A study of American option pricing for uncertain currency models with exponential O–U process

This paper prices American call and put options using a novel uncertain currency model. The model integrates the uncertain Vasicek interest rate term structure with the uncertain exponential Ornstein–Uhlenbeck exchange rate process, effectively capturing the dynamic changes in financial markets. Using the $\alpha$-path method, the study derives pricing formulas for American call and put options. The model parameters are precisely estimated using the residual-based moment estimation method, and the robustness and applicability of the model are validated through goodness-of-fit tests. The results show that option prices are significantly dependent on parameters such as the initial exchange rate, interest rates, and strike price, and the model fits actual data well. This research not only provides a new theoretical basis for financial derivative pricing but also offers valuable insights for investors’ decision-making in uncertain market environments, holding significant academic and practical importance.