In this talk, we study a quadratic hedging problem in an affine Heston model with self-exiting jumps of Hawkes type. The hedging problem is set up for a variance swap and the strategies we consider are of semi-static type, that is, they consist of a dynamic part, based on the stock and continuously re-balanced, and of a static part, that is buy-and-hold positions in a given basket of European options. Semi-static strategies have the advantage that they reduce the hedging error in comparison to purely dynamic strategies. The model we present is new and combines features of continuous stochastic volatility models and of models with self-exciting jumps in the affine framework. Our results are based on Fourier methods and therefore the affine structure plays a central role for the set-up of the semi-static variance optimal strategy. In particular, we study the Laplace transform of our model and obtain semi-explicit expressions for the hedging strategy. This is a joint work with Giorgia Callegaro, Beatrice Ongarato and Carlo Sgarrra.