Barrier swaption pricing problem in uncertain financial market

A barrier swaption gives its owner the right but not the obligation to enter into an underlying interest rate swap and only becomes activated (or extinguished) if the underlying reaches the given barrier. This paper discusses four types of barrier swaptions under the framework of uncertain finance theory, which are up-and-in payer swaption, down-and-in receiver swaption, up-and-out receiver swaption, and down-and-out payer swaption, and gives pricing formulae to calculate the price of corresponding barrier swaptions. Furthermore, corresponding numerical methods are presented when explicit solutions are unavailable. A numerical example is documented to illustrate our methods.

Automated summary

This paper discusses four types of barrier swaptions and provides pricing formulas and numerical methods, with a numerical example to illustrate the methods.