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

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Abstract 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.