A General Approach for Parisian Stopping Times under Markov Processes

Abstract

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.

A General Approach for Lookback Option Pricing under Markov Models

“…CTMC approximation has become a popular method for solving various option pricing problems under Markov models in recent years. See Mijatović and Pistorius (2013) and Cui and Taylor (2021) for barrier options, Eriksson and Pistorius (2015) for American options, Cai et al (2015), Song et al (2018) and for Asian options, Zhang and Li (2021c) for maximum drawdown options, Zhang et al (2021) for American drawdown options, Zhang and Li (2021b) for Parisian options, and Meier et al (2021) for option pricing under financial models with sticky behavior. In all these papers, the original Markov model is approximated by a CTMC, and then the option price under the CTMC model is derived.…”