扩散过程系数的约束B样条估计及其在金融数据中的应用

doi:10.7523/j.issn.2095-6134.2018.01.002

中国科学院大学学报 ›› 2018, Vol. 35 ›› Issue (1): 10-17.DOI: 10.7523/j.issn.2095-6134.2018.01.002

扩散过程系数的约束B样条估计及其在金融数据中的应用

候扬扬, 徐天戈

中国科学院大学数学科学学院, 北京 100049

收稿日期:2016-12-27 修回日期:2017-03-01 发布日期:2018-01-15
通讯作者: 候扬扬
基金资助:
Supported by the National Nature Science Foundation of China (11101419)

A restricted B-spline estimation of diffusion processes with applications to financial data

HOU Yangyang, XU Tiange

School of Mathematical Sciences, University of Chinese Academy of Sciences, Beijing 100049, China

Received:2016-12-27 Revised:2017-03-01 Published:2018-01-15
Supported by:
Supported by the National Nature Science Foundation of China (11101419)

摘要/Abstract

摘要： 时齐扩散过程在金融领域具有重要作用，它被广泛应用于描述基础资产变量的随机波动。研究时齐扩散过程的漂移系数和扩散系数的非参数估计问题，在高阶近似的基础上给出新的非参数估计方法——B样条估计。该方法通过对B样条拟合系数加以非负约束来保证扩散系数的非负性。模拟结果验证了该方法在对扩散系数的估计上优于局部多项式估计方法。

关键词: B样条, 时齐扩散过程, 波动率

Abstract: Time-homogeneous diffusion process plays an important role in the financial market, and it is widely used for describing the stochastic dynamics of the underlying economic variables. In this work, we study nonparametric estimation of the drift and diffusion functions for the time-homogeneous diffusion process, and propose a new nonparametric regression technique based on higher-order approximations, which is called B-spline approach. The nonnegativity of the diffusion function is guaranteed by the restricted B-spline method. Our simulation results show that our method indeed outperforms the local polynomial method.

Key words: B-spline, time-homogeneous diffusion process, volatility

中图分类号:

TB114

候扬扬, 徐天戈. 扩散过程系数的约束B样条估计及其在金融数据中的应用[J]. 中国科学院大学学报, 2018, 35(1): 10-17.

HOU Yangyang, XU Tiange. A restricted B-spline estimation of diffusion processes with applications to financial data[J]. , 2018, 35(1): 10-17.

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扩散过程系数的约束B样条估计及其在金融数据中的应用

A restricted B-spline estimation of diffusion processes with applications to financial data

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