  We propose a finite difference scheme to simulate solutions to a certain type
of hyperbolic stochastic partial differential equation (HSPDE). These solutions
can in turn estimate so called volatility modulated Volterra (VMV) processes
and L\'{e}vy semistationary (LSS) processes, which is a class of processes that
have been employed to model turbulence, tumor growth and electricity forward
and spot prices. We will see that our finite difference scheme converges to the
solution of the HSPDE as we take finer and finer partitions for our finite
difference scheme in both time and space. Finally, we demonstrate our method
with an example from the energy finance literature.
