Chapter 10
Multivariate Volatility Models and Their Applications
In this chapter, we generalize the univariate volatility models of Chapter 3 to the multivariate case and discuss some simple methods for modeling the dynamic relationships between volatility processes of multiple asset returns. By multivariate volatility, we mean the conditional covariance matrix of multiple asset returns. Multivariate volatilities have many important financial applications. They play an important role in portfolio selection and asset allocation, and they can be used to compute the value at risk of a financial position consisting of multiple assets.
Consider a multivariate return series 
. We adopt the same approach as the univariate case by rewriting the series as
where 
is the conditional expectation of 
given the past information 
, and 
is the shock, or innovation, of the series at time t. In addition, we ...
