fractional riccati equation solutions via convolution quadrature in the rough heston model

To implement the rough heston model, as mentioned in [2], it is necessary to solve a fractional riccati differential equation. the explicit solution to this problem is not known. while various numerical techniques have been applied to solve this equation, they often require significant processing time to yield an approximate solution. in this study, we use the convolution quadrature method to approximate the solution to the rough heston-riccati problem. our proposed solution, for any given number of time steps, outperforms the adams method in terms of accuracy and computational effciency. this approximate solution to the riccati equation can be used to accurately approximate the model’s characteristic function,which is essential for pricing and calibration problems.