Nonparametric Estimation Methods of Integrated Multivariate Volatilities
比较了Malliavin-Mancino和Hayashi-Yoshida两种非参数估计器在估计积分多变量波动率时的表现，发现Hayashi-Yoshida估计器在偏差和均方误差上最优，并应用于日本国债期货数据验证。
Estimation of integrated multivariate volatilities of an Ito process is an interesting and important issue in finance, for example, in order to evaluate portfolios. New non-parametric estimators have been recently proposed by Malliavin and Mancino (2002) and Hayashi and Yoshida (2005a) as alternative methods to classical realized quadratic covariation. The purpose of this article is to compare these alternative estimators both theoretically and empirically, when high frequency data is available. We found that the Hayashi-Yoshida estimator performs the best among the alternatives in view of the bias and the MSE. The other estimators are shown to have possibly heavy bias mostly toward the origin. We also applied these estimators to Japanese Government Bond futures to obtain the results consistent with our simulation.