IDEAS home Printed from https://ideas.repec.org/p/sce/scecf4/302.html
   My bibliography  Save this paper

Maximum likelihood estimation of the Cox-Ingersoll-Ross model using particle filters

Author

Listed:
  • Giuliano De Rossi

Abstract

I show that the QML procedure, used in many papers in the current literature to estimate the CIR model from time series data, is based on an approximation of the latent factors' density that becomes very inaccurate for typical parameter values. I also argue that this issue is not addressed by the Monte Carlo experiments carried out to support the conclusion that the QML bias is negligible. The second part of the paper describes a computationally efficient maximum likelihood estimator based on particle filters. The advantage of this estimator is that it takes into account the exact likelihood function while avoiding the huge computational burden associated with MCMC methods. The proposed methodology is implemented and tested on a sample of simulated data

Suggested Citation

  • Giuliano De Rossi, 2004. "Maximum likelihood estimation of the Cox-Ingersoll-Ross model using particle filters," Computing in Economics and Finance 2004 302, Society for Computational Economics.
    • Handle: RePEc:sce:scecf4:302
    as

    Download full text from publisher

    To our knowledge, this item is not available for download. To find whether it is available, there are three options:
    1. Check below whether another version of this item is available online.
    2. Check on the provider's web page whether it is in fact available.
    3. Perform a search for a similarly titled item that would be available.

    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. Duffee, Gregory R, 1999. "Estimating the Price of Default Risk," The Review of Financial Studies, Society for Financial Studies, vol. 12(1), pages 197-226.
    3. Unknown, 2003. "2003 Winter," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-21.
    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. Unknown, 1999. "1999 Fall," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-11.
    6. Bakshi, Gurdip S. & Zhiwu, Chen, 1997. "An alternative valuation model for contingent claims," Journal of Financial Economics, Elsevier, vol. 44(1), pages 123-165, April.
    7. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes: Reply," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 335-338, July.
    8. Carl Chiarella & Thuy-Duong Tô, 2006. "The Multifactor Nature of the Volatility of Futures Markets," Computational Economics, Springer;Society for Computational Economics, vol. 27(2), pages 163-183, May.
    9. Unknown, 2003. "2003 Spring/Summer," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-18.
    10. Unknown, 2002. "2002 Spring," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-16.
    11. 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.
    12. Unknown, 1999. "1999 Spring," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-17.
    13. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    14. 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.
    15. Duan, Jin-Chuan & Simonato, Jean-Guy, 1999. "Estimating and Testing Exponential-Affine Term Structure Models by Kalman Filter," Review of Quantitative Finance and Accounting, Springer, vol. 13(2), pages 111-135, September.
    16. Hull, John & White, Alan, 1990. "Pricing Interest-Rate-Derivative Securities," The Review of Financial Studies, Society for Financial Studies, vol. 3(4), pages 573-592.
    17. de Jong, Frank & Santa-Clara, Pedro, 1999. "The Dynamics of the Forward Interest Rate Curve: A Formulation with State Variables," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 34(1), pages 131-157, March.
    18. Akihiko Takahashi & Seisho Sato, 2001. "A Monte Carlo Filtering Approach for Estimating the Term Structure of Interest Rates," Annals of the Institute of Statistical Mathematics, Springer;The Institute of Statistical Mathematics, vol. 53(1), pages 50-62, March.
    19. Durham, Garland B & Gallant, A Ronald, 2002. "Numerical Techniques for Maximum Likelihood Estimation of Continuous-Time Diffusion Processes," Journal of Business & Economic Statistics, American Statistical Association, vol. 20(3), pages 297-316, July.
    20. Pitt, Michael K., 2002. "Smooth particle filters for likelihood evaluation and maximisation," Economic Research Papers 269464, University of Warwick - Department of Economics.
    21. Unknown, 2003. "2003 Fall," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-17.
    22. Pitt, Michael K, 2002. "Smooth Particle Filters for Likelihood Evaluation and Maximisation," The Warwick Economics Research Paper Series (TWERPS) 651, University of Warwick, Department of Economics.
    23. Unknown, 2002. "2002 Summer," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-13.
    24. Longstaff, Francis A & Schwartz, Eduardo S, 1992. "Interest Rate Volatility and the Term Structure: A Two-Factor General Equilibrium Model," Journal of Finance, American Finance Association, vol. 47(4), pages 1259-1282, September.
    25. Unknown, 1999. "1999 Winter," CWAE Newsletter, Agricultural and Applied Economics Association, Committee on Women in Agricultural Economics (CWAE), pages 1-12.
    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. Andreasen, Martin M & Meldrum, Andrew, 2015. "Market beliefs about the UK monetary policy life-off horizon: a no-arbitrage shadow rate term structure model approach," Bank of England working papers 541, Bank of England.
    2. Martin Andreasen, 2010. "How to Maximize the Likelihood Function for a DSGE Model," Computational Economics, Springer;Society for Computational Economics, vol. 35(2), pages 127-154, February.

