IDEAS home Printed from https://ideas.repec.org/a/bla/ecnote/v35y2006i3p227-252.html
   My bibliography  Save this article

A Comparison of Alternative Non‐parametric Estimators of the Short Rate Diffusion Coefficient

Author

Listed:
  • Roberto Renò
  • Antonio Roma
  • Stephen Schaefer

Abstract

In this paper we discuss the estimation of the diffusion coefficient in one‐factor models for the short rate via non‐parametric methods. We test the estimators proposed by Ait‐Sahalia (1996), Stanton (1997) and Bandi and Phillips (2003) on Monte Carlo simulations of the Vasicek and CIR model. We show that the Ait‐Sahalia estimator is not applicable for values of the mean reversion coefficient typically displayed by interest rate data, while the Stanton and Bandi–Phillips estimators perform better. Each of the three estimators depends crucially on the choice of the bandwidth parameter. Our analysis shows that the estimators give different results for both the data set analysed by Ait‐Sahalia (1996) and by Stanton (1997). Finally we show that the data sets used by Ait‐Sahalia and Stanton are inherently different and, in particular, that very short‐term data exhibit characteristics which are inconsistent with a diffusion.

Suggested Citation

  • Roberto Renò & Antonio Roma & Stephen Schaefer, 2006. "A Comparison of Alternative Non‐parametric Estimators of the Short Rate Diffusion Coefficient," Economic Notes, Banca Monte dei Paschi di Siena SpA, vol. 35(3), pages 227-252, November.
    • Handle: RePEc:bla:ecnote:v:35:y:2006:i:3:p:227-252
    DOI: 10.1111/j.1468-0300.2006.00169.x
    as

    Download full text from publisher

    File URL: https://doi.org/10.1111/j.1468-0300.2006.00169.x
    Download Restriction: no
    File URL: https://libkey.io/10.1111/j.1468-0300.2006.00169.x?utm_source=ideas
    LibKey link: if access is restricted and if your library uses this service, LibKey will redirect you to where you can use your library subscription to access this item
    ---><---

    References listed on IDEAS

    as
    1. Jiang, George J. & Knight, John L., 1997. "A Nonparametric Approach to the Estimation of Diffusion Processes, With an Application to a Short-Term Interest Rate Model," Econometric Theory, Cambridge University Press, vol. 13(5), pages 615-645, October.
    2. 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.
    3. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
    4. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(4), pages 627-627, November.
    5. French, Kenneth R. & Roll, Richard, 1986. "Stock return variances : The arrival of information and the reaction of traders," Journal of Financial Economics, Elsevier, vol. 17(1), pages 5-26, September.
    6. Duffee, Gregory R, 1996. "Idiosyncratic Variation of Treasury Bill Yields," Journal of Finance, American Finance Association, vol. 51(2), pages 527-551, June.
    7. David A. Chapman & Neil D. Pearson, 2000. "Is the Short Rate Drift Actually Nonlinear?," Journal of Finance, American Finance Association, vol. 55(1), pages 355-388, February.
    8. Michael Johannes, 2004. "The Statistical and Economic Role of Jumps in Continuous-Time Interest Rate Models," Journal of Finance, American Finance Association, vol. 59(1), pages 227-260, February.
    9. Hamilton, James D, 1996. "The Daily Market for Federal Funds," Journal of Political Economy, University of Chicago Press, vol. 104(1), pages 26-56, February.
    10. Pritsker, Matt, 1998. "Nonparametric Density Estimation and Tests of Continuous Time Interest Rate Models," The Review of Financial Studies, Society for Financial Studies, vol. 11(3), pages 449-487.
    11. Stanton, Richard, 1997. "A Nonparametric Model of Term Structure Dynamics and the Market Price of Interest Rate Risk," Journal of Finance, American Finance Association, vol. 52(5), pages 1973-2002, December.
    12. Brennan, Michael J. & Schwartz, Eduardo S., 1980. "Analyzing Convertible Bonds," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 15(4), pages 907-929, November.
    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. Renò, Roberto, 2008. "Nonparametric Estimation Of The Diffusion Coefficient Of Stochastic Volatility Models," Econometric Theory, Cambridge University Press, vol. 24(5), pages 1174-1206, October.

