Estimating the risk premium of swap spreads. Two econometric GARCH-based techniques

Two 'reduced-form' GARCH-M models are used to estimate the German swap spreads from a risk premium point of view. The first model makes use of a parametric GARCH in mean model that has been extended to the case of a vector autoregressive process. The second is a semiparametric model where the conditional variance is formalized as a GARCH process while conditional mean is an arbitrary function of it. It is shown that the monotonic relation implied by both GARCH in mean models between the delta swap spreads and its conditional variance holds for all maturities considered. Not surprisingly, the semiparametric model leads to a better explanation of the swap spreads dynamic than the parametric specification.