Optimal stopping and sensitivity analysis in regime switching models - Liu, Yue (2015)
This thesis focuses on topics related to regime-switching models. Two main problems are concerned, one is optimal stopping in regime-switching models, and the other is sensitivity analysis with its application to calculate Greeks based on regime-switching models. In particular, the regime switching model is characterized by a geometric Brownian motion with its nondeterministic drift and volatility driven by a time-continuous Markov chain which is independent with the Brownian motion. On one hand, the optimal stopping problem in this framework is separately solved by two approaches, one is to analyze it as free boundary problem and the other is to compute the value function by a recursive algorithm. On the other hand, sensitivity analysis on regime -switching models is developed by applying Malliavin calculus, besides, by establishing an integration by parts formula, Malliavin calculus regarding Markov chains can also be applied to compute the Greeks.