Conditions ensuring that are given for a Lévy process X with Lévy measure [nu] and for unbounded moment functions f. Compared with previous works, the moment functions considered here satisfy very mild conditions aimed at controlling how fast f grows at infinity. As an application of our...

We propose a feasible method for approximating the marginal distributions and densities of a bounded variation Lévy process using polynomial expansions. We provide a fast recursive formula for approximating the coefficients of the expansions and estimating the order of the approximation error....

Let X=(Xt)t=0 be a Lévy process with absolutely continuous Lévy measure [nu]. Small-time expansions of arbitrary polynomial order in t are obtained for the tails , y0, of the process, assuming smoothness conditions on the Lévy density away from the origin. By imposing additional regularity...

Thresholded Realized Power Variations (TPVs) are one of the most popular nonparametric estimators for general continuous-time processes with a wide range of applications. In spite of their popularity, a common drawback lies in the necessity of choosing a suitable threshold for the estimator, an...

We consider a stochastic volatility model with Lévy jumps for a log-return process Z=(Zt)t≥0 of the form Z=U+X, where U=(Ut)t≥0 is a classical stochastic volatility process and X=(Xt)t≥0 is an independent Lévy process with absolutely continuous Lévy measure ν. Small-time expansions, of...