Derivatives Pricing in the Positive Interest Rates Open Access

This paper examines the pricing of interest rates derivatives such as caps and swaptions in the pricing kernel framework. The underlying state variable is extended to the general infinitely divisible Levy process. For computational purposes, a simple pricing kernel as in Flesaker and Hughston (1996) and Jin and Glasserman (2001) is used. The main contribution or purpose of this paper is to find several proper positive martingales, which is key role of practical applications of the pricing kernel approach with interest rates guarantee to be positive. Particularly, this paper first finds and applies a quite general type of a positive martingale process to pricing interest rate derivatives such as swaptions and range notes in the incomplete market setting. Such interest rate derivatives are hard to find analytic solutions. Consequently, this paper shows that such a choice of the positive martingale in the kernel framework is a promising approach to price interest rate derivatives