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 Riccati 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.