Strong Taylor approximation of stochastic differential equations and application to the Lévy LIBOR model

Details Strong Taylor approximation of stochastic differential equations and application to the Lévy LIBOR model Strong Taylor approximation of stochastic differential equations and application to the Lévy LIBOR model

2009-06-30

arxiv.org/abs/0906.5581v2

Proceedings of the Actuarial and Financial Mathematics Conference, pp. 47-62, 2011

Mathematics

Probability

16 pages, 4 figures, forthcoming in the Proceedings of the Actuarial and Financial Mathematics Conference, Brussels, Belgium,

Scientific paper

In 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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