We investigate a model in which we connect slowly time varying unconditional long-run volatility with short …-run conditional volatility whose representation is given as a semi-strong GARCH (1,1) process with heavy tailed errors. We focus on … robust estimation of both long-run and short-run volatilities. Our estimation is semiparametric since the long-run volatility …

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 develop a volatility estimator that can be directly applied to tick-by-tick data. More specifically, we consider a …

return and its volatility. Although this characteristic of stock returns is well acknowledged, most studies about it are … stochastic volatility context and for high frequency data. The consistency and limit distribution of the estimators are derived …, e.g. volatility of volatility …

the total volatility function in a continuous-time jump diffusion model …

We propose a new methodology based on Fourier analysis to estimate the fourth power of the volatility function (spot … viewpoint. Extensions to higher powers of volatility and to the multivariate case are also discussed …