Stochastic Process Switching: Some Simple Solutions

When changes in the economic policy regime occur stochastically, asset prices will reflect the possibility of such shifts. In this paper we apply techniques of regulated Brownian motion to obtain closed-form analytic price solutions when policy reaction functions are subject to prospective changes. We focus on the case in which the authorities promise to peg a currency's exchange rate once it reaches a predetermined future level. We also show how an open-ended commitment to exchange-rate targeting may lead to multiple equilibria.