IDEAS home Printed from https://ideas.repec.org/p/msh/ebswps/2003-15.html
   My bibliography  Save this paper

Simulation-Based Bayesian Estimation of Affine Term Structure Models

Author

Listed:
  • Andrew D. Sanford
  • Gael M. Martin

Abstract

This paper demonstrates the application of Bayesian simulation-based estimation to a class of interest rate models known as Affine Term Structure (ATS) models. The technique used is based on a Markov Chain Monte Carlo algorithm, with the discrete observations on yields augmented by additional higher frequency latent data. The introduction of augmented yield data reduces the bias associated with estimating a continuous time model using discretely observed data. The technique is demon-strated using a one-factor ATS model, with the latent factor process that underlies the yields sampled via a single-move algorithm. Numerical application of the method is demonstrated using both simulated and empirical data. Extension of the method to a three-factor ATS model is also discussed, as well as the application of a multi-move sampler based on a Kalman Filtering and Smoothing algorithm.

Suggested Citation

  • 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.
    • Handle: RePEc:msh:ebswps:2003-15
    as

    Download full text from publisher

    File URL: http://www.buseco.monash.edu.au/ebs/pubs/wpapers/2003/wp15-03.pdf
    Download Restriction: no
    ---><---

    Other versions of this item:

    References listed on IDEAS

    as
    1. Christopher G. Lamoureux & H. Douglas Witte, 2002. "Empirical Analysis of the Yield Curve: The Information in the Data Viewed through the Window of Cox, Ingersoll, and Ross," Journal of Finance, American Finance Association, vol. 57(3), pages 1479-1520, June.
    2. Chib, Siddhartha & Greenberg, Edward, 1996. "Markov Chain Monte Carlo Simulation Methods in Econometrics," Econometric Theory, Cambridge University Press, vol. 12(3), pages 409-431, August.
    3. Babbs, Simon H. & Nowman, K. Ben, 1999. "Kalman Filtering of Generalized Vasicek Term Structure Models," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 115-130, March.
    4. John C. Cox & Jonathan E. Ingersoll Jr. & Stephen A. Ross, 2005. "A Theory Of The Term Structure Of Interest Rates," World Scientific Book Chapters, in: Sudipto Bhattacharya & George M Constantinides (ed.), Theory Of Valuation, chapter 5, pages 129-164, World Scientific Publishing Co. Pte. Ltd..
    5. Konstantijn Maes & Konstantijn Maes, 2003. "Modeling the Term Structure of Interest Rates: Where Do We Stand?," International Economics Working Papers Series wpie008, Katholieke Universiteit Leuven, Centrum voor Economische Studiën, International Economics.
    6. Elerain, Ola & Chib, Siddhartha & Shephard, Neil, 2001. "Likelihood Inference for Discretely Observed Nonlinear Diffusions," Econometrica, Econometric Society, vol. 69(4), pages 959-993, July.
    7. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
    8. Qiang Dai & Kenneth J. Singleton, 2000. "Specification Analysis of Affine Term Structure Models," Journal of Finance, American Finance Association, vol. 55(5), pages 1943-1978, October.
    9. Gregory R. Duffee, 2002. "Term Premia and Interest Rate Forecasts in Affine Models," Journal of Finance, American Finance Association, vol. 57(1), pages 405-443, February.
    10. 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.
    11. David Bolder, 2001. "Affine Term-Structure Models: Theory and Implementation," Staff Working Papers 01-15, Bank of Canada.
    Full references (including those not matched with items on IDEAS)

    Citations

    Citations are extracted by the CitEc Project, subscribe to its RSS feed for this item.
    as


    Cited by:

    1. Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.
    2. Richard Finlay & Mark Chambers, 2009. "A Term Structure Decomposition of the Australian Yield Curve," The Economic Record, The Economic Society of Australia, vol. 85(271), pages 383-400, December.
    3. Yasuhiro Omori & Toshiaki Watanabe, 2003. "Block Sampler and Posterior Mode Estimation for a Nonlinear and Non-Gaussian State-Space Model with Correlated Errors," CIRJE F-Series CIRJE-F-221, CIRJE, Faculty of Economics, University of Tokyo.
    4. Peter Feldhütter, 2016. "Can Affine Models Match the Moments in Bond Yields?," Quarterly Journal of Finance (QJF), World Scientific Publishing Co. Pte. Ltd., vol. 6(02), pages 1-56, June.
    5. Hautsch, Nikolaus & Yang, Fuyu, 2012. "Bayesian inference in a Stochastic Volatility Nelson–Siegel model," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3774-3792.
    6. Juneja, Januj, 2017. "Invariance, observational equivalence, and identification: Some implications for the empirical performance of affine term structure models," The Quarterly Review of Economics and Finance, Elsevier, vol. 64(C), pages 292-305.
    7. Jang, Bong-Gyu & Yoon, Ji Hee, 2010. "Analytic valuation formulas for range notes and an affine term structure model with jump risks," Journal of Banking & Finance, Elsevier, vol. 34(9), pages 2132-2145, September.
    8. Andrew D. Sanford & Gael Martin, 2004. "Bayesian Analysis of Continuous Time Models of the Australian Short Rate," Monash Econometrics and Business Statistics Working Papers 11/04, Monash University, Department of Econometrics and Business Statistics.
    9. Andrew D. Sanford & Gael M. Martin, 2006. "Bayesian comparison of several continuous time models of the Australian short rate," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 46(2), pages 309-326, June.

