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Jump Tails, Extreme Dependencies, and the Distribution of Stock Returns

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  • Tim Bollerslev

    () (Department of Economics, Duke University, and NBER and CREATES)

  • Viktor Todorov

    () (Department of Finance, Kellogg School of Management, Northwestern University)

Abstract

We provide a new framework for estimating the systematic and idiosyncratic jump tail risks in financial asset prices. The theory underlying our estimates are based on in-fill asymptotic arguments for directly identifying the systematic and idiosyncratic jumps, together with conventional long-span asymptotics and Extreme Value Theory (EVT) approximations for consistently estimating the tail decay parameters and asymptotic tail dependencies. On implementing the new estimation procedures with a panel of highfrequency intraday prices for a large cross-section of individual stocks and the aggregate S&P 500 market portfolio, we find that the distributions of the systematic and idiosyncratic jumps are both generally heavy-tailed and not necessarily symmetric. Our estimates also point to the existence of strong dependencies between the market-wide jumps and the corresponding systematic jump tails for all of the stocks in the sample. We also show how the jump tail dependencies deduced from the high-frequency data together with the day-to-day temporal variation in the volatility are able to explain the “extreme” dependencies vis-a-vis the market portfolio.

Suggested Citation

  • Tim Bollerslev & Viktor Todorov, 2010. "Jump Tails, Extreme Dependencies, and the Distribution of Stock Returns," CREATES Research Papers 2010-64, Department of Economics and Business Economics, Aarhus University.
  • Handle: RePEc:aah:create:2010-64
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    References listed on IDEAS

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    Cited by:

    1. repec:eee:econom:v:202:y:2018:i:1:p:18-44 is not listed on IDEAS
    2. Wang, Hao & Yue, Mengqi & Zhao, Hua, 2015. "Cojumps in China's spot and stock index futures markets," Pacific-Basin Finance Journal, Elsevier, pages 541-557.
    3. Vitali Alexeev & Mardi Dungey & Wenying Yao, 2016. "Continuous and Jump Betas: Implications for Portfolio Diversification," Econometrics, MDPI, Open Access Journal, vol. 4(2), pages 1-15, June.
    4. Bollerslev, Tim & Patton, Andrew J. & Quaedvlieg, Rogier, 2016. "Exploiting the errors: A simple approach for improved volatility forecasting," Journal of Econometrics, Elsevier, pages 1-18.
    5. Tim Bollerslev & Sophia Zhengzi Li & Viktor Todorov, 2014. "Roughing up Beta: Continuous vs. Discontinuous Betas, and the Cross-Section of Expected Stock Returns," CREATES Research Papers 2014-48, Department of Economics and Business Economics, Aarhus University.
    6. António Rua, 2011. "A wavelet approach for factor‐augmented forecasting," Journal of Forecasting, John Wiley & Sons, Ltd., vol. 30(7), pages 666-678, November.
    7. Bollerslev, Tim & Li, Sophia Zhengzi & Todorov, Viktor, 2016. "Roughing up beta: Continuous versus discontinuous betas and the cross section of expected stock returns," Journal of Financial Economics, Elsevier, vol. 120(3), pages 464-490.
    8. Miguel Carvalho & António Rua, 2014. "Extremal Dependence in International Output Growth: Tales from the Tails," Oxford Bulletin of Economics and Statistics, Department of Economics, University of Oxford, vol. 76(4), pages 605-620, August.
    9. Lucio Maria Calcagnile & Giacomo Bormetti & Michele Treccani & Stefano Marmi & Fabrizio Lillo, 2015. "Collective synchronization and high frequency systemic instabilities in financial markets," Papers 1505.00704, arXiv.org.
    10. Grothe, Oliver & Korniichuk, Volodymyr & Manner, Hans, 2014. "Modeling multivariate extreme events using self-exciting point processes," Journal of Econometrics, Elsevier, vol. 182(2), pages 269-289.
    11. Tolikas, Konstantinos, 2014. "Unexpected tails in risk measurement: Some international evidence," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 476-493.
    12. Xu, Weijun & Liu, Guifang & Li, Hongyi, 2016. "A novel jump diffusion model based on SGT distribution and its applications," Economic Modelling, Elsevier, vol. 59(C), pages 74-92.
    13. De Lira Salvatierra, Irving & Patton, Andrew J., 2015. "Dynamic copula models and high frequency data," Journal of Empirical Finance, Elsevier, pages 120-135.
    14. Paolella, Marc S. & Polak, Paweł, 2015. "COMFORT: A common market factor non-Gaussian returns model," Journal of Econometrics, Elsevier, vol. 187(2), pages 593-605.
    15. Aguilar, Mike & Hill, Jonathan B., 2015. "Robust score and portmanteau tests of volatility spillover," Journal of Econometrics, Elsevier, vol. 184(1), pages 37-61.
    16. Yao, Wenying & Tian, Jing, 2015. "The role of intra-day volatility pattern in jump detection: empirical evidence on how financial markets respond to macroeconomic news announcements," Working Papers 2015-05, University of Tasmania, Tasmanian School of Business and Economics.
    17. Schwarz, Claudia, 2014. "Investor fears and risk premia for rare events," Discussion Papers 03/2014, Deutsche Bundesbank.
    18. 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.
    19. Cui, Jing & Zhao, Hua, 2015. "Intraday jumps in China's Treasury bond market and macro news announcements," International Review of Economics & Finance, Elsevier, vol. 39(C), pages 211-223.
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    More about this item

    Keywords

    Extreme events; jumps; high-frequency data; jump tails; non-parametric estimation; stochastic volatility; systematic risks; tail dependence.;

    JEL classification:

    • C13 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Estimation: General
    • C14 - Mathematical and Quantitative Methods - - Econometric and Statistical Methods and Methodology: General - - - Semiparametric and Nonparametric Methods: General
    • G10 - Financial Economics - - General Financial Markets - - - General (includes Measurement and Data)
    • G12 - Financial Economics - - General Financial Markets - - - Asset Pricing; Trading Volume; Bond Interest Rates

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