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Numerical solution of jump-diffusion LIBOR market models

Author

Listed:
  • Nicolas Merener

    (Department of Applied Physics and Applied Mathematics, Columbia University, New York, NY 10027, USA Manuscript)

  • Paul Glasserman

    (403 Uris Hall, Graduate School of Business, Columbia University, New York, NY 10027, USA)

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.

Suggested Citation

  • Nicolas Merener & Paul Glasserman, 2003. "Numerical solution of jump-diffusion LIBOR market models," Finance and Stochastics, Springer, vol. 7(1), pages 1-27.
    • Handle: RePEc:spr:finsto:v:7:y:2003:i:1:p:1-27
    Note: received: February 2001; final version received: April 2002
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    References listed on IDEAS

    as
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    More about this item

    Keywords

    Interest rate models; Monte Carlo simulation; market models; marked point processes;
    All these keywords.

    JEL classification:

    • G13 - Financial Economics - - General Financial Markets - - - Contingent Pricing; Futures Pricing
    • E43 - Macroeconomics and Monetary Economics - - Money and Interest Rates - - - Interest Rates: Determination, Term Structure, and Effects

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