مدل کوواریانس تعمیم یافته پویای نامتقارن

In this paper we extend the ADC model of Kroner and Ng [1998. Review of Financial Studies 11, 817–844] such that it allows for cross-asymmetries in conditional volatility. That is, the model allows for asymmetries in covariances after shocks of opposite signs. We find evidence for significant cross-asymmetries in the conditional volatility in stock and bond markets.

While there exists a large amount of literature on time-varying conditional variances of either stock and bond returns, the number of studies on conditional covariances between these returns is rather limited. One of the most influential studies on modeling time-varying covariances is a study by Kroner and Ng (1998). They introduced the Asymmetric Dynamic Covariance (ADC) model, a multivariate GARCH model that nests several other multivariate models and allows for asymmetric volatility. However, their approach does not take into account cross-asymmetric volatilities: the conditional variance and covariance between asset returns can be higher (or lower) after a negative shock in one asset and a positive shock in the other asset, rather than shocks of opposite signs of the same magnitude. Recently, De Goeij and Marquering (2004) showed that cross-asymmetries can be statistically and economically significant in a multivariate GJR (Glosten et al., 1993) setting. As we concentrate in this note on the interaction between stocks and bonds, we observe many shocks of opposite signs. We propose an extension of the ADC model that incorporates cross-asymmetries in conditional variances and covariances. We refer to this model as the Generalized Asymmetric Dynamic Covariance (GADC) model. To test the appropriateness of the model we examine the asymmetric volatility behavior of stock and bond market returns.

The empirical results show that the GADC model better fits the data than the ADC model. We show that there are cross-asymmetric effects in the conditional variances and covariance of stock and bond returns. In contrast to the bond market variance, the model predicts that the conditional stock market variance responds asymmetrically to stock and bond market shocks. The GADC model predicts that the conditional covariance is relatively low after negative stock return shocks and positive bond return shocks rather than shocks of opposite signs. We also find that the conditional correlation between stock and bond returns varies significantly over time. An investor that holds a diversified asset portfolio should therefore rebalance his asset holdings over time accordingly.