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

  • Maria Siopacha
  • Josef Teichmann
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    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.

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    File URL: http://arxiv.org/pdf/0704.0745
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    Paper provided by arXiv.org in its series Papers with number 0704.0745.

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    Date of creation: Apr 2007
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    Handle: RePEc:arx:papers:0704.0745
    Contact details of provider: Web page: http://arxiv.org/

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    1. Miltersen, Kristian R & Sandmann, Klaus & Sondermann, Dieter, 1997. " Closed Form Solutions for Term Structure Derivatives with Log-Normal Interest Rates," Journal of Finance, American Finance Association, vol. 52(1), pages 409-30, March.
    2. Erik Schlögl, 1999. "A Multicurrency Extension of the Lognormal Interest Rate Market Models," Research Paper Series 20, Quantitative Finance Research Centre, University of Technology, Sydney.
    3. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
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