Q: Ito's Lemma and Geometric Brownian Motion With Jumps I have a price process:
\begin{equation}
dF_t = d\Pi_t - \mu_\pi \sigma_t F_t \gamma \, dt + \sigma_t F_t \, dz
\end{equation}
And wish to simulate the process $x_t = \ln(F_t)$ by Euler method, where the volatility process is Heston's. Price jumps are captured by the jump process $\Pi_t$, which has an arrival rate which is Poisson. Normally I can apply Ito's lemma to find $x_t$ but I don't know how to handle the jump term. I understand that the jump process satisfies the Ito isometry. Here's a brief sketch of my attempt so far: 
$$x_t =\ln(F_t)\\
dx_t = \frac{dF_t}{F_t} - \frac{1}{2}\frac{dF_t^2}{F_t^2}
=\frac{d\Pi_t}{F_t} - \mu_\pi \sigma_t \gamma \, dt + \sigma_t \, dz - \frac{1}{2}\left(\sigma^2_t \, dt + \frac{d\Pi_t^2}{F_t^2}\right)$$
I'm stuck here, and I need something that I can stick into my computer to simulate. Any help would be appreciated.
