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

We apply the results of Malliavin-Thalmaier-Watanabe for strong and weak Taylor expansions of solutions of perturbed stochastic differential equations (SDEs). In particular, we determine weight expressions for the Taylor coefficients of the expansion. The results are applied to LIBOR market models in order to find precise and quick algorithms. In contrast to methods such as Euler-Maruyama-Monte-Carlo for the full SDE, we obtain more tractable expressions for accurate pricing. In particular, we present a readily tractable alternative to 'freezing the drift' in LIBOR market models that has an accuracy similar to the Euler-Maruyama-Monte-Carlo scheme for the full LIBOR market model. Numerical examples underline our results.