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Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing

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  • Syoiti Ninomiya
  • Nicolas Victoir
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    Abstract

    A new, simple algorithm of order 2 is presented to approximate weakly stochastic differential equations. It is then applied to the problem of pricing Asian options under the Heston stochastic volatility model. 2000 Mathematics Subject Classification, 65C30, 65C05.

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    File URL: http://www.tandfonline.com/doi/abs/10.1080/13504860701413958
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    Bibliographic Info

    Article provided by Taylor & Francis Journals in its journal Applied Mathematical Finance.

    Volume (Year): 15 (2008)
    Issue (Month): 2 ()
    Pages: 107-121

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    Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:107-121

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    Web page: http://www.tandfonline.com/RAMF20

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    Web: http://www.tandfonline.com/pricing/journal/RAMF20

    Related research

    Keywords: Heston model; numerical methods for stochastic differential equations; mathematical finance; quasi-Monte Carlo method;

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    Cited by:
    1. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer, vol. 20(2), pages 147-182, May.
    2. Ahdida, Abdelkoddousse & Alfonsi, Aurélien, 2013. "A mean-reverting SDE on correlation matrices," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1472-1520.
    3. Abdelkoddousse Ahdida & Aur\'elien Alfonsi, 2010. "Exact and high order discretization schemes for Wishart processes and their affine extensions," Papers 1006.2281, arXiv.org, revised Mar 2013.
    4. Denis Belomestny & Tigran Nagapetyan, 2014. "Multilevel path simulation for weak approximation schemes," Papers 1406.2581, arXiv.org, revised Jul 2014.
    5. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
    6. repec:hal:wpaper:hal-00409861 is not listed on IDEAS
    7. Mariko Ninomiya & Syoiti Ninomiya, 2009. "A new higher-order weak approximation scheme for stochastic differential equations and the Runge–Kutta method," Finance and Stochastics, Springer, vol. 13(3), pages 415-443, September.
    8. repec:hal:wpaper:hal-00491371 is not listed on IDEAS
    9. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2010. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-745, CIRJE, Faculty of Economics, University of Tokyo.

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