Total Positivity and the Classification of Term Structure Shapes in the Two-Factor Vasicek Model

Abstract

Using methods from the theory of total positivity, we provide a full classification of attainable term structure shapes in the two-factor Vasicek model. In particular, we show that the shapes normal, inverse, humped, dipped and hump-dip are always attainable. In certain parameter regimes up to four additional shapes can be produced. Our results show that the correlation and the difference in mean-reversion speeds of the two factor processes play a key role in determining the scope of attainable shapes. The mathematical tools from total positivity can likely be applied to higher-dimensional generalizations of the Vasicek model and to other interest rate models as well.