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A term structure model with level factor cannot be realistic and arbitrage free


  • Dubecq , S.
  • Gourieroux , C.


A large part of the term structure literature interprets the first underlying factors as a level factor, a slope factor, and a curvature factor. In this paper we consider factor models interpretable as a level factor model, a level and a slope factor model, respectively. We prove that such models are compatible with no-arbitrage restrictions and the positivity of rates either under rather unrealistic conditions on the dynamic of the short term interest rate, or at the cost of explosive long-term interest rates. This introduces some doubt on the relevance of the level and slope interpretations of factors in term structure models.

Suggested Citation

  • Dubecq , S. & Gourieroux , C., 2012. "A term structure model with level factor cannot be realistic and arbitrage free," Working papers 359, Banque de France.
  • Handle: RePEc:bfr:banfra:359

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    Interest Rate; Term Structure; Affine Model; No Arbitrage; Level Factor; Slope Factor.;

    JEL classification:

    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
    • E44 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Financial Markets and the Macroeconomy
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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