On the hedging of options on exploding exchange rates

We study a novel pricing operator for complete, local martingale models. The new pricing operator guarantees put-call parity to hold and the value of a forward contract to match the buy-and-hold strategy, even if the underlying follows strict local martingale dynamics. More precisely, we discuss a change of numéraire (change of currency) technique when the underlying is only a local martingale modelling for example an exchange rate. The new pricing operator assigns prices to contingent claims according to the minimal cost for replication strategies that succeed with probability one for both currencies as numéraire. Within this context, we interpret the non-martingality of an exchange-rate as a reflection of the possibility that the numéraire currency may devalue completely against the asset currency (hyperinflation).