A Jump‐diffusion Model for Exchange Rates in a Target Zone

Abstract

We propose a simple jump‐diffusion model for an exchange rate target zone. The model captures most stylized facts from the existing target zone models while remaining analytically tractable. The model is based on a modified two‐limit version of the COX, INGERSOLL and ROSS (1985) model. In the model the exchange rate is kept within the band because the variance decreases as the exchange rate approaches the upper or lower limits of the band. We also consider an extension of the model with parity adjustments, which are modeled as Poisson jumps. Estimation of the model is by GMM based on conditional moments. We derive prices of currency options in our model, assuming that realignment jump risk is idiosyncratic. Throughout, we apply the theory to EMS exchange rate data. We show that, after the EMS crisis of 1993, currencies remain in an implicit target zone which is narrower than the officially announced target zones.