Uncertain Currency Model and Currency Option Pricing

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 process, described by an uncertain differential equation driven by Liu process, and build an uncertain currency model. Then the uncertain currency option processes 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 described. keywords: Finance, foreign currency, uncertainty theory, uncertain differential equation, option pricing