Modelling multivariate volatilities: an ad hoc method

Volatility plays an important role in controlling and forecasting risks in various �nancial operations. For a univariate return series, volatility is often represented in terms of conditional variances or conditional standard deviations. Many statistical models have been developed for modelling univariate conditional variance processes. While univariate descriptions are useful and important, problems of risk assessment, asset allocation, hedging in futures markets and options pricing require a multivariate framework, since high volatilities are often observed in the same time periods across di�erent assets. Statistically this boils down to model time-varying conditional variance and covariance matrices of a vector-valued time series. Section 2 below lists some existing statistical models for multivariate volatility processes. We refer to Bauwens, Laurent and Rombouts (2005) for a more detailed survey on this topic. We propose a new and ad hoc method with numerical illustration in section 3. We concludes in section 4 with a brief summary.