We investigate the problem of calibrating an exponential Lévy model based on market prices of vanilla options. We show that this inverse problem is in general severely ill-posed and we derive exact minimax rates of convergence. The estimation procedure we propose is based on the explicit...

We study the nonparametric calibration of exponential, self-decomposable Lévy 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 a := k(0+) + k(0-) and analog parameters for...

This paper proposes a nonparametric test of causality in quantile. Zheng (1998) has proposed an idea to reduce the problem of testing a quantile restriction to a problem of testing a particular type of mean restriction in independent data. We extend Zheng's approach to the case of dependent...