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An interest rate model with a Markovian mean reverting level

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  • Robert Elliott
  • Rogemar Mamon

Abstract

A two-factor Vasicek model, where the mean reversion level changes according to a continuous time finite state Markov chain, is considered. This model could capture the behaviour of monetary authorities who normally set a reference rate which changes from time to time. We derive the term structure via the analytic expression of the bond price that involves a fundamental matrix. The validity of the bond price closed form solution is verified via the forward rate dynamics.

Suggested Citation

  • Robert Elliott & Rogemar Mamon, 2002. "An interest rate model with a Markovian mean reverting level," Quantitative Finance, Taylor & Francis Journals, vol. 2(6), pages 454-458.
    • Handle: RePEc:taf:quantf:v:2:y:2002:i:6:p:454-458
    DOI: 10.1080/14697688.2002.0000012
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    References listed on IDEAS

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    1. V. Cvsa & P. Ritchken, 2001. "Pricing Claims Under GARCH-Level Dependent Interest Rate Processes," Management Science, INFORMS, vol. 47(12), pages 1693-1711, December.
    2. Robert Elliott & Paul Fischer & Eckhard Platen, 1999. "Filtering and Parameter Estimation for a Mean Reverting Interest Rate Model," Research Paper Series 17, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Narasimhan Jegadeesh & George Pennacchi, 1996. "The behavior of interest rates implied by the term structure of Eurodollar future," Proceedings, Federal Reserve Bank of Cleveland, issue Aug, pages 426-451.
    5. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 115-130, March.
    6. Robert J. Elliott & John van der Hoek, 2001. "Stochastic flows and the forward measure," Finance and Stochastics, Springer, vol. 5(4), pages 511-525.
    7. 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.
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    Cited by:

    1. Chen, Yiyang & Mamon, Rogemar & Spagnolo, Fabio & Spagnolo, Nicola, 2022. "Renewable energy and economic growth: A Markov-switching approach," Energy, Elsevier, vol. 244(PB).
    2. Foad Shokrollahi & Marcin Marcin Magdziarz, 2020. "Equity warrant pricing under subdiffusive fractional Brownian motion of the short rate," Papers 2007.12228, arXiv.org, revised Nov 2020.
    3. Fabio Antonelli & Alessandro Ramponi & Sergio Scarlatti, 2013. "Option-based risk management of a bond portfolio under regime switching interest rates," Decisions in Economics and Finance, Springer;Associazione per la Matematica, vol. 36(1), pages 47-70, May.
    4. Dávid Zoltán Szabó & Zsolt Bihary, 2023. "The riskiness of stock versus money market investment with stochastic rates," Central European Journal of Operations Research, Springer;Slovak Society for Operations Research;Hungarian Operational Research Society;Czech Society for Operations Research;Österr. Gesellschaft für Operations Research (ÖGOR);Slovenian Society Informatika - Section for Operational Research;Croatian Operational Research Society, vol. 31(2), pages 393-415, June.
    5. Gao, Huan & Mamon, Rogemar & Liu, Xiaoming & Tenyakov, Anton, 2015. "Mortality modelling with regime-switching for the valuation of a guaranteed annuity option," Insurance: Mathematics and Economics, Elsevier, vol. 63(C), pages 108-120.
    6. Radkov, Petar, 2010. "An interest rate model with Markov chain volatility level," MPRA Paper 60179, University Library of Munich, Germany.
    7. Xiaojing Xi & Rogemar Mamon, 2014. "Capturing the Regime-Switching and Memory Properties of Interest Rates," Computational Economics, Springer;Society for Computational Economics, vol. 44(3), pages 307-337, October.
    8. 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.
    9. Shen, Yang & Siu, Tak Kuen, 2013. "Pricing bond options under a Markovian regime-switching Hull–White model," Economic Modelling, Elsevier, vol. 30(C), pages 933-940.
    10. Robert Elliott & Katsumasa Nishide, 2014. "Pricing of discount bonds with a Markov switching regime," Annals of Finance, Springer, vol. 10(3), pages 509-522, August.

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