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On the jump activity index for semimartingales

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  • Jing, Bing-Yi
  • Kong, Xin-Bing
  • Liu, Zhi
  • Mykland, Per
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    Abstract

    Empirical evidence of asset price discontinuities or “jumps” in financial markets has been well documented in the literature. Recently, Aït-Sahalia and Jacod (2009b) defined a general “jump activity index” to describe the degree of jump activities for asset price semimartingales, and provided a consistent estimator when the underlying process contains both a continuous and a jump component. However, only large increments were used in their estimator so that the effective sample size is very small even for large sample sizes. In this paper, we explore ways to improve the Aït-Sahalia and Jacod estimator by making use of all increments, large and small. The improvement is verified through simulations. A real example is also given.

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    Bibliographic Info

    Article provided by Elsevier in its journal Journal of Econometrics.

    Volume (Year): 166 (2012)
    Issue (Month): 2 ()
    Pages: 213-223

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    Handle: RePEc:eee:econom:v:166:y:2012:i:2:p:213-223

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    Web page: http://www.elsevier.com/locate/jeconom

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    Keywords: Semimartingale; Power variation; High frequency; Jump activity index; Stable convergence;

    References

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    1. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Econometrics of testing for jumps in financial economics using bipower variation," Economics Papers 2003-W21, Economics Group, Nuffield College, University of Oxford.
    2. Jacod, Jean, 2008. "Asymptotic properties of realized power variations and related functionals of semimartingales," Stochastic Processes and their Applications, Elsevier, vol. 118(4), pages 517-559, April.
    3. Fan, Jianqing & Wang, Yazhen, 2007. "Multi-Scale Jump and Volatility Analysis for High-Frequency Financial Data," Journal of the American Statistical Association, American Statistical Association, vol. 102, pages 1349-1362, December.
    4. Jérémy Poirot & Peter Tankov, 2006. "Monte Carlo Option Pricing for Tempered Stable (CGMY) Processes," Asia-Pacific Financial Markets, Springer, vol. 13(4), pages 327-344, December.
    5. Yacine Ait-Sahalia, 2001. "Telling from Discrete Data Whether the Underlying Continuous-Time Model is a Diffusion," NBER Working Papers 8504, National Bureau of Economic Research, Inc.
    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. Zhao, Zhibiao & Wu, Wei Biao, 2009. "Nonparametric inference of discretely sampled stable Lévy processes," Journal of Econometrics, Elsevier, vol. 153(1), pages 83-92, November.
    8. Viktor Todorov & George Tauchen, 2010. "Limit Theorems for Power Variations of Pure-Jump Processes with Application to Activity Estimation," Working Papers 10-74, Duke University, Department of Economics.
    9. Ait-Sahalia, Yacine, 2004. "Disentangling diffusion from jumps," Journal of Financial Economics, Elsevier, vol. 74(3), pages 487-528, December.
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    Cited by:
    1. Figueroa-López, José E. & Nisen, Jeffrey, 2013. "Optimally thresholded realized power variations for Lévy jump diffusion models," Stochastic Processes and their Applications, Elsevier, vol. 123(7), pages 2648-2677.

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