In this paper, following Nourdin-Peccati’s methodology, we combine the Malliavin
calculus and Stein’s method to provide general bounds on the Wasserstein distance between
the law of functionals of a compound Hawkes process and the one of a Gaussian random
variable. To achieve this, we rely on the Poisson imbedding representation of a Hawkes
process to provide a Malliavin calculus for the Hawkes processes, and more generally for
compound Hawkes processes. As an application, we close a gap in the literature by providing
a quantitative Central Limit Theorem for the compound Hawkes process.