Pricing and hedging foreign equity options under Hawkes jump-diffusion processes

In this paper, we propose a valuation of foreign equity options using a Hawkes jump-diffusion model that allows for clustered jumps as well as cross-market jump propagation. We derive the semi-analytical valuation formulae for these options using Fourier transform method. The Greeks and the optimal option hedging strategies under mean-variance criterion are also given. We find that Hawkes jump-diffusion model produces heavier tailed distributions with higher peaks than Poisson jump-diffusion model, which accordingly results in higher option prices under Hawkes model for deep out-of-the-money options.