We obtain a uniform central limit theorem with square root n rate on the assumption that the smoothness of the functionals is larger than the ill-posedness of the problem, which is given by the polynomial decay rate of the characteristic function of the error. The limit distribution is a...

We provide necessary and sufficient conditions on the characteristics of an infinitely divisible distribution under which its characteristic function φ decays polynomially. Under a mild regularity condition this polynomial decay is equivalent to 1/φ being a Fourier multiplier on Besov spaces.

We study the nonparametric calibration of exponential, self-decomposable Levy models whose jump density can be characterized by the k-function, which is typically nonsmooth at zero. On the one hand the estimation of the drift, the activity measure alpha:= k(0+) + k(0-) and analog parameters for...

Observing prices of European put and call options, we calibrate exponential L\'evy models nonparametrically. We discuss the efficient implementation of the spectral estimation procedures for L\'evy models of finite jump activity as well as for self-decomposable L\'evy models. Based on finite...

Observing prices of European put and call options, we calibrate exponential Lévy models nonparametrically. We discuss the implementation of the spectral estimation procedures for Lévy models of finite jump activity as well as for self-decomposable Lévy models and improve these methods....

Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. To this end, we show joint asymptotic normality in the spectral calibration method for the estimators of the volatility, the drift,...

This paper studies polar sets for anisotropic Gaussian random fields, i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical metric associated with the Gaussian...

Confidence intervals and joint confidence sets are constructed for the nonparametric calibration of exponential Lévy models based on prices of European options. This is done by showing joint asymptotic normality for the estimation of the volatility, the drift, the intensity and the Lévy...

This paper studies polar sets of anisotropic Gaussian random fields, i.e. sets which a Gaussian random field does not hit almost surely. The main assumptions are that the eigenvalues of the covariance matrix are bounded from below and that the canonical metric associated with the Gaussian random...