Modeling Multivariate Volatilities via Latent Common Factors

Volatility, represented in the form of conditional heteroscedasticity, plays an important role in controlling and forecasting risks in various financial operations including asset pricing, portfolio allocation, and hedging futures. However, modeling and forecasting multi-dimensional conditional heteroscedasticity are technically challenging. As the volatilities of many financial assets are often driven by a few common and latent factors, we propose in this article a dimension-reduction method to model a multivariate volatility process and to estimate a lower-dimensional space, to be called the volatility space, within which the dynamics of the multivariate volatility process is confined. The new method is simple to use, as technically it boils down to an eigenanalysis for a nonnegative definite matrix. Hence, it is applicable to the cases when the number of assets concerned is in the order of thousands (using an ordinary PC/laptop). On the other hand, the model has the capability to cater for complex conditional heteroscedasticity behavior for multi-dimensional processes. Some asymptotic properties for the new method are established. We further illustrate the new method using both simulated and real data examples.