Abstract
In this paper, we consider a model of valuing callable financial securities when the underlying asset price dynamic depends on a finite-state Markov chain. The callable securities enable both an issuer and an investor to exercise their rights to call. We formulate this problem as a coupled stochastic game for the optimal stopping problem with two stopping boundaries. Then, we show that there exists a unique optimal price of the callable contingent claim which is a unique fixed point of a contraction mapping. We derive analytical properties of optimal stopping rules of the issuer and the investor under general payoff functions by applying a contraction mapping approach. 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.
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