The rough Heston model has recently attracted the attention of many financial practitioners and researchers because it maintains the basic structure of the classic Heston model and has an advantage in describing the microstructure foundation of the market. In this paper, we study the distributed-order rough Heston model with an exponential tempered factor, and from the characteristic function of log-price in this model, we obtain a nonlinear parametric Volterra integral equation. Finally, the Fourier-cosine methods are combined with the Adams methods to price the option.
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