Before revision:  This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the  intensity and the L\'evy density at finitely many points in the spectral calibration method.
After revision:  This is done by showing joint asymptotic normality in the spectral calibration method for the estimators of the volatility, the drift, the intensity and the L\'evy density at finitely many points in the spectral calibration method.