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Finite-dimensional Realizations of Regime-switching HJM Models

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  • Mikael Elhouar

Abstract

This paper studies Heath-Jarrow-Morton-type models with regime-switching stochastic volatility. In this setting the forward rate volatility is allowed to depend on the current forward rate curve as well as on a continuous time Markov chain y with finitely many states. Employing the framework developed by Bjork and Svensson we find necessary and sufficient conditions on the volatility guaranteeing the representation of the forward rate process by a finite-dimensional Markovian state space model. These conditions allow us to investigate regime-switching generalizations of some well-known models such as those by Ho-Lee, Hull-White, and Cox-Ingersoll-Ross.

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  • Mikael Elhouar, 2008. "Finite-dimensional Realizations of Regime-switching HJM Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 331-354.
    • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:4:p:331-354
    DOI: 10.1080/13504860801987133
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    1. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    2. Asbjørn T. Hansen & Rolf Poulsen, 2000. "A simple regime switching term structure model," Finance and Stochastics, Springer, vol. 4(4), pages 409-429.
    3. Qiang Dai & Kenneth J. Singleton & Wei Yang, 2007. "Regime Shifts in a Dynamic Term Structure Model of U.S. Treasury Bond Yields," Review of Financial Studies, Society for Financial Studies, vol. 20(5), pages 1669-1706, 2007 12.
    4. 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, March.
    5. Garcia, Rene & Perron, Pierre, 1996. "An Analysis of the Real Interest Rate under Regime Shifts," The Review of Economics and Statistics, MIT Press, vol. 78(1), pages 111-125, February.
    6. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    7. 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.
    8. 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, April.
    9. Tomas Björk & Bent Jesper Christensen, 1999. "Interest Rate Dynamics and Consistent Forward Rate Curves," Mathematical Finance, Wiley Blackwell, vol. 9(4), pages 323-348, October.
    10. Inui, Koji & Kijima, Masaaki, 1998. "A Markovian Framework in Multi-Factor Heath-Jarrow-Morton Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 33(3), pages 423-440, September.
    11. Björk, Tomas, 2003. "On the Geometry of Interest Rate Models," SSE/EFI Working Paper Series in Economics and Finance 545, Stockholm School of Economics.
    12. Camilla Landén & Tomas Björk, 2002. "On the construction of finite dimensional realizations for nonlinear forward rate models," Finance and Stochastics, Springer, vol. 6(3), pages 303-331.
    13. 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 1011-1029, December.
    14. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    15. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    16. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure1," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72, January.
    17. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    18. Stoyan Valchev, 2004. "Stochastic volatility Gaussian Heath-Jarrow-Morton models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 11(4), pages 347-368.
    19. Hamilton, James D., 1988. "Rational-expectations econometric analysis of changes in regime : An investigation of the term structure of interest rates," Journal of Economic Dynamics and Control, Elsevier, vol. 12(2-3), pages 385-423.
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    2. Robert J. Elliott & Tak Kuen Siu, 2016. "Pricing regime-switching risk in an HJM interest rate environment," Quantitative Finance, Taylor & Francis Journals, vol. 16(12), pages 1791-1800, December.
    3. Samuel Chege Maina, 2011. "Credit Risk Modelling in Markovian HJM Term Structure Class of Models with Stochastic Volatility," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 5, July-Dece.

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