The Markov-Switching Jump Diffusion Libor Market Model

Posted: 14 Nov 2013 Last revised: 4 Jun 2018

See all articles by Lea Borchert

Lea Borchert

University of Mannheim

Rudi Zagst

Technische Universität München (TUM) - Chair of Mathematical Finance

Anatoliy V. Swishchuk

University of Calgary

Date Written: October 22, 2013

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

Suggested Citation

Borchert, Lea and Zagst, Rudi and Swishchuk, Anatoliy V., The Markov-Switching Jump Diffusion Libor Market Model (October 22, 2013). Available at SSRN: https://ssrn.com/abstract=2350671 or http://dx.doi.org/10.2139/ssrn.2350671

Lea Borchert (Contact Author)

University of Mannheim ( email )

L9, 1-2
Mannheim, 68131
Germany

Rudi Zagst

Technische Universität München (TUM) - Chair of Mathematical Finance ( email )

Parkring 11
Garching-Hochbrueck, 85748
Germany
+49 89 289 17400 (Phone)

Anatoliy V. Swishchuk

University of Calgary ( email )

University Drive
Calgary, Alberta T2N 1N4
Canada

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