Advanced Search
MyIDEAS: Login

Parameter estimation and bias correction for diffusion processes

Contents:

Author Info

  • Tang, Cheng Yong
  • Chen, Song Xi

Abstract

This paper considers parameter estimation for continuous-time diffusion processes which are commonly used to model dynamics of financial securities including interest rates. To understand why the drift parameters are more difficult to estimate than the diffusion parameter, as observed in previous studies, we first develop expansions for the bias and variance of parameter estimators for two of the most employed interest rate processes, Vasicek and CIR processes. Then, we study the first order approximate maximum likelihood estimator for linear drift processes. A parametric bootstrap procedure is proposed to correct bias for general diffusion processes with a theoretical justification. Simulation studies confirm the theoretical findings and show that the bootstrap proposal can effectively reduce both the bias and the mean square error of parameter estimates, for both univariate and multivariate processes. The advantages of using more accurate parameter estimators when calculating various option prices in finance are demonstrated by an empirical study.

Download Info

If you experience problems downloading a file, check if you have the proper application to view it first. In case of further problems read the IDEAS help page. Note that these files are not on the IDEAS site. Please be patient as the files may be large.
File URL: http://www.sciencedirect.com/science/article/B6VC0-4V0TD7N-1/2/940a38b99cdf7f86d1748d5e8ce18a36
Download Restriction: Full text for ScienceDirect subscribers only

As the access to this document is restricted, you may want to look for a different version under "Related research" (further below) or search for a different version of it.

Bibliographic Info

Article provided by Elsevier in its journal Journal of Econometrics.

Volume (Year): 149 (2009)
Issue (Month): 1 (April)
Pages: 65-81

as in new window
Handle: RePEc:eee:econom:v:149:y:2009:i:1:p:65-81

Contact details of provider:
Web page: http://www.elsevier.com/locate/jeconom

Related research

Keywords: Bias correction Bootstrap Continuous-time models Diffusion processes Jackknife Parameter estimation;

References

References listed on IDEAS
Please report citation or reference errors to , or , if you are the registered author of the cited work, log in to your RePEc Author Service profile, click on "citations" and make appropriate adjustments.:
as in new window
  1. Tauchen, George E. & Gallant, A. Ronald, 1995. "Which Moments to Match," Working Papers 95-20, Duke University, Department of Economics.
  2. Merton, Robert C., 1980. "On estimating the expected return on the market : An exploratory investigation," Journal of Financial Economics, Elsevier, vol. 8(4), pages 323-361, December.
  3. Peter C. B. Phillips, 2005. "Jackknifing Bond Option Prices," Review of Financial Studies, Society for Financial Studies, vol. 18(2), pages 707-742.
  4. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  5. Ait-Sahalia, Yacine & Kimmel, Robert L., 2008. "Estimating Affine Multifactor Term Structure Models Using Closed-Form Likelihood Expansions," Working Paper Series 2008-19, Ohio State University, Charles A. Dice Center for Research in Financial Economics.
  6. Ball, Clifford A. & Torous, Walter N., 1996. "Unit roots and the estimation of interest rate dynamics," Journal of Empirical Finance, Elsevier, vol. 3(2), pages 215-238, June.
  7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
  8. Lo, Andrew W., 1988. "Maximum Likelihood Estimation of Generalized Itô Processes with Discretely Sampled Data," Econometric Theory, Cambridge University Press, vol. 4(02), pages 231-247, August.
  9. Hansen, Lars Peter & Scheinkman, Jose Alexandre, 1995. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," Econometrica, Econometric Society, vol. 63(4), pages 767-804, July.
  10. Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
  11. Bergstrom, A.R., 1984. "Continuous time stochastic models and issues of aggregation over time," Handbook of Econometrics, in: Z. Griliches† & M. D. Intriligator (ed.), Handbook of Econometrics, edition 1, volume 2, chapter 20, pages 1145-1212 Elsevier.
  12. Vasicek, Oldrich Alfonso, 1977. "Abstract: An Equilibrium Characterization of the Term Structure," Journal of Financial and Quantitative Analysis, Cambridge University Press, vol. 12(04), pages 627-627, November.
  13. 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.
  14. Sargan, J D, 1976. "Econometric Estimators and the Edgeworth Approximation," Econometrica, Econometric Society, vol. 44(3), pages 421-48, May.
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 in new window

