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Estimation of Jump Tails

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  • Tim Bollerslev
  • Viktor Todorov

Abstract

We propose a new and flexible non-parametric framework for estimating the jump tails of Itô semimartingale processes. The approach is based on a relatively simple-to-implement set of estimating equations associated with the compensator for the jump measure, or its "intensity", that only utilizes the weak assumption of regular variation in the jump tails, along with in-fill asymptotic arguments for uniquely identifying the \large" jumps from the data. The estimation allows for very general dynamic dependencies in the jump tails, and does not restrict the continuous part of the process and the temporal variation in the stochastic volatility. On implementing the new estimation procedure with actual high-frequency data for the S&P 500 aggregate market portfolio, we find strong evidence for richer and more complex dynamic dependencies in the jump tails than hitherto entertained in the literature.

Suggested Citation

  • Tim Bollerslev & Viktor Todorov, 2010. "Estimation of Jump Tails," Working Papers 10-37, Duke University, Department of Economics.
  • Handle: RePEc:duk:dukeec:10-37
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    References listed on IDEAS

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    1. Andersen T. G & Bollerslev T. & Diebold F. X & Labys P., 2001. "The Distribution of Realized Exchange Rate Volatility," Journal of the American Statistical Association, American Statistical Association, vol. 96, pages 42-55, March.
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    5. 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.
    6. Todorov, Viktor, 2009. "Estimation of continuous-time stochastic volatility models with jumps using high-frequency data," Journal of Econometrics, Elsevier, vol. 148(2), pages 131-148, February.
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    10. Torben G. Andersen & Tim Bollerslev & Francis X. Diebold, 2007. "Roughing It Up: Including Jump Components in the Measurement, Modeling, and Forecasting of Return Volatility," The Review of Economics and Statistics, MIT Press, vol. 89(4), pages 701-720, November.
    11. Robert J. Barro, 2006. "Rare Disasters and Asset Markets in the Twentieth Century," The Quarterly Journal of Economics, Oxford University Press, vol. 121(3), pages 823-866.
    12. Mark Broadie & Mikhail Chernov & Michael Johannes, 2009. "Understanding Index Option Returns," Review of Financial Studies, Society for Financial Studies, vol. 22(11), pages 4493-4529, November.
    13. Zhang, Lan & Mykland, Per A. & Ait-Sahalia, Yacine, 2005. "A Tale of Two Time Scales: Determining Integrated Volatility With Noisy High-Frequency Data," Journal of the American Statistical Association, American Statistical Association, vol. 100, pages 1394-1411, December.
    14. Xavier Gabaix, 2012. "Variable Rare Disasters: An Exactly Solved Framework for Ten Puzzles in Macro-Finance," The Quarterly Journal of Economics, Oxford University Press, vol. 127(2), pages 645-700.
    15. Woerner Jeannette H. C., 2003. "Variational sums and power variation: a unifying approach to model selection and estimation in semimartingale models," Statistics & Risk Modeling, De Gruyter, vol. 21(1/2003), pages 47-68, January.
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    Citations

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    Cited by:

    1. Escribano Sáez, Álvaro & Blazsek, Szabolcs Istvan & Ayala, Astrid, 2017. "Dynamic conditional score models with time-varying location, scale and shape parameters," UC3M Working papers. Economics 25043, Universidad Carlos III de Madrid. Departamento de Economía.
    2. Blanke, D. & Bosq, D., 2016. "Detecting and estimating intensity of jumps for discretely observed ARMAD(1,1) processes," Journal of Multivariate Analysis, Elsevier, vol. 146(C), pages 119-137.
    3. Dewachter, Hans & Erdemlioglu, Deniz & Gnabo, Jean-Yves & Lecourt, Christelle, 2014. "The intra-day impact of communication on euro-dollar volatility and jumps," Journal of International Money and Finance, Elsevier, vol. 43(C), pages 131-154.
    4. Neil Shephard & Kevin Sheppard, 2012. "Efficient and feasible inference for the components of financial variation using blocked multipower variation," Economics Series Working Papers 593, University of Oxford, Department of Economics.
    5. Nguyen, Duc Binh Benno & Prokopczuk, Marcel & Wese Simen, Chardin, 2017. "The Risk Premium of Gold," Hannover Economic Papers (HEP) dp-616, Leibniz Universität Hannover, Wirtschaftswissenschaftliche Fakultät.
    6. 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.
    7. Hoffmann, Michael & Vetter, Mathias, 2017. "Weak convergence of the empirical truncated distribution function of the Lévy measure of an Itō semimartingale," Stochastic Processes and their Applications, Elsevier, vol. 127(5), pages 1517-1543.
    8. Kaeck, Andreas, 2013. "Asymmetry in the jump-size distribution of the S&P 500: Evidence from equity and option markets," Journal of Economic Dynamics and Control, Elsevier, vol. 37(9), pages 1872-1888.
    9. Andersen, Torben G. & Bollerslev, Tim & Christoffersen, Peter F. & Diebold, Francis X., 2013. "Financial Risk Measurement for Financial Risk Management," Handbook of the Economics of Finance, Elsevier.
    10. Sévi, Benoît, 2013. "An empirical analysis of the downside risk-return trade-off at daily frequency," Economic Modelling, Elsevier, vol. 31(C), pages 189-197.
    11. Bollerslev, Tim & Todorov, Viktor, 2014. "Time-varying jump tails," Journal of Econometrics, Elsevier, vol. 183(2), pages 168-180.
    12. Bollerslev, Tim & Todorov, Viktor & Li, Sophia Zhengzi, 2013. "Jump tails, extreme dependencies, and the distribution of stock returns," Journal of Econometrics, Elsevier, vol. 172(2), pages 307-324.
    13. Bollerslev, Tim & Todorov, Viktor & Xu, Lai, 2015. "Tail risk premia and return predictability," Journal of Financial Economics, Elsevier, vol. 118(1), pages 113-134.
    14. Behfar, Stefan Kambiz, 2016. "Long memory behavior of returns after intraday financial jumps," Physica A: Statistical Mechanics and its Applications, Elsevier, vol. 461(C), pages 716-725.
    15. Tim Bollerslev & Jia Li & Yuan Xue, 2016. "Volume, Volatility and Public News Announcements," CREATES Research Papers 2016-19, Department of Economics and Business Economics, Aarhus University.

    More about this item

    Keywords

    Extreme events; jumps; high-frequency data; jump tails; non-parametric estimation; stochastic volatility;

    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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