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Bayesian Analysis of Continuous Time Models of the Australian Short Rate

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Author Info
Andrew D. Sanford ()
Gael Martin ()

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Abstract

This paper provides an empirical analysis of a range of alternative single-factor continuous time models for the Australian short-term interest rate. The models are indexed by the level effect parameter for the volatility in the short rate process. The inferential approach adopted is Bayesian, with estimation of the models proceeding via a Markov Chain Monte Carlo simulation scheme. Discrimination between the alternative models is based on Bayes factors, estimated from the simulation output using the Savage-Dickey density ratio. A data augmentation approach is used to improve the accuracy of the discrete time approximation of the continuous time models. An empirical investigation is conducted using weekly observations on the Australian 90 day interest rate from January 1990 to July 2000. The Bayes factors indicate that the square root diffusion model has the highest posterior probability of all the nested models.

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Publisher Info
Paper provided by Monash University, Department of Econometrics and Business Statistics in its series Monash Econometrics and Business Statistics Working Papers with number 11/04.

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Length: 40 pages
Date of creation: May 2004
Date of revision:
Handle: RePEc:msh:ebswps:2004-11

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Related research
Keywords: Interest Rate Models; Markov Chain Monte Carlo; Data Augmentation;

Other versions of this item:

Find related papers by JEL classification:
C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Bayesian Analysis
C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods: General - - - Statistical Simulation Methods
E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Determination of Interest Rates; Term Structure of Interest Rates

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  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. Dahlquist, Magnus, 1996. "On alternative interest rate processes," Journal of Banking & Finance, Elsevier, vol. 20(6), pages 1093-1119, July. [Downloadable!] (restricted)
  3. 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)
  4. 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(01), pages 85-107, March. [Downloadable!]
  5. Neil Shephard, 2005. "Stochastic Volatility," Economics Papers 2005-W17, Economics Group, Nuffield College, University of Oxford. [Downloadable!]
  6. A. S. Hurn & K. A. Lindsay & V. L. Martin, 2003. "On the efficacy of simulated maximum likelihood for estimating the parameters of stochastic differential Equations," Journal of Time Series Analysis, Blackwell Publishing, vol. 24(1), pages 45-63, 01. [Downloadable!] (restricted)
  7. 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)
  8. Han C. & Carlin B. P., 2001. "Markov Chain Monte Carlo Methods for Computing Bayes Factors: A Comparative Review," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 1122-1132, September. [Downloadable!] (restricted)
  9. Courtadon, Georges, 1982. "The Pricing of Options on Default-Free Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 17(01), pages 75-100, March. [Downloadable!]
  10. Schotman, Peter & van Dijk, Herman K., 1991. "A Bayesian analysis of the unit root in real exchange rates," Journal of Econometrics, Elsevier, vol. 49(1-2), pages 195-238. [Downloadable!] (restricted)
    Other versions:
  11. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(03), pages 409-431, August. [Downloadable!]
  12. Andrew D. Sanford & Gael M. Martin, 2003. "Simulation-Based Bayesian Estimation of Affine Term Structure Models," Monash Econometrics and Business Statistics Working Papers 15/03, Monash University, Department of Econometrics and Business Statistics. [Downloadable!]
  13. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-93, July.
    Other versions:
  14. repec:cup:etheor:v:12:y:1996:i:3:p:409-31 is not listed on IDEAS
  15. Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-91, April.
  16. Koop, Gary & Potter, Simon M., 1998. "Bayes factors and nonlinearity: Evidence from economic time series1," Journal of Econometrics, Elsevier, vol. 88(2), pages 251-281, November. [Downloadable!] (restricted)
  17. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 16(3), pages 793-843, July. [Downloadable!] (restricted)
  18. Conley, Timothy G, et al, 1997. "Short-Term Interest Rates as Subordinated Diffusions," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 10(3), pages 525-77.
  19. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Oxford University Press for Society for Financial Studies, vol. 9(2), pages 385-426. [Downloadable!] (restricted)
    Other versions:
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