Multivariate volatility models

Multivariate Volatility Models belong to the class of nonlinear models for financial data. Here we want to focus on multivariate GARCH models. These models assume that the variance of the innovation distribution follows a time dependent process conditional on information which is generated by the history of the process. In this chapter we demonstrate how to use the bigarch quantlet of XploRe to estimate the conditional covariance of a bivariate (high frequency) return process. In particular we consider a system of exchange rates of two currencies measured against the US Dollar (USO), namely the Deutsche Mark (DEM) and the British Pound Sterling (GBP). For this example process we compare the dynamic properties of the bivariate model with univariate GARCH specifications where cross sectional dependecies are ignored. Moreover, to illustrate the scope of the bivariate model we employ the estimated model to price call options written on foreign exchange rates.