The valuation of currency call options in selected target zones: a theoretical formulation

The market for currency call options is growing rapidly with the number of options contracts traded daily in April 2016 at $254 billion, as reported in the Triennial Bank Survey of Foreign Exchange and OTC Derivatives (Bank for International Settlements, 2018). A European currency call option gives the owner the right to purchase foreign currency at a specified exercise price within a specified time period, suggesting that it offers gains for appreciating currencies. Speculators invest in currency call options to earn abnormal returns upon currency appreciation. The call option's chief purpose in trade is to hedge against adverse appreciations in foreign currency. An importer making future payment in foreign currency does not wish to increase payment due to appreciating values of foreign currency. The purchase of currency calls will permit the exchange of foreign currency at the exercise price, which if lower than the market exchange rate, yields a small gain to the option holder. If the exercise price is higher than the market exchange rate, the option would simply expire, with purchase of foreign currency at market rates.