    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. Giuliano De Rossi, 2010. "Maximum Likelihood Estimation of the Cox–Ingersoll–Ross Model Using Particle Filters," Computational Economics, Springer;Society for Computational Economics, vol. 36(1), pages 1-16, June.
    2. Troy Tassier, 2013. "Handbook of Research on Complexity, by J. Barkley Rosser, Jr. and Edward Elgar," Eastern Economic Journal, Palgrave Macmillan;Eastern Economic Association, vol. 39(1), pages 132-133.
    3. Antonio Doria, Francisco, 2011. "J.B. Rosser Jr. , Handbook of Research on Complexity, Edward Elgar, Cheltenham, UK--Northampton, MA, USA (2009) 436 + viii pp., index, ISBN 978 1 84542 089 5 (cased)," Journal of Economic Behavior & Organization, Elsevier, vol. 78(1-2), pages 196-204, April.
    4. Jury Falini, 2009. "Pricing caps with HJM models: the benefits of humped volatility," Department of Economics University of Siena 563, Department of Economics, University of Siena.
    5. Wilfred Dolfsma, 2013. "Government Failure," Books, Edward Elgar Publishing, number 15372.
    6. Duffie, Darrell, 2003. "Intertemporal asset pricing theory," Handbook of the Economics of Finance, in: G.M. Constantinides & M. Harris & R. M. Stulz (ed.), Handbook of the Economics of Finance, edition 1, volume 1, chapter 11, pages 639-742, Elsevier.
    7. Falini, Jury, 2010. "Pricing caps with HJM models: The benefits of humped volatility," European Journal of Operational Research, Elsevier, vol. 207(3), pages 1358-1367, December.
    8. repec:wyi:journl:002109 is not listed on IDEAS
    9. 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.
    10. Giuseppe Arbia & Michele Di Marcantonio, 2015. "Forecasting Interest Rates Using Geostatistical Techniques," Econometrics, MDPI, vol. 3(4), pages 1-28, November.
    11. Diebold, Francis X. & Li, Canlin, 2006. "Forecasting the term structure of government bond yields," Journal of Econometrics, Elsevier, vol. 130(2), pages 337-364, February.
    12. de Jong, Frank, 2000. "Time Series and Cross-Section Information in Affine Term-Structure Models," Journal of Business & Economic Statistics, American Statistical Association, vol. 18(3), pages 300-314, July.
    13. Junker, Markus & Szimayer, Alex & Wagner, Niklas, 2006. "Nonlinear term structure dependence: Copula functions, empirics, and risk implications," Journal of Banking & Finance, Elsevier, vol. 30(4), pages 1171-1199, April.
    14. Kleppe, Tore Selland & Skaug, Hans Julius, 2012. "Fitting general stochastic volatility models using Laplace accelerated sequential importance sampling," Computational Statistics & Data Analysis, Elsevier, vol. 56(11), pages 3105-3119.
    15. Lekkos, Ilias, 2007. "Modelling multiple term structures of defaultable bonds with common and idiosyncratic state variables," Journal of Empirical Finance, Elsevier, vol. 14(5), pages 783-817, December.
    16. Qiang Dai & Kenneth Singleton, 2003. "Term Structure Dynamics in Theory and Reality," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 631-678, July.
    17. 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.
    18. Buraschi, Andrea & Corielli, Francesco, 2005. "Risk management implications of time-inconsistency: Model updating and recalibration of no-arbitrage models," Journal of Banking & Finance, Elsevier, vol. 29(11), pages 2883-2907, November.
    19. Luca Benati, 2006. "Affine term structure models for the foreign exchange risk premium," Bank of England working papers 291, Bank of England.
    20. Andrew Jeffrey & Linton, Oliver Linton & Thong Nguyen & Peter C.B. Phillips, 2001. "Nonparametric Estimation of a Multifactor Heath-Jarrow-Morton Model: An Integrated Approach," Cowles Foundation Discussion Papers 1311, Cowles Foundation for Research in Economics, Yale University.
    21. 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.

    More about this item

    Keywords

    Particle filtering; Term structure of interest rates;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General

    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:sce:scecf4:302. 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: Christopher F. Baum (email available below). General contact details of provider: https://edirc.repec.org/data/sceeeea.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.