American barrier swaption pricing problem of exponential Ornstein–Uhlenbeck model in uncertain financial market

Barrier swaption is a financial derivative that integrates aspects of a traditional swaption with the distinctive features of a barrier option. In this study, based on the premise that floating interest rates obey the exponential Ornstein–Uhlenbeck model, we derive the pricing formulas for two types of American barrier swaptions for payer and receiver, respectively, and design corresponding algorithms. In the empirical part, we select the Hong Kong Interbank Offer Rate (HIBOR) data from the real financial market to estimate the parameters of the uncertain differential equation that governs floating interest rates and test the hypothesis. It is worth noting that through rigorous hypothesis testing, we verify the applicability of the equation. Finally, we use the actual estimated parameters combined with the uncertain differential equation to carry out a range of numerical experiments, which provides a strong support for the pricing of American barrier swaptions.