Numerical solution of jump-diffusion LIBOR market models

Nicolas Merener and Paul Glasserman ()
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Paul Glasserman: 403 Uris Hall, Graduate School of Business, Columbia University, New York, NY 10027, USA

Finance and Stochastics, 2003, vol. 7, issue 1, 27 pages

Abstract: This paper develops, analyzes, and tests computational procedures for the numerical solution of LIBOR market models with jumps. We consider, in particular, a class of models in which jumps are driven by marked point processes with intensities that depend on the LIBOR rates themselves. While this formulation offers some attractive modeling features, it presents a challenge for computational work. As a first step, we therefore show how to reformulate a term structure model driven by marked point processes with suitably bounded state-dependent intensities into one driven by a Poisson random measure. This facilitates the development of discretization schemes because the Poisson random measure can be simulated without discretization error. Jumps in LIBOR rates are then thinned from the Poisson random measure using state-dependent thinning probabilities. Because of discontinuities inherent to the thinning process, this procedure falls outside the scope of existing convergence results; we provide some theoretical support for our method through a result establishing first and second order convergence of schemes that accommodates thinning but imposes stronger conditions on other problem data. The bias and computational efficiency of various schemes are compared through numerical experiments.

Keywords: Interest rate models; Monte Carlo simulation; market models; marked point processes (search for similar items in EconPapers)
JEL-codes: E43 G13 (search for similar items in EconPapers)
Date: 2002-11-13
Note: received: February 2001; final version received: April 2002
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Citations: View citations in EconPapers (26)

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