Abstract

Although stochastic volatility and GARCH (generalized autoregressive conditional heteroscedasticity) models have successfully described the volatility dynamics of univariate asset returns, extending them to the multivariate models with dynamic correlations has been difficult due to several major problems. First, there are too many parameters to estimate if available data are only daily returns, which results in unstable estimates. One solution to this problem is to incorporate additional observations based on intraday asset returns, such as realized covariances. Second, since multivariate asset returns are not synchronously traded, we have to use the largest time intervals such that all asset returns are observed to compute the realized covariance matrices. However, in this study, we fail to make full use of the available intraday informations when there are less frequently traded assets. Third, it is not straightforward to guarantee that the estimated (and the realized) covariance matrices are positive definite.

Our contributions are the following: (1) we obtain the stable parameter estimates for the dynamic correlation models using the realized measures, (2) we make full use of intraday informations by using pairwise realized correlations, (3) the covariance matrices are guaranteed to be positive definite, (4) we avoid the arbitrariness of the ordering of asset returns, (5) we propose the flexible correlation structure model (e.g., such as setting some correlations to be zero if necessary), and (6) the parsimonious specification for the leverage effect is proposed. Our proposed models are applied to the daily returns of nine U.S. stocks with their realized volatilities and pairwise realized correlations and are shown to outperform the existing models with respect to portfolio performances.

摘要

尽管随机波动率和GARCH（广义自回归条件异方差）模型已经成功地描述了单变量资产收益率的波动性动态，但由于几个主要问题，很难将它们扩展到具有动态相关性的多元模型。首先，有太多参数无法估计可用数据是否仅是每日收益，从而导致估计不稳定。解决此问题的一种方法是根据日内资产收益（例如已实现的协方差）合并其他观察值。其次，由于多元资产收益率不能同步交易，因此我们必须使用最大的时间间隔，以便观察所有资产收益率以计算实现的协方差矩阵。但是，在这项研究中 当资产交易频率较低时，我们将无法充分利用可用的日内信息。第三，要保证估计的（和实现的）协方差矩阵是正定的并不容易。

我们的贡献如下：（1）我们使用已实现的测度获得动态相关模型的稳定参数估​​计，（2）我们通过使用成对实现的相关性充分利用了日内信息，（3）保证协方差矩阵能够是正定的；（4）我们避免资产收益率排序的任意性；（5）我们提出了灵活的相关结构模型（例如，如有必要，将某些相关性设为零），以及（6）简约规范提出了杠杆效应。我们提出的模型应用于九支美国股票的日收益率，它们具有已实现的波动率和成对实现的相关性，并且在投资组合绩效方面表现出优于现有模型。