Yield curve shapes of Vasicek interest rate models, measure transformations and an application for the simulation of pension products

We consider two aspects of Vasicek interest rate models arising from chance-risk classification of German pension products. First, we show that the two-factor Vasicek model can explain significantly more effects that are observed at the market than its one-factor variant. Among them are humped shapes independent of the interest rate level and the occurrence of dipped yield curves. We further introduce a general change of measure framework for the Monte Carlo simulation of the Vasicek model under a subjective measure. In chance-risk classification it can then be used to avoid the occurrence of a far too high frequency of inverse yield curves with growing time.