Derivative Pricing Based on the Exchange Rate in a Target Zone with Realignment

We propose a tractable model for the exchange rate in a target zone with realignment. The target zone exchange rate dynamics is assumed to obey a bounded regular diffusion with two-sided unattainable barriers. The realignment is modeled as a continuous-time two-state Markov chain. Under the stationary setting of the Markov chain, a general pricing formula for the derivative written on the exchange rate is derived in the presence of the realignment risk. The Jacobi diffusion model is studied as an example and numerical results are presented for illustration