Interest Rate Dynamics and Consistent Forward Rate Curves
AbstractWe consider as given an arbitrage free interest rate model M, and a parametrized family of forward rate curves G. We study the question as to when the given family G is consistent with the dynamics of the interest rate model M, in the sense that M actually will produce forward rate curves belonging to G. We allow the interest rate model to be driven by a multidimensional Wiener process, as well as by a marked point process, and we give necessary and sufficient conditions for consistency. As test cases, we study some popular models, obtaining both positive and negative results about consistency. We also introduce a natural exponential-polynomial family of forward rate curves, and for this family we give necessary and sufficient conditions for the existence of consistent interest rate models with deterministic volatility functions.
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Bibliographic InfoPaper provided by School of Economics and Management, University of Aarhus in its series Management Working Papers with number 1999-4.
Length: 31 pages
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Web page: http://www.econ.au.dk/afv/
forward rate curves; interest rate models; invariant manifolds; marked point processes;
Other versions of this item:
- Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348.
- Björk, Tomas & Christensen, Bent Jesper, 1997. "Interest Rate Dynamics and Consistent Forward Rate Curves," Working Paper Series in Economics and Finance 209, Stockholm School of Economics.
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
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