    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. Jun Yu & Peter C. B. Phillips, 2001. "A Gaussian approach for continuous time models of the short-term interest rate," Econometrics Journal, Royal Economic Society, vol. 4(2), pages 1-3.
    2. Christopher S. Jones, 2003. "Nonlinear Mean Reversion in the Short-Term Interest Rate," The Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 793-843, July.
    3. Bandi, Federico M., 2002. "Short-term interest rate dynamics: a spatial approach," Journal of Financial Economics, Elsevier, vol. 65(1), pages 73-110, July.
    4. Ruijun Bu & Fredj Jawadi & Yuyi Li, 2020. "A multifactor transformed diffusion model with applications to VIX and VIX futures," Econometric Reviews, Taylor & Francis Journals, vol. 39(1), pages 27-53, January.
    5. Suresh M. Sundaresan, 2000. "Continuous‐Time Methods in Finance: A Review and an Assessment," Journal of Finance, American Finance Association, vol. 55(4), pages 1569-1622, August.
    6. Hou, Ai Jun & Suardi, Sandy, 2011. "Modelling and forecasting short-term interest rate volatility: A semiparametric approach," Journal of Empirical Finance, Elsevier, vol. 18(4), pages 692-710, September.
    7. repec:wyi:journl:002108 is not listed on IDEAS
    8. Al-Zoubi, Haitham A., 2009. "Short-term spot rate models with nonparametric deterministic drift," The Quarterly Review of Economics and Finance, Elsevier, vol. 49(3), pages 731-747, August.
    9. Zongwu Cai & Yongmiao Hong, 2013. "Some Recent Developments in Nonparametric Finance," Working Papers 2013-10-14, Wang Yanan Institute for Studies in Economics (WISE), Xiamen University.
    10. Gao, Jiti, 2007. "Nonlinear time series: semiparametric and nonparametric methods," MPRA Paper 39563, University Library of Munich, Germany, revised 01 Sep 2007.
    11. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
    12. Dennis Kristensen, 2004. "A Semiparametric Single-Factor Model of the Term Structure," FMG Discussion Papers dp501, Financial Markets Group.
    13. Cai, Zongwu & Hong, Yongmiao, 2003. "Nonparametric Methods in Continuous-Time Finance: A Selective Review," SFB 373 Discussion Papers 2003,15, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    14. Zhang, Shulin & Song, Peter X.-K. & Shi, Daimin & Zhou, Qian M., 2012. "Information ratio test for model misspecification on parametric structures in stochastic diffusion models," Computational Statistics & Data Analysis, Elsevier, vol. 56(12), pages 3975-3987.
    15. Chen, Bin & Song, Zhaogang, 2013. "Testing whether the underlying continuous-time process follows a diffusion: An infinitesimal operator-based approach," Journal of Econometrics, Elsevier, vol. 173(1), pages 83-107.
    16. Czellar, Veronika & Karolyi, G. Andrew & Ronchetti, Elvezio, 2007. "Indirect robust estimation of the short-term interest rate process," Journal of Empirical Finance, Elsevier, vol. 14(4), pages 546-563, September.
    17. Song, Zhaogang, 2011. "A martingale approach for testing diffusion models based on infinitesimal operator," Journal of Econometrics, Elsevier, vol. 162(2), pages 189-212, June.
    18. Fan J. & Zhang C., 2003. "A Reexamination of Diffusion Estimators With Applications to Financial Model Validation," Journal of the American Statistical Association, American Statistical Association, vol. 98, pages 118-134, January.
    19. Choi Seungmoon, 2009. "Regime-Switching Univariate Diffusion Models of the Short-Term Interest Rate," Studies in Nonlinear Dynamics & Econometrics, De Gruyter, vol. 13(1), pages 1-41, March.
    20. Das, Sanjiv R., 2002. "The surprise element: jumps in interest rates," Journal of Econometrics, Elsevier, vol. 106(1), pages 27-65, January.
    21. Radu Tunaru, 2015. "Model Risk in Financial Markets:From Financial Engineering to Risk Management," World Scientific Books, World Scientific Publishing Co. Pte. Ltd., number 9524, January.

    More about this item

    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:bla:ecnote:v:35:y:2006:i:3:p:227-252. 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: Wiley Content Delivery (email available below). General contact details of provider: http://www.blackwellpublishing.com/journal.asp?ref=0391-5026 .

    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.