Approximating Lévy Semistationary Processes via Fourier Methods in the Context of Power Markets

The present paper discusses simulation of Lévy semistationary (LSS) processes in the context of power markets. A disadvantage of applying numerical integration to obtain trajectories of LSS processes is that such a scheme is not iterative. We address this problem by introducing and analyzing a Fourier simulation scheme for obtaining trajectories of these processes in an iterative manner. Furthermore, we demonstrate that our proposed scheme is well suited for simulation of a wide range of LSS processes, including, in particular, LSS processes indexed by a kernel function which is steep close to the origin. Finally, we put our simulation scheme to work for simulating the price of path-dependent options to demonstrate the advantages of the proposed Fourier simulation scheme.