Multivariate volatility models

Ruey S. Tsay

Abstract

Correlations between asset returns are important in many financial applications. In recent years, multivariate volatility models have been used to describe the time-varying feature of the correlations. However, the curse of dimensionality quickly becomes an issue as the number of correlations is $k(k-1)/2$ for $k$ assets. In this paper, we review some of the commonly used models for multivariate volatility and propose a simple approach that is parsimonious and satisfies the positive definite constraints of the time-varying correlation matrix. Real examples are used to demonstrate the proposed model.

First Page:
Primary Subjects: 62M10
Secondary Subjects: 62M20
Keywords: multivariate GARCH model; BEKK model; positive definite matrix; volatility serie
Full-text: Open access