Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model
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.
|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|
|Contact details of provider:|| Web page: http://arxiv.org/|
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