The Realized Laplace Transform of Volatility

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Testing for pure-jump processes for high-frequency data (2015, background): “This implies that an estimator of σt (or its functionals) for a general semimartingale based on the characteristic function would very likely be robust to jumps of finite variation, which is confirmed in Todorov and Tauchen (2012) and Jacod and Todorov (2014).”
Time-Varying Periodicity in Intraday Volatility (2019, background): “and the result in [38] that (the real part of) the empirical characteristic function of the highfrequency increments in X is an estimate for the Laplace transform of stochastic volatility.”
Adaptive estimation of continuous-time regression models using high-frequency data (2017, methodology): “The 9 Wealso performa time-of-day adjustment to the truncation level as in Todorov and Tauchen (2012) to account for the well-known diurnal pattern in volatility.”