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. Furthermore, the asymptotic normality result leads to a test on the value of the volatility in exponential L\'evy models .
After 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 .