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

  • Tim Bollerslev

    ()

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

  • Viktor Todorov

    ()

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

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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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
Contact details of provider: Web page: http://www.econ.au.dk/afn/

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  1. François Longin, 2001. "Extreme Correlation of International Equity Markets," Journal of Finance, American Finance Association, vol. 56(2), pages 649-676, 04.
  2. Merton, Robert C., 1975. "Option pricing when underlying stock returns are discontinuous," Working papers 787-75., Massachusetts Institute of Technology (MIT), Sloan School of Management.
  3. Bollerslev, Tim, 1987. "A Conditionally Heteroskedastic Time Series Model for Speculative Prices and Rates of Return," The Review of Economics and Statistics, MIT Press, vol. 69(3), pages 542-47, August.
  4. Matteo Barigozzi & Christian T. Brownlees & Giampiero M. Gallo & David Veredas, 2010. "Disentangling Systematic and Idiosyncratic Risk for Large Panels of Assets," Econometrics Working Papers Archive wp2010_06, Universita' degli Studi di Firenze, Dipartimento di Statistica, Informatica, Applicazioni "G. Parenti".
  5. Tim Bollerslev & Viktor Todorov, 2010. "Estimation of Jump Tails," Working Papers 10-37, Duke University, Department of Economics.
  6. 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.
  7. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Clara Vega, 2002. "Micro Effects of Macro Announcements: Real-Time Price Discovery in Foreign Exchange?," Center for Financial Institutions Working Papers 02-23, Wharton School Center for Financial Institutions, University of Pennsylvania.
  8. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold & Paul Labys, 2001. "Modeling and Forecasting Realized Volatility," Center for Financial Institutions Working Papers 01-01, Wharton School Center for Financial Institutions, University of Pennsylvania.
  9. 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.
  10. 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.
  11. Darrell Duffie & Jun Pan & Kenneth Singleton, 2000. "Transform Analysis and Asset Pricing for Affine Jump-Diffusions," Econometrica, Econometric Society, vol. 68(6), pages 1343-1376, November.
  12. Todorov, Viktor & Bollerslev, Tim, 2010. "Jumps and betas: A new framework for disentangling and estimating systematic risks," Journal of Econometrics, Elsevier, vol. 157(2), pages 220-235, August.
  13. Andersen, Torben G. & Bollerslev, Tim, 1997. "Intraday periodicity and volatility persistence in financial markets," Journal of Empirical Finance, Elsevier, vol. 4(2-3), pages 115-158, June.
  14. J Einmahl, .H. & de Haan, L. & Sinha, A., 1997. "Estimating the spectral measure of an extreme value distribution," Other publications TiSEM ac22e123-1e5d-448a-981e-a, School of Economics and Management.
  15. Phillip Kearns & Adrian Pagan, 1997. "Estimating The Density Tail Index For Financial Time Series," The Review of Economics and Statistics, MIT Press, vol. 79(2), pages 171-175, May.
  16. Tim Bollerslev & Viktor Todorov, 2009. "Tails, Fears and Risk Premia," CREATES Research Papers 2009-26, School of Economics and Management, University of Aarhus.
  17. Starica, Catalin, 1999. "Multivariate extremes for models with constant conditional correlations," Journal of Empirical Finance, Elsevier, vol. 6(5), pages 515-553, December.
  18. Bollerslev, Tim & Law, Tzuo Hann & Tauchen, George, 2008. "Risk, jumps, and diversification," Journal of Econometrics, Elsevier, vol. 144(1), pages 234-256, May.
  19. repec:ner:tilbur:urn:nbn:nl:ui:12-125733 is not listed on IDEAS
  20. Ser-Huang Poon, 2004. "Extreme Value Dependence in Financial Markets: Diagnostics, Models, and Financial Implications," Review of Financial Studies, Society for Financial Studies, vol. 17(2), pages 581-610.
  21. 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.
  22. 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.
  23. Ole E. Barndorff-Nielsen & Neil Shephard, 2003. "Power and bipower variation with stochastic volatility and jumps," Economics Papers 2003-W17, Economics Group, Nuffield College, University of Oxford.
  24. 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.
  25. Niklas Wagner & Terry A. Marsh, 2004. "Measuring Tail Thickness under GARCH and an Application to Extreme Exchange Rate Changes," Econometrics 0401008, EconWPA.
  26. Benoit Mandelbrot, 1963. "The Variation of Certain Speculative Prices," The Journal of Business, University of Chicago Press, vol. 36, pages 394.
  27. 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.
  28. Ang, Andrew & Chen, Joseph, 2002. "Asymmetric correlations of equity portfolios," Journal of Financial Economics, Elsevier, vol. 63(3), pages 443-494, March.
  29. Yacine Aït-Sahalia & Julio Cacho-Diaz & Roger J.A. Laeven, 2010. "Modeling Financial Contagion Using Mutually Exciting Jump Processes," NBER Working Papers 15850, National Bureau of Economic Research, Inc.
  30. 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.
  31. Wagner, Niklas & Marsh, Terry A., 2005. "Measuring tail thickness under GARCH and an application to extreme exchange rate changes," Journal of Empirical Finance, Elsevier, vol. 12(1), pages 165-185, January.
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