Hedging of exotic options in Hawkes jump-diffusion models by Malliavin calculus

Abstract

In financial mathematics, the calculation of the Greeks, especially the delta, is emphasized due to its role in risk management. In this article, we employ Malliavin calculus to determine the delta of European and Asian options, where the underlying asset evolves according to a Hawkes jump-diffusion process. A central feature is that the Hawkes jump intensity is stochastic, which substantially affects the delta representation.