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On weak approximations of CIR equation with high volatility

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  • Mackevičius, Vigirdas

Abstract

We propose two new positive weak second-order approximations for the CIR equation dXt=(a−bXt)dt+σXtdBt based on splitting, at each step, the equation into the deterministic part dXt=(a−bXt)dt, which is solved exactly, and the stochastic part dXt=σXtdBt, which is approximated in distribution. The schemes are illustrated by encouraging simulation results.

Suggested Citation

  • 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.
    • Handle: RePEc:eee:matcom:v:80:y:2010:i:5:p:959-970
    DOI: 10.1016/j.matcom.2009.11.001
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    References listed on IDEAS

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    1. Cox, John C. & Ingersoll Junior, Jonathan E. & Ross, Stephen A., 2007. "A theory of the term structure of interest rates," RAE - Revista de Administração de Empresas, FGV-EAESP Escola de Administração de Empresas de São Paulo (Brazil), vol. 47(2), April.
    2. 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.
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