Advanced Search
MyIDEAS: Login to save this paper or follow this series

Estimation in Two Classes of Semiparametric Diffusion Models

Contents:

Author Info

  • Dennis Kristensen

    ()

Abstract

In this paper we propose an estimation method for two classes of semiparametric scalar diffusion models driven by a Brownian motion: In the first class, only the diffusion term is parameterised while the drift is unspecified; in the second, the drift term is specified while the diffusion term is of unknown form. The estimation method is based on the assumption of stationarity of the observed process. This allows us to express the unspecified term as a functional of the parametric part and the stationary density. A MLE-like estimator for the parametric part and a kernel estimator of the nonparametric part are defined for a discrete sample with a fixed time distance between the observations. We show that the parametric part of the estimator is n-consistent, while the nonparametric part has a slower convergence rate. Also, the asymptotic distribution of the estimator is derived. We give a brief discussion of the issue of semiparametric efficiency, and present a small simulation study of the finite-sample performance of our estimator.

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.lse.ac.uk/fmg/workingPapers/discussionPapers/fmgdps/dp500.pdf
Download Restriction: no

Bibliographic Info

Paper provided by Financial Markets Group in its series FMG Discussion Papers with number dp500.

as in new window
Length:
Date of creation: Jun 2004
Date of revision:
Handle: RePEc:fmg:fmgdps:dp500

Contact details of provider:
Web page: http://www.lse.ac.uk/fmg/

Related research

Keywords:

Other versions of this item:

Find related papers by JEL classification:

