短期利率跳跃-扩散模型的非参数门限估计

中国管理科学 ›› 2012, Vol. ›› Issue (1): 8-15.

短期利率跳跃-扩散模型的非参数门限估计

谈正达, 胡海鸥

上海交通大学安泰经济与管理学院,上海 200052

收稿日期:2011-02-25 修回日期:2011-10-11 出版日期:2012-02-29 发布日期:2012-03-09
基金资助:
国家自然科学基金资助项目(71001069)

Nonparametric Threshold Estimation on Jump-diffusion Model of Short Rate

TAN Zheng-da, HU Hai-ou

Antai College of Economics & Management, Shanghai Jiao Tong University, Shanghai 200052,China

Received:2011-02-25 Revised:2011-10-11 Online:2012-02-29 Published:2012-03-09

摘要/Abstract

摘要： 跳跃行为是短期利率动态过程的一个重要特征,跳跃-扩散模型能更好的描述短期利率行为。本文应用非参数门限估计对短期利率的跳跃-扩散模型进行了仿真实验和实证分析。仿真实验表明,门限估计能有效消除传统非参数估计对跳跃-扩散模型的估计偏差,估计参数具有无偏性。对上海银行间同业拆借利率(Shibor)的实证分析发现,门限估计有效探测到了短期Shibor的跳跃行为,且这种跳跃行为和宏微观的经济金融现象相一致。最后和扩散模型的实证比较得到,基于门限估计的跳跃-扩散模型对短期利率分布的偏度和峰度的拟合能力更优。

关键词: 短期利率, 跳跃-扩散, 门限估计

Abstract: Jumping behavior is an important feature of short interest rate dynamic process. Jump-diffusion model can better describe the behavior of short rate process. Simulation experiments show that nonparametric threshold estimators perform better in finite sample than alternative model. Empirical analysis on the Shanghai Interbank Offered Rate (Shibor) finds that threshold estimators can effectively detect the jump behavior of short-term Shibor, which consistent with the micro-macro economic and financial phenomena. Comparing with diffusion model, jump - diffusion model based on threshold estimates can more accurately describe the interest rates distribution of skewness and kurtosis, and better reflect the volatility behavior of interest rate.

Key words: short rate, jump-diffusion, threshold estimation

中图分类号:

F830.9

谈正达, 胡海鸥. 短期利率跳跃-扩散模型的非参数门限估计[J]. 中国管理科学, 2012, (1): 8-15.

TAN Zheng-da, HU Hai-ou. Nonparametric Threshold Estimation on Jump-diffusion Model of Short Rate[J]. Chinese Journal of Management Science, 2012, (1): 8-15.

参考文献

[1] Ahn, C., Thompson, H.. Jump-diffusion processes and the term structure of interest rates[J]. Journal of Finance, 1988,43(1): 155-174.
[2] Das, S.R.. The surprise element: Jumps in interest rates[J]. Journal of Econometrics, 2002,106(1): 27-65.
[3] Andersen, T., Benzoni, L., Lund, J.. Stochastic volatility, mean drift and jumps in the short-term interest rate.Unpublished Working Paper, http://www. jesperlund. com, 2004.
[4] Piazzesi, M.. Bond yields and the Federal Reserve[J]. Journal of Political Economy, 2005,113(2).
[5] Florens-Zmirou, D.. On estimating the diffusion coefficient from discrete observations[J]. Journal of Applied Probability, 1993,30(4): 790-804.
[6] Ait-Sahalia, Y.. Nonparametric pricing of interest rate derivative securities[J]. Econometrica: Journal of the Econometric Society, 1996,64(3): 527-560.
[7] Stanton, R.. A nonparametric model of term structure dynamics and the market price of interest rate risk[J]. Journal of Finance, 1997,52(5): 1973-2002.
[8] Johannes, M.. The statistical and economic role of jumps in continuous-time interest rate models[J]. Journal of Finance, 2004,59(1): 227-260.
[9] Bandi, F., Nguyen, T.. On the functional estimation of jump-diffusion models[J]. Journal of Econometrics, 2003,116(1-2): 293-328.
[10] Mancini, C., Renò, R.. Threshold estimation of Markov models with jumps and interest rate modeling[J]. Journal of Econometrics, 2011,160(1): 77-92.
[11] 李和金, 郑兴山, 李湛. 非参数利率期限结构模型的实证检验[J]. 上海交通大学学报, 2003,37(4): 607-609.
[12] 宋永安, 陆立强. 非参数利率期限结构动态模型及衍生品定价[J]. 复旦学报: 自然科学版, 2008,47(2): 213-219.
[13] 潘婉彬, 陶利斌, 缪柏其. 时间相依利率扩散模型的非参数估计[J]. 中国管理科学, 2006,14(6): 1-5.
[14] Scott, D.. Multivariate density estimation: theory, practice, and visualization[M]. Wiley-Interscience, 1992.
[15] Bandi, F., Phillips, P.. Fully nonparametric estimation of scalar diffusion models[J]. Econometrica,2003,71(1): 241-283.
[16] Mancini, C.. Estimation of the parameters of jump of a general Poisson-diffusion model[J]. Scandinavian Actuarial Journal, 2004,1: 42-52.
[17] Nelson, D.B.. Filtering and forecasting with misspecified ARCH models I:: Getting the right variance with the wrong model[J]. Journal of Econometrics, 1992,52(1-2): 61-90.
[18] 洪永淼, 林海. 中国市场利率动态研究——基于短期国债回购利率的实证分析[J]. 经济学(季刊), 2006,5(2): 511-532.