Economy – Quantitative Finance – Computational Finance
Scientific paper
2007-04-05
Economy
Quantitative Finance
Computational Finance
18 pages
Scientific paper
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.
Siopacha Maria
Teichmann Josef
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