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When Is The Short Rate Markovian?

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  • Andrew Carverhill
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    Abstract

    We answer this question in the very general context of the n-factor Heath, Jarrow, and Morton model for the evolution of the term structure of interest rates, with nonrandom volatility. the answer is that a constraint is imposed on the behavior of the volatility structure. We explain the importance of this result for the design of efficient numerical algorithms for the valuation of options on the term structure. Copyright 1994 Blackwell Publishers.

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    File URL: http://www.blackwell-synergy.com/doi/abs/10.1111/j.1467-9965.1994.tb00060.x
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    Bibliographic Info

    Article provided by Wiley Blackwell in its journal Mathematical Finance.

    Volume (Year): 4 (1994)
    Issue (Month): 4 ()
    Pages: 305-312

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    Handle: RePEc:bla:mathfi:v:4:y:1994:i:4:p:305-312

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    Cited by:
    1. Carl Chiarella & Oh Kwon, 2003. "Finite Dimensional Affine Realisations of HJM Models in Terms of Forward Rates and Yields," Review of Derivatives Research, Springer, vol. 6(2), pages 129-155, May.
    2. Junwu Gan, 2005. "Analytic Backward Induction Of Option Cash Flows: A New Application Paradigm For The Markovian Interest Rate Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1019-1057.
    3. Munk, Claus & Sorensen, Carsten, 2004. "Optimal consumption and investment strategies with stochastic interest rates," Journal of Banking & Finance, Elsevier, vol. 28(8), pages 1987-2013, August.
    4. Carl Chiarella & Thuy-Duong To, 2005. "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach," Research Paper Series 150, Quantitative Finance Research Centre, University of Technology, Sydney.
    5. Ram Bhar & Carl Chiarella, 2000. "Approximating Heath-Jarrow-Morton Non-Markovian Term Structure of Interest Rate Models with Markovian Systems," Working Paper Series 76, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    6. 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.
    7. Christina Nikitopoulos-Sklibosios, 2005. "A Class of Markovian Models for the Term Structure of Interest Rates Under Jump-Diffusions," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 6.
    8. Gapeev, Pavel V., 2004. "On arbitrage and Markovian short rates in fractional bond markets," Statistics & Probability Letters, Elsevier, vol. 70(3), pages 211-222, December.
    9. Biagini, Francesca & Fink, Holger & Klüppelberg, Claudia, 2013. "A fractional credit model with long range dependent default rate," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1319-1347.
    10. Dai, Qiang & Singleton, Kenneth J., 2003. "Fixed-income pricing," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 20, pages 1207-1246 Elsevier.
    11. Ramaprasad Bhar, 2010. "Stochastic Filtering With Applications In Finance:," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 7736.
    12. Carl Chiarella & Oh-Kang Kwon, 2000. "A Complete Stochastic Volatility Model in the HJM Framework," Research Paper Series 43, Quantitative Finance Research Centre, University of Technology, Sydney.
    13. Carl Chiarella & Nadima El-Hassan, 1999. "Pricing American Interest Rate Options in a Heath-Jarrow-Morton Framework Using Method of Lines," Research Paper Series 12, Quantitative Finance Research Centre, University of Technology, Sydney.
    14. Ramaprasad Bhar & Carl Chiarella, 1997. "Interest rate futures: estimation of volatility parameters in an arbitrage-free framework," Applied Mathematical Finance, Taylor & Francis Journals, vol. 4(4), pages 181-199.
    15. Gapeev, Pavel V. & Küchler, Uwe, 2003. "On Markovian Short Rates in Term Structure Models Driven by Jump-Diffusion Processes," SFB 373 Discussion Papers 2003,44, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    16. Casassus, Jaime & Collin-Dufresne, Pierre & Goldstein, Bob, 2005. "Unspanned stochastic volatility and fixed income derivatives pricing," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2723-2749, November.
    17. repec:wyi:wpaper:002014 is not listed on IDEAS
    18. Ram Bhar & Carl Chiarella, 1995. "The Estimation of the Heath-Jarrow-Morton Model by Use of Kalman Filtering Techniques," Working Paper Series 54, Finance Discipline Group, UTS Business School, University of Technology, Sydney.

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