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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, Universit´a di Padova)

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

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

Note: Type of Document - pdf; pages: 29
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G - Financial Economics

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Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
  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 1209-27, July. [Downloadable!] (restricted)
  2. 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. [Downloadable!]
  3. Ram Bhar & Carl Chiarella, 1995. "Transformation of Heath-Jarrow-Morton Models to Markovian Systems," Working Paper Series 53, School of Finance and Economics, University of Technology, Sydney. [Downloadable!]
  4. 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. [Downloadable!] (restricted)
  5. 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. [Downloadable!] (restricted)
  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 and Southwestern Finance Association, vol. 26(3), pages 389-404. [Downloadable!] (restricted)
  7. Nowman, K Ben, 1998. "Continuous-Time Short Term Interest Rate Models," Applied Financial Economics, Taylor and Francis Journals, vol. 8(4), pages 401-07, August. [Downloadable!] (restricted)
  8. 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. [Downloadable!] (restricted)
  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. [Downloadable!]
  10. 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. [Downloadable!]
  11. 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. [Downloadable!] (restricted)
  12. 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, Oxford University Press for Society for Financial Studies, vol. 12(4), pages 763-806.
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  1. Carl Chiarella & Hing Hung & Thuy-Duong To, 2005. "The Volatility Structure of the Fixed Income Market under the HJM Framework: A Nonlinear Filtering Approach," Research Paper Series 151, Quantitative Finance Research Centre, University of Technology, Sydney. [Downloadable!]
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