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Algebraic Structure of Vector Fields in Financial Diffusion Models and its Applications

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  • Yusuke Morimoto
  • Makiko Sasada

Abstract

High order discretization schemes of SDEs by using free Lie algebra valued random variables are introduced by Kusuoka, Lyons-Victoir, Ninomiya-Victoir and Ninomiya-Ninomiya. These schemes are called KLNV methods. They involve solving the flows of vector fields associated with SDEs and it is usually done by numerical methods. The authors found a special Lie algebraic structure on the vector fields in the major financial diffusion models. Using this structure, we can solve the flows associated with vector fields analytically and efficiently. Numerical examples show that our method saves the computation time drastically.

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  • 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.
    • Handle: RePEc:arx:papers:1510.02013
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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. 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.
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