arXiv subjects

Maria Siopacha

Publications and source records attributed to Maria Siopacha.

2 recordsLinked to original sources

arXiv2010

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

In this article we develop a method for the strong approximation of stochastic differential equations (SDEs) driven by Lévy 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 Lévy LIBOR model illustrates our method.

math.PR↗

arXiv2007

Weak and Strong Taylor methods for numerical solutions of stochastic differential equations

We apply results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we work out weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to deal with the typical stochastic drift and with stochastic volatility. In contrast to other accurate methods like numerical schemes for the full SDE, we obtain easily tractable expressions for accurate pricing. In particular, we present an easily tractable alternative to ``freezing the drift'' in LIBOR market models, which has an accuracy similar to the full numerical scheme. Numerical examples underline the results.

q-fin.CP↗