Pricing currency options in target zone regime: Some consequences of state-dependent realignment

In this paper the pricing of currency options in a target zone model is discussed. The movement of the currency index is a product of the movement within the target zone and jumps in the target zone itself in the form of re- or devaluations. The probability of a re- or devaluation is modelled as dependent on the position of the exchange rate within the target zone. The traditional assumption of no dependence between the position of the exchange rate within the target zone and the probability of a re- or devaluation is compared with a model allowing state-dependent jumps. It is shown that the assumption of state-independent jump probabilities may lead to highly unrealistic outcomes, outcomes that will not arise if the probability of re- or devaluations is allowed to depend on the location of the exchange rate within the target zone. A comparison is made with the prices produced by the widely used Garman and Kohlhagen [Journal of International Money and Finance (1983), Vol. 2, pp. 231-237] option pricing model.