The Dynamic Valuation of Callable Contingent Claims With a Partially Observable Regime Switch

Abstract

In this paper, we consider a model for valuing callable financial securities when the underlying asset price dynamic is unobservable but can be partially observed by receiving a signal stochastically related to the state of the real economy. In callable securities, both the issuer and the investor have the right to call. We formulate this problem as a coupled stochastic game for the optimal stopping problem within a partially observable Markov decision process. We show that there exists a unique optimal value for the callable contingent claim, and it is a unique fixed point of a contraction mapping. We derive analytical properties of the optimal stopping rules for the issuer and the investor under two types (put and call) of general payoff functions. We provide a numerical example to illustrate specific stopping boundaries for each player; this is done by specifying the payoff function of the callable securities.