We study the shape of the log-returns density $f(x)$ in a CGMY L\'evy process $X$ with given skewness $S$ and kurtosis $K$ of $X(1)$ and without a Brownian component. The jump part of such a process is specified by the L\'evy density which is $C\e^{-Mx}/x^{1+Y}$ for $x0$ and...

Phase-type (PH) distributions are defined as distributions of lifetimes of finite continuous-time Markov processes. Their traditional applications are in queueing, insurance risk, and reliability, but more recently, also in finance and, though to a lesser extent, to life and health insurance....