Pricing of spread and exchange options in a rough jump-diffusion market

This article studies the pricing of spread and exchange options in a market made up of two risky assets driven by a rough Heston model with jumps. Firstly, we rewrite this non-Markov model as an infinite dimensional Markov process. We next consider a finite dimensional approximation and show that the characteristic function of log-returns admits a representation in terms of forward differential equations. By passing to the limit, we infer that the characteristic function of the rough jump Heston model depends on a hybrid system of ordinary and fractional differential equations. Bivariate options are next priced with a one or two dimensional discrete Fourier Transform. We conclude by a numerical illustration analyzing the impact of roughness on exchange and spread options.