The Markov-Switching Jump Diffusion Libor Market Model

Abstract

In this paper, we introduce an extension to the LIBOR Market model that is suitable to incorporate both sudden market shocks as well as changes in the overall economic climate into the interest rate dynamics. This is achieved by substituting the simple diffusion process of the original LIBOR Market model by a regime-switching jump diffusion. We demonstrate that the new Markov-switching jump diffusion (MSJD) LIBOR Market model can be embedded into a generalized regime-switching Heath-Jarrow-Morton (HJM) model and prove that the considered market is arbitrage-free. We derive pricing formulas for caps, floors, and interest rate swaps using Fourier pricing techniques and show how the model can be calibrated to real data.

Keywords: LIBOR Market Model,
Jump Diffusion,
Markov Switching,
Heath-Jarrow-Morton Model,
Pricing,
Parameter Estimation

JEL Classification: C02, C60, G12, G13