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Efficient integrated volatility estimation in the presence of infinite variation jumps via debiased truncated realized variations

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  • Boniece, B. Cooper
  • Figueroa-López, José E.
  • Han, Yuchen

Abstract

Statistical inference for stochastic processes based on high frequency observations has been an active research area for more than two decades. One of the most well-known and widely studied problems has been the estimation of the quadratic variation of the continuous component of an Itô semimartingale with jumps. Several rate- and variance-efficient estimators have been proposed in the literature when the jump component is of bounded variation. However, to date, very few methods can deal with jumps of unbounded variation. By developing new high-order expansions of the truncated moments of a locally stable Lévy process, we propose a new rate- and variance-efficient volatility estimator for a class of Itô semimartingales whose jumps behave locally like those of a stable Lévy process with Blumenthal–Getoor index Y∈(1,8/5) (hence, of unbounded variation). The proposed method is based on a two-step debiasing procedure for the truncated realized quadratic variation of the process and can also cover the case Y<1. Our Monte Carlo experiments indicate that the method outperforms other efficient alternatives in the literature in the setting covered by our theoretical framework.

Suggested Citation

  • Boniece, B. Cooper & Figueroa-López, José E. & Han, Yuchen, 2024. "Efficient integrated volatility estimation in the presence of infinite variation jumps via debiased truncated realized variations," Stochastic Processes and their Applications, Elsevier, vol. 176(C).
  • Handle: RePEc:eee:spapps:v:176:y:2024:i:c:s0304414924001352
    DOI: 10.1016/j.spa.2024.104429
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    References listed on IDEAS

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    1. Mancini, Cecilia, 2011. "The speed of convergence of the Threshold estimator of integrated variance," Stochastic Processes and their Applications, Elsevier, vol. 121(4), pages 845-855, April.
    2. 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.
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    6. José E. Figueroa-López & Ruoting Gong & Christian Houdré, 2016. "High-Order Short-Time Expansions For Atm Option Prices Of Exponential Lévy Models," Mathematical Finance, Wiley Blackwell, vol. 26(3), pages 516-557, July.
    7. José E. Figueroa-López & Ruoting Gong & Yuchen Han, 2022. "Estimation of Tempered Stable Lévy Models of Infinite Variation," Methodology and Computing in Applied Probability, Springer, vol. 24(2), pages 713-747, June.
    8. 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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