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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.
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Suggested Citation

  • Tim Bollerslev & Viktor Todorov, 2011. "Estimation of Jump Tails," Econometrica, Econometric Society, vol. 79(6), pages 1727-1783, November.
    • Handle: RePEc:ecm:emetrp:v:79:y:2011:i:6:p:1727-1783
    DOI: ECTA9240
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    More about this item

    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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