Pricing Options on Foreign Currency with a Preset Exchange Rate

Abstract

This paper presents a new option that can be used by agents for managing foreign exchange risk. Unlike the Garman Kolhagen model [1], (GK), this paper presents a new model with a preset exchange rate (PE), that allows the agent to take advantage of the his/her view on both the direction and magnitude of rate movement and as such provides this agent with more choices. The model has a provision for an automatic exchange of the payoff at a preset exchange rate, and upon expiration gives the agent the choice of keeping the payoff in the foreign currency or exchanging it back to the pricing currency. At the time of writing, the buyer selects the preset exchange rate. Depending on the value selected, the PE option's price and payoff will be equal to, greater than or less than those of the GK model. A decision rule for choosing between the PE and GK models is developed by determining the expiration spot rate that equates the two models' returns. The range of spot rates that makes the PE option's return greater than the GK's return is the PE preferred range. If the agent expects the expiration spot rate will be within the preferred range, the PE option is purchased. The size of the preferred range is a decreasing function of time to expiration, a decreasing function of spot rate volatility and an increasing function of the basis point spread between foreign and domestic interest rates.