Is Jump Robust Two Times Scaled Estimator Superior among Realized Volatility Competitors?

• Published in: Mathematics (Basel) Vol. 10; no. 12; p. 2124
• Main Authors: Čuljak, Maria, Arnerić, Josip, Žigman, Ante
• Format: Journal Article
• Language: English
• Published: Basel MDPI AG 01.06.2022
• Subjects: Benchmarks; Bias; Estimators; Financing; high-frequency observations; Integral transforms; Mathematics; microstructure noise; price jumps; Prices; realized volatility benchmark; Robustness; sampling frequency selection; Securities markets; Statistical analysis; Stock exchanges; Variance; Volatility
• DOI: 10.3390/math10122124
• ISSN: 2227-7390

This paper compares the empirical performance of the realized volatility estimators on an extensive high-frequency dataset of stock indices from four developed European markets with thick trading and intensive intraday activity. Even though the proposed estimators have distinctive properties, it is not clear which one has a better performance in terms of unbiasedness and consistency. Some of them are robust to microstructure noise only, and others are robust solely to price jumps, whereas a few of them are robust to both. Therefore, the main purpose is finding a benchmark estimator among alternative competitors, as the best proxy of integrated variance, and empirical demonstration of its superiority. The vast majority of the existing studies largely rely on developed US data or simulation data, but inferences obtained on such data might deviate from European developed markets. This study aims to fill in that niche. In particular, the optimal sampling frequency of proposed benchmark estimator is determined with respect to the trade-off between its bias and the variance of each stock index individually. Afterwards, probability integral transformation, Mincer–Zarnowitz regression and upper tail correlation from appropriate copula function are considered as an adequate pairwise comparison methods. Notable contributions of this paper include unambiguously proven superiority of robust two times scaled estimator for selected European developed markets within the range of optimal slow time frequency from 10 to 30 s. Finally, recommendations for research and practitioners regarding the usage of jump robust two times scaled estimator are given. In fact, asset managers, institutional investors as well as market regulators could benefit from proposed realized volatility benchmark in making long-term investment decisions, leading to sustainable finance.