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Semiparametric Diffusion Estimation and Application to a Stock Market Index

The analysis of diffusion process in financial models is crucially dependent on the form of the drift and diffusion coefficient functions. A methodology is proposed for estimating and testing coefficient functions for ergodic diffusions that are not directly observable. It is based on semiparametric and nonparametric estimates. The testing is performed via the wild bootstrap resampling technique. The method is illustrated on S&P 500 index.

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File URL: http://www.qfrc.uts.edu.au/research/research_papers/rp51.pdf
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Paper provided by Quantitative Finance Research Centre, University of Technology, Sydney in its series Research Paper Series with number 51.

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Length: 20 pages
Date of creation: 01 Mar 2001
Date of revision:
Publication status: Published as: Hardle, W., Kleinow, A., Logeay, C. and Platen, E., 2008, "Semiparametric Diffusion Estimation and Application to a Stock Market Index", Qantitative Finance, 8(1), 81-92.
Handle: RePEc:uts:rpaper:51
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  1. Duan, Jin-Chuan, 1997. "Augmented GARCH (p,q) process and its diffusion limit," Journal of Econometrics, Elsevier, vol. 79(1), pages 97-127, July.
  2. GHYSELS, Eric & HARVEY, Andrew & RENAULT, Eric, 1995. "Stochastic Volatility," CORE Discussion Papers 1995069, Université catholique de Louvain, Center for Operations Research and Econometrics (CORE).
  3. Hardle, W., 1992. "Applied Nonparametric Methods," Papers 9204, Catholique de Louvain - Institut de statistique.
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  5. Platen, Eckhard, 2000. "Risk premia and financial modelling without measure transformation," SFB 373 Discussion Papers 2000,92, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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  10. Hansen, Lars Peter & Alexandre Scheinkman, Jose & Touzi, Nizar, 1998. "Spectral methods for identifying scalar diffusions," Journal of Econometrics, Elsevier, vol. 86(1), pages 1-32, June.
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  12. 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.
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  15. 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(05), pages 615-645, October.
  16. Frey, Rüdiger, 1997. "Derivative Asset Analysis in Models with Level-Dependent and Stochastic Volatility," Discussion Paper Serie B 401, University of Bonn, Germany.
  17. Wolfgang HÄRDLE & A. TSYBAKOV, 1995. "Local Polynomial Estimators of the Volatility Function in Nonparametric Autoregression," SFB 373 Discussion Papers 1995,42, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
  18. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
  19. Eckhard Platen, 2003. "Modeling the Volatility and Expected Value of a Diversified World Index," Research Paper Series 103, Quantitative Finance Research Centre, University of Technology, Sydney.
  20. Hall, Peter, 1985. "Resampling a coverage pattern," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 231-246, September.
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