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A simple regime switching term structure model

Author

Listed:
  • Asbjørn T. Hansen

    (Global Equities, Dresdner Kleinwort Benson, 20 Fenchurch Street, London EC3P 3DB, UK)

  • Rolf Poulsen

    (Department of Statistics and Operations Research, University of Copenhagen, Universitetsparken 5, DK-2100, Denmark Manuscript)

Abstract

We extend the short rate model of Vasicek (1977) to include jumps in the local mean. Conditions ensuring existence of a unique equivalent martingale measure are given, implying that the model is arbitrage-free and complete. We develop efficient numerical methods for computation of zero coupon bond prices, illustrate how the model is easily calibrated to market data and show how other interest rate derivatives can be priced.

Suggested Citation

  • Asbjørn T. Hansen & Rolf Poulsen, 2000. "A simple regime switching term structure model," Finance and Stochastics, Springer, vol. 4(4), pages 409-429.
    • Handle: RePEc:spr:finsto:v:4:y:2000:i:4:p:409-429
    Note: received: March 1998; final version received: November 1999
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    References listed on IDEAS

    as
    1. Chan, K C, et al, 1992. "An Empirical Comparison of Alternative Models of the Short-Term Interest Rate," Journal of Finance, American Finance Association, vol. 47(3), pages 1209-1227, July.
    2. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    3. Camilla LandÊn, 2000. "Bond pricing in a hidden Markov model of the short rate," Finance and Stochastics, Springer, vol. 4(4), pages 371-389.
    4. 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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    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. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    8. Hiroshi Shirakawa, 1991. "Interest Rate Option Pricing With Poisson‐Gaussian Forward Rate Curve Processes," Mathematical Finance, Wiley Blackwell, vol. 1(4), pages 77-94, October.
    9. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," The Review of Financial Studies, Society for Financial Studies, vol. 10(3), pages 525-577.
    10. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    Full references (including those not matched with items on IDEAS)

    Citations

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    Cited by:

    1. Pedro P. Mota & Manuel L. Esqu�vel, 2013. "On a continuous time stock price model with regime switching, delay, and threshold," Quantitative Finance, Taylor & Francis Journals, vol. 14(8), pages 1479-1488, December.
    2. Kuang-Liang Chang & Nan-Kuang Chen & Charles Leung, 2011. "Monetary Policy, Term Structure and Asset Return: Comparing REIT, Housing and Stock," The Journal of Real Estate Finance and Economics, Springer, vol. 43(1), pages 221-257, July.
    3. Hidenori Futami, 2009. "Multi-factor Affine Term Structure Model with Single Regime Shift: Real Term Structure under Zero Interest Rate," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 16(4), pages 347-369, December.
    4. Mikael Elhouar, 2008. "Finite-dimensional Realizations of Regime-switching HJM Models," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(4), pages 331-354.
    5. Francesco Audrino & Marcelo C. Medeiros, 2011. "Modeling and forecasting short‐term interest rates: The benefits of smooth regimes, macroeconomic variables, and bagging," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 26(6), pages 999-1022, September.
    6. 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.
    7. Yuri Kabanov & Masaaki Kijima & Sofiane Rinaz, 2007. "A positive interest rate model with sticky barrier," Quantitative Finance, Taylor & Francis Journals, vol. 7(3), pages 269-284.
    8. 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 1-2011, January-A.
    9. 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.
    10. Francesco Audrino & Marcelo C. Medeiros, 2008. "Smooth Regimes, Macroeconomic Variables, and Bagging for the Short-Term Interest Rate Process," University of St. Gallen Department of Economics working paper series 2008 2008-16, Department of Economics, University of St. Gallen.
    11. Hainaut, Donatien, 2013. "A fractal version of the Hull–White interest rate model," Economic Modelling, Elsevier, vol. 31(C), pages 323-334.
    12. Huang, Jia-Ping & Sumita, Ushio, 2015. "Development of computational algorithms for pricing European bond options under the influence of macro-economic conditions," Applied Mathematics and Computation, Elsevier, vol. 251(C), pages 453-468.
    13. 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.
    14. 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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    More about this item

    Keywords

    Regime switching; term structure of interest rates; numerical methods; option pricing;
    All these keywords.

    JEL classification:

    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • C63 - Mathematical and Quantitative Methods - - Mathematical Methods; Programming Models; Mathematical and Simulation Modeling - - - Computational Techniques
    • 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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