Pricing Currency Call Options

Abstract

This paper presents a theoretical model to price foreign currency call options. Currency options are employed in international trade to reduce the risk of loss due to the reduction of revenues obtained in depreciating foreign currency for an exporter, or the escalation of expense from appreciating foreign currency for an importer. Other users include banks and hedge funds who engage in currency speculation. Given the fluctuation of option prices over time, the model describes the distribution of foreign currency as a Weiner process for macroeconomically constrained foreign currencies followed by a Laplace distribution for unconstrained currencies. In a departure from existing currency option models, this model expresses foreign currencies as dependent upon the change in macroeconomic variables, such as inflation, interest rates, and government deficits. The distribution of currency calls is described as a Levy process in the context of an option trader’s risk preferences to account for the multiple discontinuities of a jump process. The paper concludes with three models of price functions of the Weiner process for Euro-related currency options, a Weiner process for stable currency options, and a Levy-Khintchine process for volatile currency calls.