A Discrete Time Valuation of Callable Financial Securities with Regime Switches

In this paper, we consider a model of valuing callable financial securities when the underlying asset price dynamic is modeled by a regime switching process. The callable securities enable both an issuer and an investor to exercise their rights to call. We show that such a model can be formulated as a coupled stochastic game for the optimal stopping problem with two sopping boundaries. We provide analytical results of optimal stopping rules of the issuer and the investor under general payoff functions defined on the underlying asset price, the state of the economy and the time. In particular, we derive specific stopping boundaries for the both players by specifying for the callable securities to be the callable American call and put options. Also, numerical examples are presented to investigate the impact of parameters on the value function as well as on the optimal stopping rules.