An Explicit Mapping of Currency Target Zone Models to Option Prices

Currency target zones have been under scrutiny for the past three decades, which led to the development of two broad classes of quantitative models: Phenomenological ones that explicitly take into consideration the market's perception of the bounded exchange rate, and more mechanical ones that rely on put and call options. Until now, the two models have only been compared qualitatively. Here, we derive, for the first time, a quantitative link between these two approaches. Specifically, we show how the former approach has to be generalized in order to recover the second one. This mapping lets us relate the phenomenological parameter of the first approach to economically well-known quantities