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Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing

Author

Listed:
  • Syoiti Ninomiya
  • Nicolas Victoir

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.

Suggested Citation

  • Syoiti Ninomiya & Nicolas Victoir, 2008. "Weak Approximation of Stochastic Differential Equations and Application to Derivative Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 15(2), pages 107-121.
  • Handle: RePEc:taf:apmtfi:v:15:y:2008:i:2:p:107-121
    DOI: 10.1080/13504860701413958
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    Citations

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    Cited by:

    1. Denis Belomestny & Tigran Nagapetyan, 2014. "Multilevel path simulation for weak approximation schemes," Papers 1406.2581, arXiv.org, revised Oct 2014.
    2. 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.
    3. Kazuhiro Yoshikawa, 2015. "An Approximation Scheme for Diffusion Processes Based on an Antisymmetric Calculus over Wiener Space," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 22(2), pages 185-207, May.
    4. Anis Al Gerbi & Benjamin Jourdain & Emmanuelle Cl'ement, 2015. "Ninomiya-Victoir scheme: strong convergence, antithetic version and application to multilevel estimators," Papers 1508.06492, arXiv.org, revised Oct 2015.
    5. Benjamin Jourdain & Mohamed Sbai, 2013. "High order discretization schemes for stochastic volatility models," Post-Print hal-00409861, HAL.
    6. Mackevičius, Vigirdas, 2010. "On weak approximations of CIR equation with high volatility," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 80(5), pages 959-970.
    7. Al Gerbi Anis & Jourdain Benjamin & Clément Emmanuelle, 2016. "Ninomiya–Victoir scheme: Strong convergence, antithetic version and application to multilevel estimators," Monte Carlo Methods and Applications, De Gruyter, vol. 22(3), pages 197-228, September.
    8. 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.
    9. Ahdida, Abdelkoddousse & Alfonsi, Aurélien, 2013. "A mean-reverting SDE on correlation matrices," Stochastic Processes and their Applications, Elsevier, vol. 123(4), pages 1472-1520.
    10. Masahiro Nishiba, 2013. "Pricing Exotic Options and American Options: A Multidimensional Asymptotic Expansion Approach," Asia-Pacific Financial Markets, Springer;Japanese Association of Financial Economics and Engineering, vol. 20(2), pages 147-182, May.
    11. Christian Bayer & Peter K. Friz & Paul Gassiat & Joerg Martin & Benjamin Stemper, 2017. "A regularity structure for rough volatility," Papers 1710.07481, arXiv.org.
    12. Kenichiro Shiraya & Akihiko Takahashi & Masashi Toda, 2009. "Pricing Barrier and Average Options under Stochastic Volatility Environment," CIRJE F-Series CIRJE-F-682, CIRJE, Faculty of Economics, University of Tokyo.
    13. Yusuke Morimoto & Makiko Sasada, 2015. "Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications," Papers 1510.02013, arXiv.org, revised Dec 2015.
    14. 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.
    15. Lenkšas, A. & Mackevičius, V., 2015. "Weak approximation of Heston model by discrete random variables," Mathematics and Computers in Simulation (MATCOM), Elsevier, vol. 113(C), pages 1-15.
    16. repec:bpj:mcmeap:v:23:y:2017:i:1:p:1-12:n:1 is not listed on IDEAS

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