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The Volatility of the Instantaneous Spot Interest Rate Implied by Arbitrage Pricing - A Dynamic Bayesian Approach

Author

Listed:
  • Ram Bhar

    (School of Banking & Finance, University of New South Wales)

  • Carl Chiarella

    (School of Finance & Economics, University of Technology, Sydney)

  • Hing Hung

    (School of Finance & Economics, University of Technology, Sydney)

  • Wolfgang Runggaldier

    (Dipartimento di Matematica Pura ed Applicata, Universit´a di Padova)

Abstract

This paper considers the estimation of the volatility of the instantaneous short interest rate from a new perspective. Rather than using discretely compounded market rates as a proxy for the instantaneous short rate of interest, we derive a relationship between observed LIBOR rates and certain unobserved instantaneous forward rates. We determine the stochastic dynamics for these rates under the risk- neutral measure and propose a filtering estimation algorithm for a time- discretised version of the resulting interest rate dynamics based on dynamic Bayesian updating. The method is applied to US Treasury rates of various maturities and is found to give a reasonable model fit.

Suggested Citation

  • Ram Bhar & Carl Chiarella & Hing Hung & Wolfgang Runggaldier, 2004. "The Volatility of the Instantaneous Spot Interest Rate Implied by Arbitrage Pricing - A Dynamic Bayesian Approach," Finance 0409002, University Library of Munich, Germany.
    • Handle: RePEc:wpa:wuwpfi:0409002
    Note: Type of Document - pdf; pages: 29
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    References listed on IDEAS

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    1. Licheng Sun, 2003. "Nonlinear Drift And Stochastic Volatility: An Empirical Investigation Of Short‐Term Interest Rate Models," Journal of Financial Research, Southern Finance Association;Southwestern Finance Association, vol. 26(3), pages 389-404, September.
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    5. Brenner, Robin J. & Harjes, Richard H. & Kroner, Kenneth F., 1996. "Another Look at Models of the Short-Term Interest Rate," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 31(1), pages 85-107, March.
    6. Ram Bhar & Carl Chiarella & Wolfgang Runggaldier, 2001. "Estimation in Models of the Instantaneous Short Term Interest Rate By Use of a Dynamic Bayesian Algorithm," Research Paper Series 68, Quantitative Finance Research Centre, University of Technology, Sydney.
    7. Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," The Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
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    11. Carl Chiarella & Sara Pasquali & Wolfgang J. Runggaldier, 2001. "On Filtering in Markovian Term Structure Models," World Scientific Book Chapters, in: Jiongmin Yong (ed.), Recent Developments In Mathematical Finance, chapter 12, pages 139-150, World Scientific Publishing Co. Pte. Ltd..
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    Cited by:

    1. Chiarella, Carl & Hung, Hing & T, Thuy-Duong, 2009. "The volatility structure of the fixed income market under the HJM framework: A nonlinear filtering approach," Computational Statistics & Data Analysis, Elsevier, vol. 53(6), pages 2075-2088, April.

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