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 positivitycan likely be applied to higher-dimensional generalizations of the Vasicek model and to other interest rate models as well .
We provide a full classification of all attainable term structure shapes in the two-factor Vasicek model of interest rates . 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 apply to both forward and yield curves and 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 key mathematical tool is the theory of total positivity, pioneered by Samuel Karlin and others in the 1950ies .
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Using methods from the theory of total positivity, we
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all
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of interest rates
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apply to both forward and yield curves and
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mathematical tools from total positivitycan likely be applied to higher-dimensional generalizations of the Vasicek model and to other interest rate models as well
key mathematical tool is the theory of total positivity, pioneered by Samuel Karlin and others in the 1950ies