Sample path generation of Lévy-driven continuous-time autoregressive moving average processes (Q518863)

The goal of the paper is to provide the easily applicable sample path simulation schemes of Lévy-driven CARMA processes. Apart certain special cases, it is difficult to construct exact simulation schemes for general higher-order CARMA processes with multivariate background driving Lévy processes. The author addresses the issue of sample path simulation of the desired CARMA processes in relatively general settings, along with verifiable error analysis. The paper describes construction of the approximate discrete-time simulation schemes based on the so-called series representation of infinitely divisible laws and associated Lévy processes. The methods proposed are applicable to many different problem settings: the stable marginal, the second-order case with infinite and finite Lévy measures, and the non-negative case with infinite and finite first moments. The problems explicitly addressed in the paper comprise: stable CARMA processes with Gaussian CARMA approximation, second-order CARMA process, non-negative Lévy-driven CARMA process. Comparison with the Euler-Maruyama discretization framework is outlined claiming that the proposed simulation schemes are often much simpler. The results can be used for actual implementation, numerical examples and a verifiable error analysis are provided. Although the author names only applications in financial economics, almost every other field can profit from the proposed simulation schemas.