Optimal Candlestick-Based Spot Volatility Estimation: New Tricks and Feasible Inference Procedures

Tim Bollerslev, Jia Li, Qiyuan Li and Yifan Li

Journal of Financial Econometrics, 2026, vol. 24, issue 1, nbaf023.

Abstract: We contribute to the growing literature on high-frequency spot volatility estimation by deriving a new integral representation for the recently introduced asymptotic minimum risk equivariant (AMRE) candlestick-based class of estimators. Our new theoretical representation enables the practical numerical computation of the hitherto impractical to compute optimal estimators based on multiple adjacent candlesticks. We also propose a new exact sampling scheme for high-frequency candlestick data, which facilitates straightforward calculation of the asymptotic risk and confidence intervals for the estimators. The resulting critical values for the highest-density intervals highlight the substantial efficiency gains from incorporating more than one candlestick in the estimation process. We showcase the practical value of the new techniques in elucidating the behavior of financial market volatility around the time of important news announcements.

Keywords: high-frequency candlestick data; nonparametric estimation; numerical methods; range-based estimation; spot volatility (search for similar items in EconPapers)
JEL-codes: C14 C22 (search for similar items in EconPapers)
Date: 2026
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