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Volatility Activity: Specification and Estimation

  • Viktor Todorov
  • George Tauchen
  • Iaryna Grynkiv

The paper examines volatility activity and its asymmetry and undertakes further specification analysis of volatility models based on it. We develop new nonparametric statistics using high frequency option-based VIX data to test for asymmetry in volatility jumps. We also develop methods to estimate and evaluate, using price data alone, a general encompassing model for volatility dynamics where volatility activity is unrestricted. The nonparametric application to VIX data, along with model estimation for S&P Index returns, suggests that volatility moves are best captured by infinite variation pure-jump martingale with symmetric jump distribution. The latter provides a parsimonious generalization of the jump-diffusions commonly used for volatility modeling.

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Paper provided by Duke University, Department of Economics in its series Working Papers with number 11-23.

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Length: 32
Date of creation: 2011
Date of revision:
Handle: RePEc:duk:dukeec:11-23
Contact details of provider: Postal: Department of Economics Duke University 213 Social Sciences Building Box 90097 Durham, NC 27708-0097
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  1. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
  2. Mikhail Chernov & A. Ronald Gallant & Eric Ghysels & George Tauchen, 2002. "Alternative Models for Stock Price Dynamics," CIRANO Working Papers 2002s-58, CIRANO.
  3. Todorov, Viktor & Tauchen, George, 2011. "Volatility Jumps," Journal of Business & Economic Statistics, American Statistical Association, vol. 29(3), pages 356-371.
  4. George Tauchen & Viktor Todorov, 2010. "Activity Signature Functions for High-Frequency Data Analysis," Working Papers 10-08, Duke University, Department of Economics.
  5. 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.
  6. 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.
  7. Viktor Todorov & Iaryna Grynkiv & George Tauchen, 2010. "Realized Laplace Transforms for Estimation of Jump Diffusive Volatility Models," Working Papers 10-75, Duke University, Department of Economics.
  8. 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, 06.
  9. Viktor Todorov & George Tauchen, 2010. "The Realized Laplace Transform of Volatility," Working Papers 10-72, Duke University, Department of Economics.
  10. 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.
  11. 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.
  12. 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.
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