The pricing and hedging of structured notes with systematic jump risk: An analysis of the USD knock-out reversed swap

Most of the interest rate derivative pricing models are jump-diffusion models, where the jump risk is assumed diversifiable. In this paper, we propose a Heath-Jarrow-Morton model with systematic jump risk to derive the no-arbitrage condition using Esscher transformation. Based on the Heath-Jarrow-Morton model with systematic jump risk, the dynamic process of the LIBOR market model with systematic jump risk is then developed. By decomposing the USD knock-out reversed swap into three derivative components, i.e., interest rate swap, interest rate digital call (IRDC) and cap, the pricing of the swap can be obtained from the dynamic process of the LIBOR market model with systematic jump risk. We show how the swap issuers/investors can hedge the swap risk using these three derivative components. The numerical analyses are conducted to show the impact of jump risk on the values of IRDC, cap and swap.