To calculate stock path of Lévy process, I need to calculate the mean-correcting equivalent martingale measure: $\omega= log (E[e^{X_t}| y(0)])$. I found in a thesis that $\omega$ can be calculated and for VG, for example, is equal to: $-c*log((M-1)(G+1)/MG))$. How this can be calculated?
Moreover, I need the mean correcting argument for Lèvy models with stochastic time, so :
$E[e^{X_Y(t)}| y(0)]$
How I can achieve this? Do you have any paper about it?
Thanks in advance