参数估计及实证分析[D]: [硕士学位论文]. 上海: 上海财经大学, 2022.
[5] 张玉桂, 苏云鹏, 杨宝臣. 基于Vasicek和CIR模型的SHIBOR期限结构实证分析[J]. 统计与信息论坛, 2009, 24(6): 44-48.
[6] 吴思远. CIR模型在中国市场的应用[D]: [硕士学位论文]. 合肥: 中国科学技术大学, 2017.
[7] 吴方滢. 随机环境下平稳CIR模型的参数估计[D]: [硕士学位论文]. 银川: 北方民族大学, 2023.
[8] 王泽锋, 刘俊锋. 单因子利率期限结构模型的实证检验[J]. 统计与决策, 2007(21): 28-30.
[9] Valdivieso, L., Schoutens, W. and Tuerlinckx, F. (2009) Maximum Likelihood Estimation in Processes of Ornstein- Uhlenbeck Type. Statistical Inference for Stochastic Processes, 12, 1-19. [Google Scholar] [CrossRef] 
[10] Schneider, G., Craigmile, P.F. and Herbei, R. (2017) Maximum Likelihood Estimation for Stochastic Differential Equations Using Sequential Gaussian-Process-Based Optimization. Tech-nometrics, 59, 178-188. [Google Scholar] [CrossRef] 
[11] 王素丽, 吕燕. 一类非线性随机微分方程的参数估计[J]. 吉林大学学报(理学院), 2017, 55(2): 289-293.
[12] Fergusson, K. and Platen, E. (2015) Application of Maximum Likelihood Estimation to Sto-chastic Short Rate Models. Annals of Financial Economics, 10, Article ID: 150009. [Google Scholar] [CrossRef] 
[13] Kladívko, K. (2007) Maximum Likelihood Estimation of the Cox-Ingersoll-Ross Process: The Matlab Implementation. Technical Computing Prague, 7, 1-8.
[14] Aït-Sahalia, Y. (2002) Maximum Likelihood Estimation of Discretely Sampled Diffusions: A Closed-Form Approximation Approach. Econometrica, 70, 223-262. [Google Scholar] [CrossRef] 
[15] Beskos, A., Papaspiliopoulos, O. and Roberts, G. (2009) Monte Carlo Maximum Likelihood Estimation for Discretely Observed Diffusion Processes. The Annals of Statistics, 37, 223-245. [Google Scholar] [CrossRef] 
[16] Singer, H. (2002) Parameter Estimation of Nonlinear Stochastic Differential Equations: Simulated Maximum Likelihood versus Extended Kalman Filter and Itô-Taylor Expansion. Journal of Computational and Graphical Statistics, 11, 972-995. [Google Scholar] [CrossRef] 
[17] 齐凤团. 随机微分方程的参数估计[D]: [硕士学位论文]. 济南: 山东大学, 2017.
[18] 潘冠中. 单因子利率期限结构模型参数估计的数据选择[J]. 数量经济技术经济研究, 2004, 21(9): 71-77.
[19] Cox, J.C., Ingersoll, J.E. and Ross, S.A. (1985) A Theory of the Term Structure of Interest Rates. Econometrica, 53, 385-407. [Google Scholar] [CrossRef] 
[20] Fan, J.Q. and Zhang, C.M. (2003) A Reexamination of Diffusion Estimators with Applications to Financial Model Validation. Journal of the American Statistical Association, 98, 118-134. [Google Scholar] [CrossRef] 

为你推荐