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Levy Process Models for High Frequency Financial Data


  • George Tauchen


In this paper we present parametric estimation of models for stock returns by describing price dynamic as the sum of two independent Levy components. The increments (moves) are viewed as discrete-time log price changes that follow an infinitely divisible distribution, i.e. stationary and independent price changes (zero drift) that follow a Levy-type distribution. We explore empirical plausibility of two parametric models: Jump-Diffusion (C-J) and pure jump model (TS-J). The first process describes dynamics of small frequent moves and is modeled by Brownian motion in C-J model and by tempered stable Levy process in TS-J model. The second process is responsible for big rare moves in asset prices and is modeled by compound Poisson process in both models. The estimation is performed via continuously updated GMM by matching the characteristic function implied by the model with the observed characteristic function. Using high frequency data on 13 stocks of different market capitalization for 2006-2008 sample period we find that C-J model performs well only for large cap stocks, while medium cap stock dynamics are captured by TS-J model. We also report evidence of positive relation between activity index of the process for stock returns and its frequency of trading.

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  • George Tauchen, 2011. "Levy Process Models for High Frequency Financial Data," Working Papers 11-22, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:11-22

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    References listed on IDEAS

    1. Todorov, Viktor & Tauchen, George, 2010. "Activity signature functions for high-frequency data analysis," Journal of Econometrics, Elsevier, vol. 154(2), pages 125-138, February.
    2. Torben G. Andersen & Luca Benzoni & Jesper Lund, 2002. "An Empirical Investigation of Continuous-Time Equity Return Models," Journal of Finance, American Finance Association, vol. 57(3), pages 1239-1284, June.
    3. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
    4. Viktor Todorov & George Tauchen, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, Taylor & Francis Journals, vol. 29(3), pages 356-371, July.
    5. Carrasco, Marine & Chernov, Mikhail & Florens, Jean-Pierre & Ghysels, Eric, 2007. "Efficient estimation of general dynamic models with a continuum of moment conditions," Journal of Econometrics, Elsevier, vol. 140(2), pages 529-573, October.
    6. Viktor Todorov & George Tauchen, 2012. "The Realized Laplace Transform of Volatility," Econometrica, Econometric Society, vol. 80(3), pages 1105-1127, May.
    7. Chernov, Mikhail & Ronald Gallant, A. & Ghysels, Eric & Tauchen, George, 2003. "Alternative models for stock price dynamics," Journal of Econometrics, Elsevier, vol. 116(1-2), pages 225-257.
    8. Ole E. Barndorff-Nielsen, 2004. "Power and Bipower Variation with Stochastic Volatility and Jumps," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 2(1), pages 1-37.
    9. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2011. "Realized Laplace transforms for estimation of jump diffusive volatility models," Journal of Econometrics, Elsevier, vol. 164(2), pages 367-381, October.
    10. Cecilia Mancini, 2009. "Non-parametric Threshold Estimation for Models with Stochastic Diffusion Coefficient and Jumps," Scandinavian Journal of Statistics, Danish Society for Theoretical Statistics;Finnish Statistical Society;Norwegian Statistical Association;Swedish Statistical Association, vol. 36(2), pages 270-296.
    11. Ole E. Barndorff-Nielsen & Neil Shephard, 2001. "Non-Gaussian Ornstein-Uhlenbeck-based models and some of their uses in financial economics," Journal of the Royal Statistical Society Series B, Royal Statistical Society, vol. 63(2), pages 167-241.
    12. Peter Carr & Helyette Geman, 2002. "The Fine Structure of Asset Returns: An Empirical Investigation," The Journal of Business, University of Chicago Press, vol. 75(2), pages 305-332, April.
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    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
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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