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A high-order recombination algorithm for weak approximation of stochastic differential equations

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  • Syoiti Ninomiya
  • Yuji Shinozaki

Abstract

This paper presents an algorithm for applying the high-order recombination method, originally introduced by Lyons and Litterer in ``High-order recombination and an application to cubature on Wiener space'' (Ann. Appl. Probab. 22(4):1301--1327, 2012), to practical problems in mathematical finance. A refined error analysis is provided, yielding a sharper condition for space partitioning. Based on this condition, a computationally feasible recursive partitioning algorithm is developed. Numerical examples are also included, demonstrating that the proposed algorithm effectively avoids the explosive growth in the cardinality of the support required to achieve high-order approximations.

Suggested Citation

  • Syoiti Ninomiya & Yuji Shinozaki, 2025. "A high-order recombination algorithm for weak approximation of stochastic differential equations," Papers 2504.19717, arXiv.org, revised May 2025.
    • Handle: RePEc:arx:papers:2504.19717
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    References listed on IDEAS

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    1. 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.
    2. Ninomiya Syoiti, 2003. "A partial sampling method applied to the Kusuoka approximation," Monte Carlo Methods and Applications, De Gruyter, vol. 9(1), pages 27-38, January.
    3. Heston, Steven L, 1993. "A Closed-Form Solution for Options with Stochastic Volatility with Applications to Bond and Currency Options," The Review of Financial Studies, Society for Financial Studies, vol. 6(2), pages 327-343.
    4. Syoiti Ninomiya & Yuji Shinozaki, 2019. "Higher-order Discretization Methods of Forward-backward SDEs Using KLNV-scheme and Their Applications to XVA Pricing," Applied Mathematical Finance, Taylor & Francis Journals, vol. 26(3), pages 257-292, May.
    5. 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.
    6. Crisan Dan & Lyons Terry, 2002. "Minimal Entropy Approximations and Optimal Algorithms," Monte Carlo Methods and Applications, De Gruyter, vol. 8(4), pages 343-356, December.
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