The main contribution of the paper is proving that the Fourier spot volatility estimator introduced in [Malliavin and …. Moreover, we complete the asymptotic theory for the Fourier spot volatility estimator in the absence of noise, originally … implementation of the Fourier spot volatility estimator with noisy high-frequency data and provide support to its accuracy both …

We introduce a statistical test for simultaneous jumps in the price of a financial asset and its volatility process … volatility jumps, we design and analyze a nonparametric spectral estimator of the spot volatility process. A simulation study and … important role played by price volatility co-jumps. …