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Bayesian Estimation of Short-Rate Models

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  • Philip Gray

    (UQ Business School, The University of Queensland, St Lucia QLD 4072.)

Abstract

Estimating continuous-time short-rate models is challenging since the likelihood function for most popular models is unknown. While approximate likelihood functions are often used, this practice induces bias into the estimation process. This paper explores a Bayesian method of estimating short-rate models. While the approach also employs an approximate likelihood data augmentation is utilised to mitigate discretisation bias. The results suggest that Bayesian estimates of posterior densities for model parameters closely resemble true posterior densities. While nonessential for point estimation, a small degree of data augmentation is useful in recovering accurate posterior densities and reducing the bias in estimates of bond price. These findings are encouraging for the many cases where exact likelihood-based estimation is impossible and approximations must be relied upon.

Suggested Citation

  • Philip Gray, 2005. "Bayesian Estimation of Short-Rate Models," Australian Journal of Management, Australian School of Business, vol. 30(1), pages 1-22, June.
    • Handle: RePEc:sae:ausman:v:30:y:2005:i:1:p:1-22
    DOI: 10.1177/031289620503000102
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    References listed on IDEAS

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    1. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(2), pages 231-247, August.
    2. Sangjoon Kim & Neil Shephard & Siddhartha Chib, 1998. "Stochastic Volatility: Likelihood Inference and Comparison with ARCH Models," Review of Economic Studies, Oxford University Press, vol. 65(3), pages 361-393.
    3. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    4. 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 1209-1227, July.
    5. Eraker, Bjorn, 2001. "MCMC Analysis of Diffusion Models with Application to Finance," Journal of Business & Economic Statistics, American Statistical Association, vol. 19(2), pages 177-191, April.
    6. Marsh, Terry A & Rosenfeld, Eric R, 1983. "Stochastic Processes for Interest Rates and Equilibrium Bond Prices," Journal of Finance, American Finance Association, vol. 38(2), pages 635-646, May.
    7. Singleton, Kenneth J., 2001. "Estimation of affine asset pricing models using the empirical characteristic function," Journal of Econometrics, Elsevier, vol. 102(1), pages 111-141, May.
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    Cited by:

    1. Vijay A. Murik, 2013. "Bond pricing with a surface of zero coupon yields," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 53(2), pages 497-512, June.
    2. Chua, Chew Lian & Suardi, Sandy & Tsiaplias, Sarantis, 2013. "Predicting short-term interest rates using Bayesian model averaging: Evidence from weekly and high frequency data," International Journal of Forecasting, Elsevier, vol. 29(3), pages 442-455.
    3. Faff, Robert & Gray, Philip, 2006. "On the estimation and comparison of short-rate models using the generalised method of moments," Journal of Banking & Finance, Elsevier, vol. 30(11), pages 3131-3146, November.

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