A Multivariate Generalized ARCH Approach to Modeling Risk Premia in Forward Foreign Exchange Markets

Abstract

This study examines spot and forward exchange rates at a weekly level for four different currencies. It is shown that the vector of forward market forecast errors can be parameterized as a vector moving average (MA) process where the MA coefficients can be theoretically determined from knowledge of the martingale behavior of exchange rates. The conditional covariance matrix is then estimated by assuming a multivariate GARCH structure which depends on a relatively small number of parameters. A range of LM tests confirms that the model provides an adequate description of the first- and second-order moments of the conditional density of the data. The vector MA process is then used to provide some bounds on the magnitude of the risk premium. Series of tests are also applied to the estimated model to test for the inclusion of terms that would be implied by a time varying risk premium. The results are not consistent with any standard model of asset pricing, but do provide evidence for the existence of this type of effect.