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中国工业与应用数学学会会刊
主管：中华人民共和国教育部
主办：西安交通大学
ISSN 1005-3085  CN 61-1269/O1
工程数学学报

工程数学学报 ›› 2015, Vol. 32 ›› Issue (4): 485-496.doi: 10.3969/j.issn.1005-3085.2015.04.002

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基于P-样条方法的短期利率模型参数估计

江  良1,   林鸿熙2   

  1. 1- 莆田学院数学学院，福建 莆田 351100
    2- 莆田学院商学院，福建 莆田 351100
  • 收稿日期:2013-10-08 接受日期:2015-03-26 出版日期:2015-08-15 发布日期:2015-10-15
  • 基金资助:
    国家自然科学基金 (11471175)；福建省自然科学基金 (2015J05012)；莆田学院育苗基金 (2014060; 2014061).

P-spline Estimation for Short-term Interest Rate Model

JIANG Liang1,   LIN Hong-xi2   

  1. 1- Department of Mathematics, Putian University, Putian, Fujian 351100
    2- School of Business, Putian University, Putian, Fujian 351100
  • Received:2013-10-08 Accepted:2015-03-26 Online:2015-08-15 Published:2015-10-15
  • Supported by:
    The National Natural Science Foundation of China (11471175); the Natural Science Foundation of Fujian Province (2015J05012); the Putian University Raising Foundation of China (2014060; 2014061).

PDF (PC)

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摘要： 由于在Hull-White短期利率模型中均值是时间的函数，因此本文将应用两阶段方法估计上述模型中的均值函数和其它常数参数值，其中对于均值函数使用P-样条方法，并给出了相应正则化参数选取的方法，而且也证明了两阶段估计方法的相容性和参数的渐进性性质．最后，基于零息债券数据，实证结果表明了引入均值函数模型对于债券价格的回归没有显著的区别，这一现象归因于债券价格对于短期利率不太敏感的性质．

关键词: Hull-White模型, P-样条, 半参数估计

Abstract:

Since the mean reverting is a function in the Hull-White model, this paper develops the estimator and provides the estimation of the mean revering function, which will be estimated by using P-spline estimator and other constant parameters. In addition, we also present an alternative approach to select the regularization parameter. Furthermore, we prove the consistency of the two-stage method and its asymptotic normality of parameters. Finally, based on the zero coupon bond price data, empirical evidences show that there is a slightly less difference between the goodness-of-fit and the constant parameter estimates arising from the bond price less sensitive to short-term rate.

Key words: Hull-White model, P-spline, semiparametric estimation

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