Abstract: We considered the continuous up-and-out Paris option pricing problem. Firstly, an implicit difference scheme with the first order in time and the second order in space was given for this type of Paris option. Secondly, the inequality amplification method and Fourier expansion method were used to discuss the stability, solvability and convergence of the difference scheme, respectively. Finally, the numerical pricing results of continuous up-and-out Paris options were analyzed by using the difference scheme.

Key words: continuous up-and-out Paris option, numerical simulation, stability, convergence, solvability