    Most related items

    These are the items that most often cite the same works as this one and are cited by the same works as this one.
    1. Collin-Dufresne, Pierre & Goldstein, Robert S. & Jones, Christopher S., 2009. "Can interest rate volatility be extracted from the cross section of bond yields?," Journal of Financial Economics, Elsevier, vol. 94(1), pages 47-66, October.
    2. Januj Amar Juneja, 2022. "A Computational Analysis of the Tradeoff in the Estimation of Different State Space Specifications of Continuous Time Affine Term Structure Models," Computational Economics, Springer;Society for Computational Economics, vol. 60(1), pages 173-220, June.
    3. repec:wyi:journl:002109 is not listed on IDEAS
    4. Andrew D. Sanford & Gael Martin, 2004. "Bayesian Analysis of Continuous Time Models of the Australian Short Rate," Monash Econometrics and Business Statistics Working Papers 11/04, Monash University, Department of Econometrics and Business Statistics.
    5. Fendel, Ralf, 2004. "Towards a Joint Characterization of Monetary Policy and the Dynamics of the Term Structure of Interest Rates," Discussion Paper Series 1: Economic Studies 2004,24, Deutsche Bundesbank.
    6. Juneja, Januj, 2014. "Term structure estimation in the presence of autocorrelation," The North American Journal of Economics and Finance, Elsevier, vol. 28(C), pages 119-129.
    7. Driessen, Joost & Melenberg, Bertrand & Nijman, Theo, 2005. "Testing affine term structure models in case of transaction costs," Journal of Econometrics, Elsevier, vol. 126(1), pages 201-232, May.
    8. Frederik Lundtofte, 2013. "The quality of public information and the term structure of interest rates," Review of Quantitative Finance and Accounting, Springer, vol. 40(4), pages 715-740, May.
    9. Aït-Sahalia, Yacine & Kimmel, Robert L., 2010. "Estimating affine multifactor term structure models using closed-form likelihood expansions," Journal of Financial Economics, Elsevier, vol. 98(1), pages 113-144, October.
    10. 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.
    11. Peter Feldhütter & Christian Heyerdahl-Larsen & Philipp Illeditsch, 2018. "Risk Premia and Volatilities in a Nonlinear Term Structure Model [Quadratic term structure models: theory and evidence]," Review of Finance, European Finance Association, vol. 22(1), pages 337-380.
    12. Andrew D. Sanford & Gael M. Martin, 2006. "Bayesian comparison of several continuous time models of the Australian short rate," Accounting and Finance, Accounting and Finance Association of Australia and New Zealand, vol. 46(2), pages 309-326, June.
    13. Andrew Carverhill & Dan Luo, 2020. "Pricing and integration of credit default swap index tranches," Journal of Futures Markets, John Wiley & Sons, Ltd., vol. 40(4), pages 503-526, April.
    14. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    15. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
    16. Filipović, Damir & Mayerhofer, Eberhard & Schneider, Paul, 2013. "Density approximations for multivariate affine jump-diffusion processes," Journal of Econometrics, Elsevier, vol. 176(2), pages 93-111.
    17. Wolfgang Lemke & Deutsche Bundesbank, 2006. "Term Structure Modeling and Estimation in a State Space Framework," Lecture Notes in Economics and Mathematical Systems, Springer, number 978-3-540-28344-7, December.
    18. Michael A H Dempster & Elena A Medova & Michael Villaverde, 2010. "Long-term interest rates and consol bond valuation," Journal of Asset Management, Palgrave Macmillan, vol. 11(2), pages 113-135, June.
    19. Griffin, J.E. & Steel, M.F.J., 2006. "Inference with non-Gaussian Ornstein-Uhlenbeck processes for stochastic volatility," Journal of Econometrics, Elsevier, vol. 134(2), pages 605-644, October.
    20. Choong Tze Chua & Dean Foster & Krishna Ramaswamy & Robert Stine, 2008. "A Dynamic Model for the Forward Curve," Review of Financial Studies, Society for Financial Studies, vol. 21(1), pages 265-310, January.
    21. Lin-Yee Hin & Nikolai Dokuchaev, 2016. "Short Rate Forecasting Based On The Inference From The Cir Model For Multiple Yield Curve Dynamics," Annals of Financial Economics (AFE), World Scientific Publishing Co. Pte. Ltd., vol. 11(01), pages 1-33, March.

    More about this item

    Keywords

    Interest Rate Models; Markov Chain Monte Carlo; Data Augmentation; Nonlinear State Space Models; Kalman Filtering.;
    All these keywords.

    JEL classification:

    • C11 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Bayesian Analysis: General
    • C15 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Statistical Simulation Methods: General
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

    NEP fields

    This paper has been announced in the following NEP Reports:

    Statistics

    Access and download statistics

    Corrections

    All material on this site has been provided by the respective publishers and authors. You can help correct errors and omissions. When requesting a correction, please mention this item's handle: RePEc:msh:ebswps:2003-15. See general information about how to correct material in RePEc.

    If you have authored this item and are not yet registered with RePEc, we encourage you to do it here. This allows to link your profile to this item. It also allows you to accept potential citations to this item that we are uncertain about.

    If CitEc recognized a bibliographic reference but did not link an item in RePEc to it, you can help with this form .

    If you know of missing items citing this one, you can help us creating those links by adding the relevant references in the same way as above, for each refering item. If you are a registered author of this item, you may also want to check the "citations" tab in your RePEc Author Service profile, as there may be some citations waiting for confirmation.

    For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: Professor Xibin Zhang (email available below). General contact details of provider: https://edirc.repec.org/data/dxmonau.html .

    Please note that corrections may take a couple of weeks to filter through the various RePEc services.

    IDEAS is a RePEc service. RePEc uses bibliographic data supplied by the respective publishers.