Uncertain barrier swaption pricing problem based on the fractional differential equation in Caputo sense

This paper primarily investigates uncertain barrier swaption pricing problem based on the fractional differential equation in Caputo sense and analyzes the corresponding efficiency index (validity index and survival index). To a certain extent, barrier swaption can control the gains or losses of swaption investors within a certain range. The existing barrier swaption pricing model cannot fully reflect the hereditability and memorability of the real financial market, so this paper aims to solve such difficulties and further measure the exercise ability of the barrier swaption pricing model. Firstly, the floating interest rate is regarded as an uncertain process because there exists difficult to obtain historical data for real financial model. Then the Caputo type fractional differential operator is introduced into the original barrier swaption pricing model, and a new uncertain barrier swaption model of floating interest rate is established. Secondly, based on the first hitting time, the pricing formulas and the corresponding efficiency index of four kinds of barrier swaptions under the floating rate model are derived, respectively. Finally, the rationality of the model is verified by numerical examples and corresponding methods, and gives the monotonicity of four numerical examples.