  We consider the simulation of a system of decoupled forward-backward
stochastic differential equations (FBSDEs) driven by a pure jump L\'evy process
$L$ and an independent Brownian motion $B$. We allow the L\'evy process $L$ to
have an infinite jump activity. Therefore, it is necessary for the simulation
to employ a finite approximation of its L\'evy measure. We use the generalized
shot noise series representation method by Rosinski (2001) to approximate the
driving L\'evy process $L$. We compute the $L^p$ error, $p\ge2$, between the
true and the approximated FBSDEs which arises from the finite truncation of the
shot noise series (given sufficient conditions for existence and uniqueness of
the FBSDE). We also derive the $L^p$ error between the true solution and the
discretization of the approximated FBSDE using an appropriate backward Euler
scheme.