Cited by:
  1. Qiankun Zhou & Jun Yu, 2012. "Asymptotic Distributions of the Least Squares Estimator for Diffusion Processes," Working Papers 11-2012, Singapore Management University, School of Economics.
  2. Jun Yu, 2009. "Bias in the Estimation of the Mean Reversion Parameter in Continuous Time Models," Microeconomics Working Papers 23045, East Asian Bureau of Economic Research.
  3. Peter C. B. Phillips & Jun Yu, 2009. "Simulation-Based Estimation of Contingent-Claims Prices," Review of Financial Studies, Society for Financial Studies, vol. 22(9), pages 3669-3705, September.
  4. Chang, Jinyuan & Chen, Songxi, 2011. "On the Approximate Maximum Likelihood Estimation for Diffusion Processes," MPRA Paper 46279, University Library of Munich, Germany.
  5. Xu, Weijun & Sun, Qi & Xiao, Weilin, 2012. "A new energy model to capture the behavior of energy price processes," Economic Modelling, Elsevier, vol. 29(5), pages 1585-1591.
  6. Choi, Hwan-sik & Jeong, Minsoo & Park, Joon Y., 2014. "An asymptotic analysis of likelihood-based diffusion model selection using high frequency data," Journal of Econometrics, Elsevier, vol. 178(P3), pages 539-557.
  7. Xiaohu Wang & Peter C.B. Phillips & Jun Yu, 2011. "Bias in Estimating Multivariate and Univariate Diffusions," Cowles Foundation Discussion Papers 1778, Cowles Foundation for Research in Economics, Yale University.
  8. Wang, Yunyan & Zhang, Lixin & Tang, Mingtian, 2012. "Local M-estimation for jump-diffusion processes," Statistics & Probability Letters, Elsevier, vol. 82(7), pages 1273-1284.
  9. Ye Chen & Jun Yu, 2012. "Optimal Jackknife for Discrete Time and Continuous Time Unit Root Models," Working Papers 15-2012, Singapore Management University, School of Economics.
  10. Xiaohu Wang & Jun Yu, 2012. "Double Asymptotics for Explosive Continuous Time Models," Working Papers 16-2012, Singapore Management University, School of Economics.
  11. Bao, Yong & Ullah, Aman & Zinde-Walsh, Victoria, 2013. "On existence of moment of mean reversion estimator in linear diffusion models," Economics Letters, Elsevier, vol. 120(2), pages 146-148.
  12. Noh, Jungsik & Lee, Seung Y. & Lee, Sangyeol, 2012. "Quantile regression estimation for discretely observed SDE models with compound Poisson jumps," Economics Letters, Elsevier, vol. 117(3), pages 734-738.
  13. Ka-Fai Li & Cho-Hoi Hui & Tsz-Kin Chung, 2012. "Determinants and Dynamics of Price Disparity in Onshore and Offshore Renminbi Forward Exchange Rate Markets," Working Papers 242012, Hong Kong Institute for Monetary Research.
  14. Picchini, Umberto & Ditlevsen, Susanne, 2011. "Practical estimation of high dimensional stochastic differential mixed-effects models," Computational Statistics & Data Analysis, Elsevier, vol. 55(3), pages 1426-1444, March.

Lists

This item is not listed on Wikipedia, on a reading list or among the top items on IDEAS.

Statistics

Access and download statistics

Corrections

When requesting a correction, please mention this item's handle: RePEc:eee:econom:v:149:y:2009:i:1:p:65-81. See general information about how to correct material in RePEc.

For technical questions regarding this item, or to correct its authors, title, abstract, bibliographic or download information, contact: (Zhang, Lei).

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 references are entirely missing, you can add them using this form.

If the full references list an item that is present in RePEc, but the system did not link 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 profile, as there may be some citations waiting for confirmation.

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