Abstract
In this paper we consider a model of valuing callable financial commodities which enable both an issuer and an investor to exercise their rights, respectively. We show that such a model can be formulated as a coupled stochastic game for the optimal stopping problem with two reflecting barriers. It is also shown that there exists a pair of optimal stopping rules and the value of the stochastic game. Most previous work concerning American options, Israeli options, convertible bonds and callable derivatives has required the specific payoff function when either of the issuer or the investor has exercise their option. However, we deal with a rather general payoff function of the underlying asset price and the time. We also explore some analytical properties of optimal stopping rules of the issuer and the investor.
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