On the construction of finite dimensional realizations for nonlinear forward rate models
AbstractWe consider interest rate models of Heath-Jarrow-Morton type where the forward rates are driven by a multidimensional Wiener process, and where the volatility structure is allowed to be a smooth functional of the present forward rate curve. In a recent paper , Björk and Svensson give necessary and sufficient conditions for the existence of a finite dimensional Markovian state space realization (FDR) for such a forward rate model, and in the present paper we provide a general method for the actual construction of an FDR. We illustrate the method by constructing FDR:s for a number of concrete models. These FDR:s generalize previous results by allowing for a more general volatility structure. Furthermore the dimension of the realizations obtained by using our method is typically smaller than that of the corresponding previously known realizations.
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Bibliographic InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 6 (2002)
Issue (Month): 3 ()
Note: received: January 2001; final version received: August 2001
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Web page: http://www.springerlink.com/content/101164/
Find related papers by JEL classification:
- E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects
- G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
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- Gaspar, Raquel M., 2004. "On Finite Dimensional Realizations of Forward Price Term Structure Models," Working Paper Series in Economics and Finance 569, Stockholm School of Economics.
- Mikael Elhouar, 2008. "Finite-dimensional Realizations of Regime-switching HJM Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 331-354.
- Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6.
- Carl Chiarella & Samuel Chege Maina & Christina Nikitopoulos-Sklibosios, 2010. "Markovian Defaultable HJM Term Structure Models with Unspanned Stochastic Volatility," Research Paper Series 283, Quantitative Finance Research Centre, University of Technology, Sydney.
- Björk, Tomas, 2003. "On the Geometry of Interest Rate Models," Working Paper Series in Economics and Finance 545, Stockholm School of Economics.
- Bjork, Tomas, 2009. "Arbitrage Theory in Continuous Time," OUP Catalogue, Oxford University Press, edition 3, number 9780199574742.
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