Uncertain Currency Model and Currency Option Pricing

Abstract

The Liu process is a new tool to deal with the noise process based on uncertainty theory. In this paper, we view the foreign exchange rate as an uncertain processes, described by uncertain differential equations driven by the Liu process, and build an uncertain currency model. Then, the uncertain currency option problems are discussed. Moreover, European and American currency option pricing formulas are derived for the proposed uncertain currency model and some mathematical properties are studied. Finally, two numerical examples are documented.