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The rough Heston model is a very popular recent model in mathematicalfinance; however, the lack of Markov and semimartingale properties posessignificant challenges in both theory and practice. A way to resolve thisproblem is to use Markovian approximations of the model. Several previous workshave shown that these approximations can be very accurate even when the numberof additional factors is very low. Existing error analysis is largely based onthe strong error, corresponding to the $L^2$ distance between the kernels.Extending earlier results by [Abi Jaber and El Euch, SIAM Journal on FinancialMathematics 10(2):309--349, 2019], we show that the weak error of the Markovianapproximations can be bounded using the $L^1$-error in the kernel approximationfor general classes of payoff functions for European style options. Moreover,we give specific Markovian approximations which converge super-polynomially inthe number of dimensions, and illustrate their numerical superiority in optionpricing compared to previously existing approximations. The new approximationsalso work for the hyper-rough case $H > -1/2$.

Weak Markovian Approximations of Rough Heston