A general approach for Parisian stopping times under Markov processes
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AbstractWe 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.
All Author(s) ListGongqiu Zhang, Lingfei Li
Journal nameFinance and Stochastics
Year2023
Month7
Volume Number27
Issue Number3
PublisherSpringer
Pages769 - 829
ISSN0949-2984
eISSN1432-1122
LanguagesEnglish-United States
KeywordsParisian stopping time, Parisian options, Parisian ruin probability, Markov chain approximation, Grid design

Last updated on 2023-18-12 at 15:39