Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields
Finite dimensional Markovian HJM term structure models provide ideal settings for the study of term structure dynamics and interest rate derivatives where the flexibility of the HJM framework and the tractability of Markovian models coexist. Consequently, these models became the focus of a series of papers including Carverhill (1994), Ritchken and Sankarasubramanian (1995), Bhar and Chiarella (1997), Inui and Kijima (1998), de Jong and Santa-Clara (1999), Björk and Svensson (2001) and Chiarella and Kwon (2001a). However, these models usually required the introduction of a large number of state variables which, at first sight, did not appear to have clear links to the market observed quantities, and the explicit realisations of the forward rate curve in terms of the state variables were unclear. In this paper, it is shown that the forward rate curves for these models are affine functions of the state variables, and conversely that the state variables in these models can be expressed as affine functions of a finite number of forward rates or yields. This property is useful, for example, in the estimation of model parameters. The paper also provides explicit formulae for the bond prices in terms of the state variables that generalise the formulae given in Inui and Kijima (1998), and applies the framework to obtain affine representations for a number of popular interest rate models. Copyright Kluwer Academic Publishers 2003
References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
- de Jong, Frank & Santa-Clara, Pedro, 1999. "The Dynamics of the Forward Interest Rate Curve: A Formulation with State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(01), pages 131-157, March.
- Carl Chiarella & Oh-Kang Kwon, 1999.
"Forward Rate Dependent Markovian Transformations of the Heath-Jarrow-Morton Term Structure Model,"
Research Paper Series
5, Quantitative Finance Research Centre, University of Technology, Sydney.
- Carl Chiarella & Oh Kang Kwon, 2001. "Forward rate dependent Markovian transformations of the Heath-Jarrow-Morton term structure model," Finance and Stochastics, Springer, vol. 5(2), pages 237-257.
- Ram Bhar & Carl Chiarella, 1995.
"Transformation of Heath-Jarrow-Morton Models to Markovian Systems,"
Working Paper Series
53, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
- R. Bhar & C. Chiarella, 1997. "Transformation of Heath?Jarrow?Morton models to Markovian systems," The European Journal of Finance, Taylor & Francis Journals, vol. 3(1), pages 1-26.
- Bliss, Robert R & Ritchken, Peter, 1996. "Empirical Tests of Two State-Variable Heath-Jarrow-Morton Models," Journal of Money, Credit and Banking, Blackwell Publishing, vol. 28(3), pages 452-76, August.
- Tomas Björk & Lars Svensson, 2001. "On the Existence of Finite-Dimensional Realizations for Nonlinear Forward Rate Models," Mathematical Finance, Wiley Blackwell, vol. 11(2), pages 205-243.
- 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.
- Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-92.
- Andrew Carverhill, 1994. "When Is The Short Rate Markovian?," Mathematical Finance, Wiley Blackwell, vol. 4(4), pages 305-312.
When requesting a correction, please mention this item's handle: RePEc:kap:revdev:v:6:y:2003:i:2:p:129-155. See general information about how to correct material in RePEc.
For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Sonal Shukla)or (Christopher F. Baum)
If references are entirely missing, you can add them using this form.