  We propose a method based on continuous time Markov chain approximation to
compute the distribution of Parisian stopping times and price Parisian options
under general one-dimensional Markov processes. We prove the convergence of the
method under a general setting and obtain sharp estimate of the convergence
rate for diffusion models. Our theoretical analysis reveals how to design the
grid of the CTMC to achieve faster convergence. Numerical experiments are
conducted to demonstrate the accuracy and efficiency of our method for both
diffusion and jump models. To show the versality of our approach, we develop
extensions for multi-sided Parisian stopping times, the joint distribution of
Parisian stopping times and first passage times, Parisian bonds and for more
sophisticated models like regime-switching and stochastic volatility models.
