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


  • Maria Siopacha
  • Josef Teichmann


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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  • Maria Siopacha & Josef Teichmann, 2007. "Weak and Strong Taylor methods for numerical solutions of stochastic differential equations," Papers 0704.0745,
  • Handle: RePEc:arx:papers:0704.0745

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    References listed on IDEAS

    1. Farshid Jamshidian, 1997. "LIBOR and swap market models and measures (*)," Finance and Stochastics, Springer, vol. 1(4), pages 293-330.
    2. Erik Schlögl, 2002. "A multicurrency extension of the lognormal interest rate Market Models," Finance and Stochastics, Springer, vol. 6(2), pages 173-196.
    3. 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 409-430, March.
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    Cited by:

    1. repec:wsi:ijtafx:v:15:y:2012:i:06:n:s0219024912500446 is not listed on IDEAS
    2. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in L\'evy term structure models," Papers 0902.3456,
    3. repec:wsi:ijtafx:v:13:y:2010:i:08:n:s0219024910006169 is not listed on IDEAS
    4. Martin Keller-Ressel & Antonis Papapantoleon & Josef Teichmann, 2009. "The affine LIBOR models," Papers 0904.0555,, revised Jul 2011.
    5. Antonis Papapantoleon & Maria Siopacha, 2009. "Strong Taylor approximation of stochastic differential equations and application to the L\'evy LIBOR model," Papers 0906.5581,, revised Oct 2010.
    6. Wolfgang Kluge & Antonis Papapantoleon, 2009. "On the valuation of compositions in Levy term structure models," Quantitative Finance, Taylor & Francis Journals, vol. 9(8), pages 951-959.

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