and the parameters $\lambda^\pm> 0$ correspond to the level of the decay of distribution of positive and negative jumps. It implies that the distribution of jumps is asymmetric and the tails of the distribution of returns are semi-heavy. Both Merton’s as well as Kou’s measure $\nu$ belong to the class of the so-called finite activity Lévy measures, i.e. $\nu(\mathbb{R})=\int_{\mathbb{R}}\nu({\mathrm{d}}z)<\infty$ having a finite variation $\int_{|z|\leq 1}|z|\nu({\mathrm{d}}z)<\infty$.

As an example of infinite activity Lévy processes we can consider the Variance Gamma (see [@DPE98]), Normal Inverse Gaussian (NIG) and CGMY processes (see [@BARNIE01]). The Variance Gamma process is a process with infinite activity, $\nu(\mathbb{R})=\int_{\mathbb{R}}\nu({\mathrm{d}}z)=\infty$ and finite variation, $\int_{|z|\leq 1}|z|\nu({\mathrm{d}}z)<\infty$ where $$\nu ({\mathrm{d}}z)= C_0 |z|^{-1}e^{Az-B|z|}{\mathrm{d}}z. 
\label{vargamma-density}$$ Here the parameters $A,B>0$ depend on the volatility and drift of the Brownian motion, $C_0>0$, and the variance of a subordinator (the Gamma process) (see [@ConTan03]). The measure $\nu$ is an admissible activity Lévy measure with shape parameters $\mu=0$, $D^{+}=A+B>0$, $D^{-}=A-B<0$, and $\alpha=1$. The NIG process is a process of infinite activity and infinite variation with the following Lévy measure: $$\nu({\mathrm{d}}z)=C |z|^{-1} e^{A z}K_{1}\left(B |z|\right){\mathrm{d}}z,
\label{nig-density}$$ where $A,B>0$ have the same meaning as in the Variance Gamma process. Here $K_1$ is the modified Bessel function of the second 