The Integration of Dual-Domain Method for Estimating the Volatility of Financial Assets

DOI：10.3770/j.issn:1000-341X.2010.03.015

 作者 单位 杜雪樵 合肥工业大学数学系, 安徽 合肥 230009 叶绪国 合肥工业大学数学系, 安徽 合肥 230009

时间域方法和状态域方法是对非参数估计金融资产波动率的两种常用方法.在真实金融市场中, 经济状况随时间而变, 对于给定的状态变量, 希望波动率依靠于时间和价格水平是合理的. 目前范剑青等人(2007)提出了基于时间域和状态域动态组合方法的思想,这个思想在波动率估计中变成了一个令人感兴趣的话题. 在本文中, 我们的目的是在波动率估计中讨论组合方法.模拟被实施去展示新提出的组合方法优于以前的估计方法, 模拟的结果被应用于展示这一事实. 更一步我们建立了它们的渐近性质.

Time- and state-domain methods are two common approaches for nonparametrically estimating the volatility of financial assets. Economic conditions vary over time in real financial market. It is reasonable to expect that volatility depends on both time and price level for a given state variable. Recently, Fan, et al (2007) proposed the idea of dynamically integrated method in both time-and state domain. This idea has become an interesting topic in the estimation of volatility. In this paper, our purpose is to discuss the integrated method in the estimation of volatility. Simulations are conducted to demonstrate that the newly integrated method outperforms some old ones, and the results of simulations demonstrate this fact. Furthermore, we establish its asymptotic properties.