5. CONCLUSIONS
In this paper, we derive a new partial integro-differential inequality
(PIDI) for shout options pricing on the assumption that the price of the
underlying asset follows the jump-diffusion model and construct the
mathematical model by combining specific features and terminal
conditions. Another innovation is that this paper proposes a new
competitive algorithm. Numerical experiments confirm the convergence in
pricing shout options and shows that the algorithm proposed in this
paper is superior to the traditional algorithm in the case of geometric
Brownian motion and jump diffusion model, respectively.