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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.

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File URL: ftp://ftp.econ.au.dk/creates/rp/10/rp10_64.pdf
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Bibliographic Info

Paper provided by School of Economics and Management, University of Aarhus in its series CREATES Research Papers with number 2010-64.

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Length: 34
Date of creation: 10 Sep 2010
Date of revision:
Handle: RePEc:aah:create:2010-64

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Web page: http://www.econ.au.dk/afn/

Related research

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

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References

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  1. Andersen, Torben G. & Bollerslev, Tim & Diebold, Francis X. & Vega, Clara, 2002. "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange," Working Papers 02-16, Duke University, Department of Economics.
  2. Hansen, Peter R. & Lunde, Asger, 2006. "Realized Variance and Market Microstructure Noise," Journal of Business & Economic Statistics, American Statistical Association, vol. 24, pages 127-161, April.
  3. 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.
  4. Tim Bollerslev & Viktor Todorov, 2011. "Tails, Fears, and Risk Premia," Journal of Finance, American Finance Association, vol. 66(6), pages 2165-2211, December.
  5. Torben G. Andersen & Tim Bollerslev & Per Frederiksen & Morten Ørregaard Nielsen, 2008. "Continuous-Time Models, Realized Volatilities, and Testable Distributional Implications for Daily Stock Returns," Working Papers 1173, Queen's University, Department of Economics.
  6. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," NBER Working Papers 8160, National Bureau of Economic Research, Inc.
  7. Ole E. Barndorff-Nielsen & Neil Shephard, 2006. "Econometrics of Testing for Jumps in Financial Economics Using Bipower Variation," Journal of Financial Econometrics, Society for Financial Econometrics, vol. 4(1), pages 1-30.
  8. Bjørn Eraker & Michael Johannes & Nicholas Polson, 2003. "The Impact of Jumps in Volatility and Returns," Journal of Finance, American Finance Association, vol. 58(3), pages 1269-1300, 06.
  9. Tim Bollerslev & Viktor Todorov, 2010. "Estimation of Jump Tails," CREATES Research Papers 2010-16, School of Economics and Management, University of Aarhus.
  10. Einmahl, J.H.J & Haan, L. de & Sinha, A., 1997. "Estimating the spectral measure of an extreme value distribution," Open Access publications from Tilburg University urn:nbn:nl:ui:12-125733, Tilburg University.
  11. 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.
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  19. Viktor Todorov & Tim Bollerslev, 2007. "Jumps and Betas: A New Framework for Disentangling and Estimating Systematic Risks," CREATES Research Papers 2007-15, School of Economics and Management, University of Aarhus.
  20. Kee-Hong Bae & G. Andrew Karolyi & René M. Stulz, 2003. "A New Approach to Measuring Financial Contagion," Review of Financial Studies, Society for Financial Studies, vol. 16(3), pages 717-763, July.
  21. Hill, Jonathan B., 2011. "Tail And Nontail Memory With Applications To Extreme Value And Robust Statistics," Econometric Theory, Cambridge University Press, vol. 27(04), pages 844-884, August.
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Citations

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Cited by:
  1. Tolikas, Konstantinos, 2014. "Unexpected tails in risk measurement: Some international evidence," Journal of Banking & Finance, Elsevier, vol. 40(C), pages 476-493.
  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. Schwarz, Claudia, 2014. "Investor fears and risk premia for rare events," Discussion Papers 03/2014, Deutsche Bundesbank, Research Centre.

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