Multivariate Stochastic Volatility Model With Realized Volatilities and Pairwise Realized Correlations
针对多元波动率模型参数过多、非同步交易和协方差矩阵正定性等难题，提出利用已实现波动率和成对已实现相关性来稳定估计、充分利用日内信息并保证正定性，应用于九只美国股票日收益率，在投资组合表现上优于现有模型。
Although stochastic volatility and GARCH (generalized autoregressive\nconditional heteroscedasticity) models have successfully described the\nvolatility dynamics of univariate asset returns, extending them to the\nmultivariate models with dynamic correlations has been difficult due to several\nmajor problems. First, there are too many parameters to estimate if available\ndata are only daily returns, which results in unstable estimates. One solution\nto this problem is to incorporate additional observations based on intraday\nasset returns, such as realized covariances. Second, since multivariate asset\nreturns are not synchronously traded, we have to use the largest time intervals\nsuch that all asset returns are observed in order to compute the realized\ncovariance matrices. However, in this study, we fail to make full use of the\navailable intraday informations when there are less frequently traded assets.\nThird, it is not straightforward to guarantee that the estimated (and the\nrealized) covariance matrices are positive definite. Our contributions are the\nfollowing: (1) we obtain the stable parameter estimates for the dynamic\ncorrelation models using the realized measures, (2) we make full use of\nintraday informations by using pairwise realized correlations, (3) the\ncovariance matrices are guaranteed to be positive definite, (4) we avoid the\narbitrariness of the ordering of asset returns, (5) we propose the flexible\ncorrelation structure model (e.g., such as setting some correlations to be zero\nif necessary), and (6) the parsimonious specification for the leverage effect\nis proposed. Our proposed models are applied to the daily returns of nine U.S.\nstocks with their realized volatilities and pairwise realized correlations and\nare shown to outperform the existing models with respect to portfolio\nperformances.\n