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A Complete Yield Curve Description Of A Markov Interest Rate Model

Author

Listed:
  • ROBERT J. ELLIOTT

    (Haskayne School of Business, University of Calgary, Calgary, Alberta, Canada, T2N 1N4, Canada)

  • ROGEMAR S. MAMON

    (Department of Statistics and Actuarial Science, University of Waterloo, Waterloo, Ontario, Canada, N2L 3G1, Canada)

Abstract

This paper aims to present a complete term structure characterisation of a Markov interest rate model. To attain this objective, we first give a proof that establishes the Unbiased Expectation Hypothesis (UEH) via the forward measure. The UEH result is then employed, which considerably facilitates the calculation of an explicit analytic expression for the forward ratef(t, T). The specification of the bond priceP(t, T), yield rateY(t, T)andf(t, T)gives a complete set of yield curve descriptions for an interest rate market where the short rateris a function of a continuous time Markov chain.

Suggested Citation

  • Robert J. Elliott & Rogemar S. Mamon, 2003. "A Complete Yield Curve Description Of A Markov Interest Rate Model," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 6(04), pages 317-326.
    • Handle: RePEc:wsi:ijtafx:v:06:y:2003:i:04:n:s0219024903001852
    DOI: 10.1142/S0219024903001852
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    Citations

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    Cited by:

    1. Çanakoglu, Ethem & Özekici, Süleyman, 2010. "Portfolio selection in stochastic markets with HARA utility functions," European Journal of Operational Research, Elsevier, vol. 201(2), pages 520-536, March.
    2. 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.
    3. Celikyurt, U. & Ozekici, S., 2007. "Multiperiod portfolio optimization models in stochastic markets using the mean-variance approach," European Journal of Operational Research, Elsevier, vol. 179(1), pages 186-202, May.
    4. U. Çakmak & S. Özekici, 2006. "Portfolio optimization in stochastic markets," Mathematical Methods of Operations Research, Springer;Gesellschaft für Operations Research (GOR);Nederlands Genootschap voor Besliskunde (NGB), vol. 63(1), pages 151-168, February.
    5. Ethem Çanakoğlu & Süleyman Özekici, 2009. "Portfolio selection in stochastic markets with exponential utility functions," Annals of Operations Research, Springer, vol. 166(1), pages 281-297, February.
    6. 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.
    7. Rüdiger Frey & Thorsten Schmidt, 2012. "Pricing and hedging of credit derivatives via the innovations approach to nonlinear filtering," Finance and Stochastics, Springer, vol. 16(1), pages 105-133, January.

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