State-dependent Realignments in Target Zone Currency Regimes

We model the realignment risk in a two-factor exchange rate target zone model using a Cox process framework. The first factor is the current exchange rate evolving inside the target zone, and the second factor is a shadow exchange rate depicting the free floating exchange rate in the absence of a target zone. By using a Cox process, as opposed to a standard Poisson process, the realignment intensity may depend on the state variables. The intensity is specified such that the probability of a realignment increases the closer the exchange rate is to one of the boundaries of the target zone, and the further away it is from the shadow exchange rate. When a realignment occurs, the central parity of the target zone as well as the exchange rate jump to the shadow exchange rate. The tension between the exchange rate and the shadow exchange rate is used to model the interest rate differential between the two countries endogenously. Moreover, we show that the model can be re-parameterized to have the current exchange rate and the interest rate differential as the two readily observable state-variables. We use this stochastic model of arbitrage free exchange rate movements to price currency derivatives using an improved numerical method.