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We provide an efficient and accurate simulation scheme for the rough Hestonmodel in the standard ($H>0$) as well as the hyper-rough regime ($H > -1/2$).The scheme is based on low-dimensional Markovian approximations of the roughHeston process derived in [Bayer and Breneis, arXiv:2309.07023], and providesweak approximation to the rough Heston process. Numerical experiments show thatthe new scheme exhibits second order weak convergence, while the computationalcost increases linear with respect to the number of time steps. In comparison,existing schemes based on discretization of the underlying stochastic Volterraintegrals such as Gatheral's HQE scheme show a quadratic dependence of thecomputational cost. Extensive numerical tests for standard and path-dependentEuropean options and Bermudan options show the method's accuracy andefficiency.

Efficient option pricing in the rough Heston model using weak simulation schemes