Multivariate Realized Stock Market Volatility

We present a new matrix-logarithm model of the realized covariance matrix of stock returns. The model uses latent factors which are functions of both lagged volatility and returns. The model has several advantages: it is parsimonious; it does not require imposing parameter restrictions; and, it results in a positive-definite covariance matrix. We apply the model to the covariance matrix of size-sorted stock returns and find that two factors are sufficient to capture most of the dynamics. We also introduce a new method to track an index using our model of the realized volatility covariance matrix.

Also published as:

Forecasting Multivariate Realized Stock Market Volatility
Journal of Econometrics (0304-4076)
January 2011. Vol. 160, Iss. 1, pp. 93-101