Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model
Probability
2015-03-13 v2 Computational Finance
Abstract
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.
Keywords
Cite
@article{arxiv.0906.5581,
title = {Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model},
author = {Antonis Papapantoleon and Maria Siopacha},
journal= {arXiv preprint arXiv:0906.5581},
year = {2015}
}
Comments
16 pages, 4 figures, forthcoming in the Proceedings of the Actuarial and Financial Mathematics Conference, Brussels, Belgium, 2010