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Volatility Jumps

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Author Info

  • Viktor Todorov
  • George Tauchen

Abstract

The article undertakes a nonparametric analysis of the high-frequency movements in stock market volatility using very finely sampled data on the VIX volatility index compiled from options data by the CBOE. We derive theoretically the link between pathwise properties of the latent spot volatility and the VIX index, such as presence of continuous martingale and/or jumps, and further show how to make statistical inference about them from the observed data. Our empirical results suggest that volatility is a pure jump process with jumps of infinite variation and activity close to that of a continuous martingale. Additional empirical work shows that jumps in volatility and price level in most cases occur together, are strongly dependent, and have opposite sign. The latter suggests that jumps are an important channel for generating leverage effect.

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File URL: http://hdl.handle.net/10.1198/jbes.2010.08342
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Bibliographic Info

Article provided by Taylor & Francis Journals in its journal Journal of Business & Economic Statistics.

Volume (Year): 29 (2011)
Issue (Month): 3 (July)
Pages: 356-371

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Handle: RePEc:taf:jnlbes:v:29:y:2011:i:3:p:356-371

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Cited by:
  1. Mencía, Javier & Sentana, Enrique, 2013. "Valuation of VIX derivatives," Journal of Financial Economics, Elsevier, vol. 108(2), pages 367-391.
  2. Torben G. Andersen & Nicola Fusari & Viktor Todorov, 2012. "Parametric Inference and Dynamic State Recovery from Option Panels," NBER Working Papers 18046, National Bureau of Economic Research, Inc.
  3. Todorov, Viktor & Tauchen, George & Grynkiv, Iaryna, 2014. "Volatility activity: Specification and estimation," Journal of Econometrics, Elsevier, vol. 178(P1), pages 180-193.
  4. Corradi, Valentina & Distaso, Walter & Mele, Antonio, 2013. "Macroeconomic determinants of stock volatility and volatility premiums," Journal of Monetary Economics, Elsevier, vol. 60(2), pages 203-220.
  5. Andras Fulop & Junye Li & Jun Yu, 2012. "Investigating Impacts of Self-Exciting Jumps in Returns and Volatility: A Bayesian Learning Approach," Global COE Hi-Stat Discussion Paper Series gd12-264, Institute of Economic Research, Hitotsubashi University.
  6. Julien Chevallier & Benoît Sévi, 2012. "On the Stochastic Properties of Carbon Futures Prices," Working Papers halshs-00720166, HAL.
  7. Audrino, Francesco & Fengler, Matthias, 2013. "Are classical option pricing models consistent with observed option second-order moments? Evidence from high-frequency data," Economics Working Paper Series 1311, University of St. Gallen, School of Economics and Political Science.
  8. Julien Chevallier & Benoît Sévi, 2014. "On the Stochastic Properties of Carbon Futures Prices," Environmental & Resource Economics, European Association of Environmental and Resource Economists, vol. 58(1), pages 127-153, May.
  9. 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.
  10. Andras Fulop & Junye Li & Jun Yu, 2011. "Bayesian Learning of Impacts of Self-Exciting Jumps in Returns and Volatility," Working Papers CoFie-10-2011, Sim Kee Boon Institute for Financial Economics.
  11. Dungey, Mardi & Henry, Olan T & Hvodzdyk, Lyudmyla, 2013. "The impact of jumps and thin trading on realized hedge ratios," Working Papers 2013-02, University of Tasmania, School of Economics and Finance, revised 28 Mar 2013.
  12. Filip Zikes & Jozef Barunik, 2013. "Semiparametric Conditional Quantile Models for Financial Returns and Realized Volatility," Papers 1308.4276, arXiv.org.
  13. Kent Daniel & Ravi Jagannathan & Soohun Kim, 2012. "Tail Risk in Momentum Strategy Returns," NBER Working Papers 18169, National Bureau of Economic Research, Inc.
  14. Benoît Sévi & César Baena, 2011. "Brownian motion vs. pure-jump processes for individual stocks," Economics Bulletin, AccessEcon, vol. 31(4), pages 3138-3152.
  15. Kaeck, Andreas, 2013. "Asymmetry in the jump-size distribution of the S&P 500: Evidence from equity and option markets," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1872-1888.
  16. Audrino, Francesco & Hu, Yujia, 2011. "Volatility Forecasting: Downside Risk, Jumps and Leverage Effect," Economics Working Paper Series 1138, University of St. Gallen, School of Economics and Political Science.
  17. Massimiliano Caporin & Eduardo Rossi & Paolo Santucci de Magistris, 2011. "Conditional jumps in volatility and their economic determinants," "Marco Fanno" Working Papers 0138, Dipartimento di Scienze Economiche "Marco Fanno".

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