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Detecting jumps from Lévy jump diffusion processes

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  • Lee, Suzanne S.
  • Hannig, Jan

Abstract

Recent asset-pricing models incorporate jump risk through Lévy processes in addition to diffusive risk. This paper studies how to detect stochastic arrivals of small and big Lévy jumps with new nonparametric tests. The tests allow for robust analysis of their separate characteristics and facilitate better estimation of return dynamics. Empirical evidence of both small and big jumps based on these tests suggests that models for individual equities and overall market indices require incorporating Lévy-type jumps. The evidence of small jumps also helps explain why jumps in the market index are uncorrelated with jumps in its component equities.

Suggested Citation

  • Lee, Suzanne S. & Hannig, Jan, 2010. "Detecting jumps from Lévy jump diffusion processes," Journal of Financial Economics, Elsevier, vol. 96(2), pages 271-290, May.
  • Handle: RePEc:eee:jfinec:v:96:y:2010:i:2:p:271-290
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    References listed on IDEAS

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    Citations

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    Cited by:

    1. Pierre Bajgrowicz & Olivier Scaillet & Adrien Treccani, 2016. "Jumps in High-Frequency Data: Spurious Detections, Dynamics, and News," Management Science, INFORMS, vol. 62(8), pages 2198-2217, August.
    2. Gilder, Dudley & Shackleton, Mark B. & Taylor, Stephen J., 2014. "Cojumps in stock prices: Empirical evidence," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 443-459.
    3. Kuttu, Saint, 2017. "Time-varying conditional discrete jumps in emerging African equity markets," Global Finance Journal, Elsevier, vol. 32(C), pages 35-54.
    4. Grothe, Oliver & Nicklas, Stephan, 2013. "Vine constructions of Lévy copulas," Journal of Multivariate Analysis, Elsevier, vol. 119(C), pages 1-15.
    5. repec:eee:econom:v:202:y:2018:i:1:p:18-44 is not listed on IDEAS
    6. Deniz Erdemlioglu & Sébastien Laurent & Christopher J. Neely, 2013. "Econometric modeling of exchange rate volatility and jumps," Chapters,in: Handbook of Research Methods and Applications in Empirical Finance, chapter 16, pages 373-427 Edward Elgar Publishing.
    7. repec:eee:dyncon:v:80:y:2017:i:c:p:75-100 is not listed on IDEAS
    8. Li, Meiyu & Gençay, Ramazan & Xue, Yi, 2016. "Is it Brownian or fractional Brownian motion?," Economics Letters, Elsevier, vol. 145(C), pages 52-55.
    9. Erdemlioglu, Deniz & Laurent, Sébastien & Neely, Christopher J., 2015. "Which continuous-time model is most appropriate for exchange rates?," Journal of Banking & Finance, Elsevier, vol. 61(S2), pages 256-268.
    10. repec:eee:insuma:v:74:y:2017:i:c:p:46-62 is not listed on IDEAS
    11. 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.
    12. Yacine Aït-Sahalia & Jean Jacod, 2010. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," NBER Working Papers 15808, National Bureau of Economic Research, Inc.
    13. Adam D. Bull, 2014. "Near-optimal estimation of jump activity in semimartingales," Papers 1409.8150, arXiv.org, revised Jan 2016.
    14. Yacine Aït-Sahalia & Jean Jacod, 2012. "Analyzing the Spectrum of Asset Returns: Jump and Volatility Components in High Frequency Data," Journal of Economic Literature, American Economic Association, vol. 50(4), pages 1007-1050, December.
    15. Aït-Sahalia, Yacine & Jacod, Jean & Li, Jia, 2012. "Testing for jumps in noisy high frequency data," Journal of Econometrics, Elsevier, vol. 168(2), pages 207-222.
    16. Jozef Barunik & Lukas Vacha, 2016. "Do co-jumps impact correlations in currency markets?," Papers 1602.05489, arXiv.org, revised Oct 2017.
    17. Aït-Sahalia, Yacine & Cacho-Diaz, Julio & Laeven, Roger J.A., 2015. "Modeling financial contagion using mutually exciting jump processes," Journal of Financial Economics, Elsevier, vol. 117(3), pages 585-606.
    18. Xin Zhang & Donggyu Kim & Yazhen Wang, 2016. "Jump Variation Estimation with Noisy High Frequency Financial Data via Wavelets," Econometrics, MDPI, Open Access Journal, vol. 4(3), pages 1-26, August.
    19. repec:gam:jecnmx:v:5:y:2017:i:4:p:51-:d:118613 is not listed on IDEAS
    20. Li, Junye, 2012. "Option-implied volatility factors and the cross-section of market risk premia," Journal of Banking & Finance, Elsevier, vol. 36(1), pages 249-260.
    21. repec:eee:ejores:v:262:y:2017:i:1:p:381-400 is not listed on IDEAS

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