Malliavin calculcus for a Hawkes process

Abstract

We develop a Malliavin calculus for nonlinear Hawkes processes in the sense of Carlen and Pardoux. This approach, based on perturbations of the jump times of the process, enables the construction of a local Dirichlet form. As an application, we establish criteria for the absolute continuity of solutions to stochastic differential equations driven by Hawkes processes. We also derive sensitivity formulas for the valuation of financial derivatives with respect to model parameters.