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Semiparametric diffusion estimation and application to a stock market index

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  • Härdle, Wolfgang
  • Kleinow, Torsten
  • Korostelev, Alexander P.
  • Logeay, Camille
  • Platen, Eckhard

Abstract

The analysis of diffusion processes 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 data.

Suggested Citation

  • Härdle, Wolfgang & Kleinow, Torsten & Korostelev, Alexander P. & Logeay, Camille & Platen, Eckhard, 2001. "Semiparametric diffusion estimation and application to a stock market index," SFB 373 Discussion Papers 2001,24, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    • Handle: RePEc:zbw:sfb373:200124
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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. Nelson, Daniel B., 1990. "ARCH models as diffusion approximations," Journal of Econometrics, Elsevier, vol. 45(1-2), pages 7-38.
    3. Ghysels, E. & Harvey, A. & Renault, E., 1995. "Stochastic Volatility," Papers 95.400, Toulouse - GREMAQ.
    4. Gallant, A. Ronald & Tauchen, George, 1996. "Which Moments to Match?," Econometric Theory, Cambridge University Press, vol. 12(4), pages 657-681, October.
    5. 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..
    6. Ait-Sahalia, Yacine, 1996. "Nonparametric Pricing of Interest Rate Derivative Securities," Econometrica, Econometric Society, vol. 64(3), pages 527-560, May.
    7. Eckhard Platen, 2006. "A Benchmark Approach To Finance," Mathematical Finance, Wiley Blackwell, vol. 16(1), pages 131-151, January.
    8. 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.
    9. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    10. Eckhard Platen, 2001. "Arbitrage in Continuous Complete Markets," Research Paper Series 72, Quantitative Finance Research Centre, University of Technology, Sydney.
    11. C. Renner & J. Peinke & R. Friedrich, 2001. "Markov properties of high frequency exchange rate data," Papers cond-mat/0102494, arXiv.org, revised Apr 2001.
    12. J. Franke & J.‐P. Kreiss & E. Mammen & M. H. Neumann, 2002. "Properties of the nonparametric autoregressive bootstrap," Journal of Time Series Analysis, Wiley Blackwell, vol. 23(5), pages 555-585, September.
    13. 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.
    14. Renner, Ch. & Peinke, J. & Friedrich, R., 2001. "Evidence of Markov properties of high frequency exchange rate data," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 298(3), pages 499-520.
    15. Eckhard Platen & Rolando Rebolledo, 1996. "Principles for modelling financial markets," Published Paper Series 1996-3, Finance Discipline Group, UTS Business School, University of Technology, Sydney.
    16. Hardle, Wolfgang & Linton, Oliver, 1986. "Applied nonparametric methods," Handbook of Econometrics, in: R. F. Engle & D. McFadden (ed.), Handbook of Econometrics, edition 1, volume 4, chapter 38, pages 2295-2339, Elsevier.
    17. 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.
    18. 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.
    19. Eckhard Platen, 2004. "Modeling The Volatility And Expected Value Of A Diversified World Index," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 7(04), pages 511-529.
    20. Hall, Peter, 1985. "Resampling a coverage pattern," Stochastic Processes and their Applications, Elsevier, vol. 20(2), pages 231-246, September.
    21. 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.
    22. Hardle, W. & Tsybakov, A., 1997. "Local polynomial estimators of the volatility function in nonparametric autoregression," Journal of Econometrics, Elsevier, vol. 81(1), pages 223-242, November.
    23. Hans Föllmer & Martin Schweizer, 1993. "A Microeconomic Approach to Diffusion Models For Stock Prices," Mathematical Finance, Wiley Blackwell, vol. 3(1), pages 1-23, January.
    24. Franke, Jürgen & Kreiss, Jens-Peter & Mammen, Enno & Neumann, Michael H., 1998. "Properties of the nonparametric autoregressive bootstrap," SFB 373 Discussion Papers 1998,54, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
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    Cited by:

    1. Härdle, Wolfgang & Horowitz, Joel L. & Kreiss, Jens-Peter, 2001. "Bootstrap methods for time series," SFB 373 Discussion Papers 2001,59, Humboldt University of Berlin, Interdisciplinary Research Project 373: Quantification and Simulation of Economic Processes.
    2. Liu, Hsing & Liao, Chi-Yo & Ko, Jing-Yuan & Lih, Jiann-Shing, 2017. "Anchoring effect on first passage process in Taiwan financial market," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 477(C), pages 114-127.
    3. Wolfgang Härdle & Joel Horowitz & Jens‐Peter Kreiss, 2003. "Bootstrap Methods for Time Series," International Statistical Review, International Statistical Institute, vol. 71(2), pages 435-459, August.

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    More about this item

    Keywords

    Identification; Bootstrap; Diffusion; Continuous-time financial models; Semiparametric methods; Kernel smoothing;
    All these keywords.

    JEL classification:

    • C51 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Construction and Estimation
    • C52 - Mathematical and Quantitative Methods - - Econometric Modeling - - - Model Evaluation, Validation, and Selection
    • G22 - Financial Economics - - Financial Institutions and Services - - - Insurance; Insurance Companies; Actuarial Studies

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