A general approach for Parisian stopping times under Markov processes

We propose a method based on continuous-time Markov chain (CTMC) approximation to compute the distribution of Parisian stopping times and to price options of Parisian style under general one-dimensional Markov processes. We prove the convergence of the method under a general setting and obtain sharp estimates 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 versatility 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, regime-switching models and stochastic volatility models.