Pricing Discrete Barrier Options Under the Jump-Diffusion Model with Stochastic Volatility and Stochastic Intensity

This paper considers the problem of numerically evaluating discrete barrier option prices when the underlying asset follows the jump-diffusion model with stochastic volatility and stochastic intensity. We derive the three-dimensional characteristic function of the log-asset price, the volatility and the jump intensity. We also provide the approximate formula of the discrete barrier option prices by the three-dimensional Fourier cosine series expansion (3D-COS) method. Numerical results show that the 3D-COS method is rather correct, fast and competent for pricing the discrete barrier options.