On Parisian option pricing for uncertain currency model

Abstract

Currency options are very important hedging tools in foreign exchange markets. As the variants of barrier options, Parisian options are increasingly favored by investors since they have a time window to protect investors. The current works on pricing Parisian options are mainly completed in random environment. However, probabilistic methods are not applicable for uncertain case. Therefore, this paper focuses on pricing problems of Parisian options for uncertain currency model. We give the pricing formulas for up-and-out put Parisian currency option and down-and-out call Parisian currency option one after another. Finally, we discuss the relationship between implied volatility and option prices.