Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model
AbstractIn this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by L\'evy processes or general semimartingales. The main ingredients of our method is the perturbation of the SDE and the Taylor expansion of the resulting parameterized curve. We apply this method to develop strong approximation schemes for LIBOR market models. In particular, we derive fast and precise algorithms for the valuation of derivatives in LIBOR models which are more tractable than the simulation of the full SDE. A numerical example for the L\'evy LIBOR model illustrates our method.
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Bibliographic InfoPaper provided by arXiv.org in its series Papers with number 0906.5581.
Date of creation: Jun 2009
Date of revision: Oct 2010
Publication status: Published in Proceedings of the Actuarial and Financial Mathematics Conference, pp. 47-62, 2011
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Web page: http://arxiv.org/
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