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

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Author Info

  • 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, UniversitĀ“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.

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File URL: http://128.118.178.162/eps/fin/papers/0409/0409002.pdf
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Bibliographic Info

Paper provided by EconWPA in its series Finance with number 0409002.

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Length: 29 pages
Date of creation: 01 Sep 2004
Date of revision:
Handle: RePEc:wpa:wuwpfi:0409002

Note: Type of Document - pdf; pages: 29
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Web page: http://128.118.178.162

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  1. Klaus Sandmann & Dieter Sondermann, 1997. "A Note on the Stability of Lognormal Interest Rate Models and the Pricing of Eurodollar Futures," Mathematical Finance, Wiley Blackwell, vol. 7(2), pages 119-125.
  2. Chapman, David A & Long, John B, Jr & Pearson, Neil D, 1999. "Using Proxies for the Short Rate: When Are Three Months Like an Instant?," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 763-806.
  3. D. Sondermann & Sandmann, K., 1994. "On the Stability of Log-Normal Interest Rate Models and the Pricing of Eurodollar Futures," Discussion Paper Serie B 263, University of Bonn, Germany.
  4. Cox, John C & Ingersoll, Jonathan E, Jr & Ross, Stephen A, 1985. "A Theory of the Term Structure of Interest Rates," Econometrica, Econometric Society, vol. 53(2), pages 385-407, March.
  5. Peter Ritchken & L. Sankarasubramanian, 1995. "Volatility Structures Of Forward Rates And The Dynamics Of The Term Structure," Mathematical Finance, Wiley Blackwell, vol. 5(1), pages 55-72.
  6. 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.
  7. 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.
  8. Andersen, Torben G. & Lund, Jesper, 1997. "Estimating continuous-time stochastic volatility models of the short-term interest rate," Journal of Econometrics, Elsevier, vol. 77(2), pages 343-377, April.
  9. 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.
  10. K. Ben Nowman, 1998. "Continuous-time short term interest rate models," Applied Financial Economics, Taylor & Francis Journals, vol. 8(4), pages 401-407.
  11. 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 1209-27, July.
  12. Koedijk, C.G. & Nissen, F. & Schotman, P.C. & Wolff, C.C.P., 1997. "The dynamics of short-term interest rate volatility reconsidered," Open Access publications from Tilburg University urn:nbn:nl:ui:12-3108628, Tilburg University.
  13. Harvey,Andrew C., 1991. "Forecasting, Structural Time Series Models and the Kalman Filter," Cambridge Books, Cambridge University Press, number 9780521405737, April.
  14. Carl Chiarella & Sara Pasquali & Wolfgang Runggaldier, 2001. "On Filtering in Markovian Term Structure Models (An Approximation Approach)," Research Paper Series 65, Quantitative Finance Research Centre, University of Technology, Sydney.
  15. Nowman, K B, 1997. " Gaussian Estimation of Single-Factor Continuous Time Models of the Term Structure of Interest Rates," Journal of Finance, American Finance Association, vol. 52(4), pages 1695-1706, September.
  16. 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.
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Cited by:
  1. Yassine El Qalli, 2010. "Recursive Bayesian Estimation In Forward Price Models Implied By Fair Pricing," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(02), pages 301-333.
  2. 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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