American option pricing in the rough Heston model

We study American options in the rough Heston model. We start from an approximation with a linear combination of affine processes of the rough volatility, defined as solution of a stochastic Volterra equation with fractional kernel. We compute the conditional Fourier-Laplace transform of the approximated volatility process and an adjusted forward process associated to. We show that this Fourier-Laplace transform converges to the one of the rough volatility and its adjusted forward process. From this property, we derive the convergence of Bermudean options written on the approximated process to the ones in the rough Heston model. We end the paper with numerical results.