Interest Rate Dynamics and Consistent Forward Rate Curves
AbstractWe derive general necessary and sufficient conditions for the mutual consistency of a given parametrized family of forward rate curves and the dynamics of a given interest rate model. Consistency in this context means that the interest rate model will produce forward rate curves belonging to the parameterized family. The interest rate model may be driven by a multidimensional Wiener process as well as by a market point process. As an application, the Nelson-Siegel family of forward curves is shown to be inconsistent with the Ho-Lee interest rate model, and with the Hull-White extension of the Vasicec model, but it may be adjusted to achieve consistency with these models and with extensions that allow for jumps in interest rates. For a natural exponential-polynomial generalization of the Nelson-Siegel family, we give necessary and sufficient conditions for the existence of a consistent interest rate model with deterministic volatility.
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Bibliographic InfoPaper provided by Stockholm School of Economics in its series Working Paper Series in Economics and Finance with number 209.
Length: 38 pages
Date of creation: 27 Nov 1997
Date of revision:
Publication status: Published in Mathematical Finance, 1999, pages 323-348.
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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.
- Bent Jesper Christensen & Tomas Björk, . "Interest Rate Dynamics and Consistent Forward Rate Curves," Management Working Papers 1999-4, School of Economics and Management, University of Aarhus.
- 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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- Robert A. Jarrow, 2009. "The Term Structure of Interest Rates," Annual Review of Financial Economics, Annual Reviews, vol. 1(1), pages 69-96, November.
- Alan Brace & Marek Musiela, 1994. "A Multifactor Gauss Markov Implementation Of Heath, Jarrow, And Morton," Mathematical Finance, Wiley Blackwell, vol. 4(3), pages 259-283.
- Ho, Thomas S Y & Lee, Sang-bin, 1986. " Term Structure Movements and Pricing Interest Rate Contingent Claims," Journal of Finance, American Finance Association, vol. 41(5), pages 1011-29, December.
- Jorion, Philippe, 1995. " Predicting Volatility in the Foreign Exchange Market," Journal of Finance, American Finance Association, vol. 50(2), pages 507-28, June.
- Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson-Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94.
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