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

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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.