Rough Heston Models with Variable Vol-of-Vol and Option Pricing

In this paper,a rough Heston model with variable volatility of volatility(vol-of-vol)is derived by modifying the generalized nonlinear Hawkes process and extending the scaling techniques.Then the nonlinear fractional Ric-cati equation for the characteristic function of the asset log-price is derived.The existence,uniqueness and regularity of the solution to the nonlinear fractional Riccati equation are proved and the equation is solved by the Adams methods.Finally the Fourier-cosine methods are combined with the Adams methods to price the options.