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.

• Publication year

  2007

• Venue

  Quantitative Finance

• Publication date

  2007-04-05

• Fields of study

  Mathematics, Economics

• Identifiers
  DOI 10.1080/14697680903493573arXiv 0704.0745
• External record

  Open on Semantic Scholar

• Source metadata

  Semantic Scholar

• No claims are published for this paper.

• No concepts are published for this paper.

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