An affine multifactor model with macro factors for the German term structure: Changing results during the recent crises

Using arbitrage-free affine models, we analyze the dynamics of German bond yields and risk premia for the period 1999 to 2010 (EMU). We estimate two model specifications, one with only latent factors, and another one with a Taylor-type rule comprising a price and a real activity factor drawn from a large macroeconomic data set as additional driving forces. We apply several statistical methods to select those time series from which the factors are actually extracted. The macroeconomic factors, notably the real activity factor, help to improve the fit of the model. Moreover, the inclusion of the macroeconomic factors allows us to analyze their effect on the risk aversion of market participants. Looking at the impact of the recent crises, we see that particularly the market prices of risk for the real activity and the price factor changed most dramatically. Offsetting safe haven flows, which affect shorter maturities in particular, explain why yield risk premia increase less at the short end as compared to longer maturities in times of crisis. A liquidity stress factor included in the macro model mirrors this slope influencing effect of the safe haven flows and leads to smoother forward rates for yield risk premia.