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. Xiaohong Chen & Oliver Linton & Ingrid Van Keilegom, 2003. "Estimation of Semiparametric Models when the Criterion Function is not Smooth," STICERD - Econometrics Paper Series /2003/450, Suntory and Toyota International Centres for Economics and Related Disciplines, LSE.
  2. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
  3. 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.
  4. Newey, Whitney K & West, Kenneth D, 1987. "A Simple, Positive Semi-definite, Heteroskedasticity and Autocorrelation Consistent Covariance Matrix," Econometrica, Econometric Society, vol. 55(3), pages 703-08, May.
  5. Newey, Whitney K, 1994. "The Asymptotic Variance of Semiparametric Estimators," Econometrica, Econometric Society, vol. 62(6), pages 1349-82, November.
  6. Andrew W. Lo, . "Maximum Likelihood Estimation of Generalized Ito Processes with Discretely Sampled Data," Rodney L. White Center for Financial Research Working Papers 15-86, Wharton School Rodney L. White Center for Financial Research.
  7. Marc Hallin & Christophe Koell & Bas Werker, 2000. "Optimal inference for discretely observed semiparametric Ornstein-Uhlenbeck processes," ULB Institutional Repository 2013/2097, ULB -- Universite Libre de Bruxelles.
  8. Peter C.B. Phillips & Joon Y. Park, 1998. "Nonstationary Density Estimation and Kernel Autoregression," Cowles Foundation Discussion Papers 1181, Cowles Foundation for Research in Economics, Yale University.
  9. Ahn, Dong-Hyun & Gao, Bin, 1999. "A Parametric Nonlinear Model of Term Structure Dynamics," Review of Financial Studies, Society for Financial Studies, vol. 12(4), pages 721-62.
  10. Sundaresan, S.M., 2000. "Continuous-Time Methods in Finance: A Review and an Assessment," Papers 00-03, Columbia - Graduate School of Business.
  11. Lars Peter Hansen & Jose Alexandre Scheinkman, 1993. "Back to the Future: Generating Moment Implications for Continuous-Time Markov Processes," NBER Technical Working Papers 0141, National Bureau of Economic Research, Inc.
  12. Elerian, O. & Chib, S. & Shephard, N., 1998. "Likelihood INference for Discretely Observed Non-linear Diffusions," Economics Papers 146, Economics Group, Nuffield College, University of Oxford.
  13. Gourieroux, C & Monfort, A & Renault, E, 1993. "Indirect Inference," Journal of Applied Econometrics, John Wiley & Sons, Ltd., vol. 8(S), pages S85-118, Suppl. De.
  14. Tauchen, George, 1985. "Diagnostic testing and evaluation of maximum likelihood models," Journal of Econometrics, Elsevier, vol. 30(1-2), pages 415-443.
  15. Newey, Whitney K., 1994. "Kernel Estimation of Partial Means and a General Variance Estimator," Econometric Theory, Cambridge University Press, vol. 10(02), pages 1-21, June.
  16. 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.
  17. Phillips, P. C. B., 1973. "The problem of identification in finite parameter continuous time models," Journal of Econometrics, Elsevier, vol. 1(4), pages 351-362, December.
  18. Drost, F.C. & Klaassen, C.A.J. & Werker, B.J.M., 1994. "Adaptive estimation in time-series models," Discussion Paper 1994-88, Tilburg University, Center for Economic Research.
  19. Powell, James L. & Stoker, Thomas M., 1996. "Optimal bandwidth choice for density-weighted averages," Journal of Econometrics, Elsevier, vol. 75(2), pages 291-316, December.
  20. Vasicek, Oldrich, 1977. "An equilibrium characterization of the term structure," Journal of Financial Economics, Elsevier, vol. 5(2), pages 177-188, November.
  21. Chunrong Ai, 1997. "A Semiparametric Maximum Likelihood Estimator," Econometrica, Econometric Society, vol. 65(4), pages 933-964, July.
  22. Ait-Sahalia, Yacine, 1996. "Testing Continuous-Time Models of the Spot Interest Rate," Review of Financial Studies, Society for Financial Studies, vol. 9(2), pages 385-426.
  23. Whitney K. Newey & Fushing Hsieh & James M. Robins, 2004. "Twicing Kernels and a Small Bias Property of Semiparametric Estimators," Econometrica, Econometric Society, vol. 72(3), pages 947-962, 05.
  24. Constantinides, George M, 1992. "A Theory of the Nominal Term Structure of Interest Rates," Review of Financial Studies, Society for Financial Studies, vol. 5(4), pages 531-52.
  25. Fan, Yanqin, 1994. "Testing the Goodness of Fit of a Parametric Density Function by Kernel Method," Econometric Theory, Cambridge University Press, vol. 10(02), pages 316-356, June.
  26. Arcones, Miguel A., 1995. "On the central limit theorem for U-statistics under absolute regularity," Statistics & Probability Letters, Elsevier, vol. 24(3), pages 245-249, August.
  27. 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 1259-82, September.
  28. Joel L. Horowitz, 2003. "Bootstrap Methods for Markov Processes," Econometrica, Econometric Society, vol. 71(4), pages 1049-1082, 07.
  29. 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 1209-27, July.
  30. Andrews, Donald W K, 1994. "Asymptotics for Semiparametric Econometric Models via Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 62(1), pages 43-72, January.
  31. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-60, May.
  32. Xiaohong Chen & Xiaotong Shen, 1998. "Sieve Extremum Estimates for Weakly Dependent Data," Econometrica, Econometric Society, vol. 66(2), pages 289-314, March.
  33. Gobet, Emmanuel & Hoffmann, Marc & Reiß, Markus, 2002. "Nonparametric estimation of scalar diffusions based on low frequency data is ill-posed," SFB 373 Discussion Papers 2002,57, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  34. Merton, Robert C., 1976. "Option pricing when underlying stock returns are discontinuous," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 125-144.
  35. Robinson, Peter M, 1988. "Root- N-Consistent Semiparametric Regression," Econometrica, Econometric Society, vol. 56(4), pages 931-54, July.
  36. Andrews, Donald W.K., 1995. "Nonparametric Kernel Estimation for Semiparametric Models," Econometric Theory, Cambridge University Press, vol. 11(03), pages 560-586, June.
  37. Newey, Whitney K, 1991. "Uniform Convergence in Probability and Stochastic Equicontinuity," Econometrica, Econometric Society, vol. 59(4), pages 1161-67, July.
  38. 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.
  39. Duffie, Darrell & Singleton, Kenneth J, 1993. "Simulated Moments Estimation of Markov Models of Asset Prices," Econometrica, Econometric Society, vol. 61(4), pages 929-52, July.
  40. 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 635-46, May.
  41. Severini, Thomas A. & Tripathi, Gautam, 2001. "A simplified approach to computing efficiency bounds in semiparametric models," Journal of Econometrics, Elsevier, vol. 102(1), pages 23-66, May.
  42. 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.
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. Gao, Jiti & Casas, Isabel, 2006. "Specification testing in discretized diffusion models: Theory and practice," MPRA Paper 11980, University Library of Munich, Germany, revised Aug 2007.
  2. Xu, Ke-Li, 2009. "Empirical likelihood-based inference for nonparametric recurrent diffusions," Journal of Econometrics, Elsevier, vol. 153(1), pages 65-82, November.
  3. Dennis Kristensen, 2009. "Pseudo-Maximum Likelihood Estimation in Two Classes of Semiparametric Diffusion Models," CREATES Research Papers 2009-41, School of Economics and Management, University of Aarhus.
  4. Kristensen, Dennis & Shin, Yongseok, 2012. "Estimation of dynamic models with nonparametric simulated maximum likelihood," Journal of Econometrics, Elsevier, vol. 167(1), pages 76-94.
  5. Yu, Jialin, 2007. "Closed-form likelihood approximation and estimation of jump-diffusions with an application to the realignment risk of the Chinese Yuan," Journal of Econometrics, Elsevier, vol. 141(2), pages 1245-1280, December.
  6. Fuchun Li, 2005. "Testing the Parametric Specification of the Diffusion Function in a Diffusion Process," Working Papers 05-35, Bank of Canada.
  7. Kristensen, Dennis, 2008. "Estimation of partial differential equations with applications in finance," Journal of Econometrics, Elsevier, vol. 144(2), pages 392-408, June.

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:fmg:fmgdps:dp500. 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: (The FMG Administration).

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.