Pricing barrier options pose a significant challenge in financial derivative valuation because they are activated only when the underlying asset reaches a predetermined barrier.The first-hitting time model was employe...Pricing barrier options pose a significant challenge in financial derivative valuation because they are activated only when the underlying asset reaches a predetermined barrier.The first-hitting time model was employed to characterize the activation process.In addition,the pricing of American barrier options with a floating interest rate is dynamically represented by an uncertain fractional differential equation.The study derives price formulas for various American barrier options,including up-andin call,down-and-in put,up-and-output,and down-and-out call options.The proposed model enhances the accuracy of capturing the long-tail distribution and tail risk of financial markets,thereby addressing their complexity and nonlinearity.Furthermore,the predictor-corrector method is utilized to compute the numerical prices for the barrier options with floating interest rates,supplemented by illustrative numerical examples.展开更多
基金supported by the National Natural Science Foundation of China(Grant No.62403156)Shandong Provincial Natural Science Foundation,China(Grant No.ZR2022QA055).
文摘Pricing barrier options pose a significant challenge in financial derivative valuation because they are activated only when the underlying asset reaches a predetermined barrier.The first-hitting time model was employed to characterize the activation process.In addition,the pricing of American barrier options with a floating interest rate is dynamically represented by an uncertain fractional differential equation.The study derives price formulas for various American barrier options,including up-andin call,down-and-in put,up-and-output,and down-and-out call options.The proposed model enhances the accuracy of capturing the long-tail distribution and tail risk of financial markets,thereby addressing their complexity and nonlinearity.Furthermore,the predictor-corrector method is utilized to compute the numerical prices for the barrier options with floating interest rates,supplemented by illustrative numerical examples.
