Numerical solution of jump-diffusion LIBOR market models
AbstractThis 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.
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Bibliographic InfoArticle provided by Springer in its journal Finance and Stochastics.
Volume (Year): 7 (2003)
Issue (Month): 1 ()
Note: received: February 2001; final version received: April 2002
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Web page: http://www.springerlink.com/content/101164/
Find related papers by 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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- Antonis Papapantoleon & John Schoenmakers & David Skovmand, 2011. "Efficient and accurate log-L\'evy approximations to L\'evy driven LIBOR models," Papers 1106.0866, arXiv.org, revised Jan 2012.
- Yuan Xia, 2011. "Multilevel Monte Carlo method for jump-diffusion SDEs," Papers 1106.4730, arXiv.org.
- Christian Fries & Joerg Kampen, 2010. "Global existence, regularity and a probabilistic scheme for a class of ultraparabolic Cauchy problems," Papers 1002.5031, arXiv.org, revised Oct 2012.
- Antonis Papapantoleon & David Skovmand, 2010. "Numerical methods for the L\'evy LIBOR model," Papers 1006.3340, arXiv.org.
- Joerg Kampen & Anastasia Kolodko & John Schoenmakers, 2008. "Monte Carlo Greeks for financial products via approximative transition densities," Papers 0807.1213, arXiv.org.
- Raoul Pietersz & Antoon Pelsser & Marcel van Regenmortel, 2005. "Fast drift approximated pricing in the BGM model," Finance 0502005, EconWPA.
- Antonis Papapantoleon & David Skovmand, 2010. "Picard approximation of stochastic differential equations and application to LIBOR models," Papers 1007.3362, arXiv.org, revised Jul 2011.
- Antonis Papapantoleon & Maria Siopacha, 2009. "Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model," Papers 0906.5581, arXiv.org, revised Oct 2010.
- Nicola Bruti-Liberati & Eckhard Platen, 2005. "On the Strong Approximation of Pure Jump Processes," Research Paper Series 164, Quantitative Finance Research Centre, University of Technology, Sydney.
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