We propose a stochastic volatility jump-diffusion model for option pricing with jumps in both spot returns and volatility dynamics. This model admits, in the spirit of Heston, a closed-form solution for European-style options. By exploiting and improving the exact algorithm by Broadie and Kaya, we also propose a method for the exact simulation of the stock price and its variance useful in the valuation of non-European options. We test the goodness of our methodology using real data of DJ Euro Stoxx 50 market, and we provide some numerical results for barrier options and their Greeks.

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