THE CLASSIFICATION OF TERM STRUCTURE SHAPES IN THE TWO-FACTOR VASICEK MODEL — A TOTAL POSITIVITY APPROACH

Martin Keller-Ressel ()
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Martin Keller-Ressel: Institute for Mathematical Stochastics, TU Dresden, 01062 Dresden, Germany

International Journal of Theoretical and Applied Finance (IJTAF), 2021, vol. 24, issue 05, 1-27

Abstract: 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 1950s.

Keywords: yield curve; forward curve; term structure; Vasicek model; interest rates; total positivity; Descartes system (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0219024921500278

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