Option pricing for Heston model with tempered fractional Brownian motion

In this paper, the Heston model with tempered fractional Brownian motion is derived by modified Hawkes processes. Based on the affine technique, we present the characteristic function under this model and prove the existence, uniqueness, and regularity of the solution to the tempered fractional Riccati equation. In addition, by combining with the Fourier cosine method, we derive a numerical formula for pricing European options under this model. Numerical results demonstrate the convergence of both the Adams method and the Fourier cosine method.