基于局部多项式拟合非时齐扩散模型参数的局部估计（英文）  

Local Estimations Based on Local Polynomial Fitting for Time-inhomogeneous Diffusion Models

作　　者：王继霞[1,2] 肖庆宪[1] 

机构地区：[1]上海理工大学管理学院,上海200093 [2]河南师范大学数学与信息科学学院,新乡453007

出　　处：《工程数学学报》2014年第6期915-929,共15页Chinese Journal of Engineering Mathematics

基　　金：The National Natural Science Foundation of China(11171221);the Leading Academic Discipline Project of Shanghai(XTKX2012)

摘　　要：本文主要研究一类非时齐扩散模型中参数的局部估计,此类问题是期权定价和风险管理中必要的组成部分.漂移参数和扩散参数是期权定价和风险管理中的关键性变量.首先,基于离散观测样本,利用局部多项式拟合,得到了漂移参数的局部多项式复合分位回归估计,并证明了其渐近性质.然后,考虑到扩散参数是非负的,本文利用对数局部多项式拟合,得到了扩散参数的局部多项式估计,并讨论了扩散项估计的渐近偏差、渐近方差和渐近正态性.最后,分别对漂移参数和扩散参数的估计采用了不同的带宽参数.模拟结果表明,本文所得到的局部复合分位回归估计比局部最小二乘估计的拟合效果更好.This paper studies local estimations of parameters for a class of time-inhomogeneous diffusion models, which is essential building blocks for option pricing and risk man-agement. The parameters in our models are the key variables in option pricing and risk management. Based on discretely observed samples, we propose the local polynomial composite quantile regression （CQR） estimation of drift parameters by using local polynomial fitting, and verify its asymptotic properties. Considering dif-fusion parameter being positive, we take it to be locally log-polynomial fitting and obtain its kernel weighted estimation. The asymptotic bias, asymptotic variance and asymptotic normality of the estimation for volatility function are discussed. Separate bandwidths are used for the estimations of drift and diffusion parameters. Simulation studies show that the proposed local CQR estimations perform better than the local least squares estimations.

关 键 词：时变参数 复合分位回归估计 局部多项式拟合 扩散模型 渐近正态性 

分 类 号：O212.1[理学—概率论与数理统计]