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Option Pricing with Lie Symmetry Analysis and Similarity Reduction Method

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  • Wenqing Bao
  • ChunLi Chen
  • Jin E. Zhang

Abstract

With some transformations, we convert the problem of option pricing under state-dependent volatility into an initial value problem of the Fokker-Planck equation with a certain potential. By using the Lie symmetry analysis and similarity reduction method, we are able to reduce the dimensions of the partial differential equation and find some of its particular solutions of the equation. A few case studies demonstrate that our new method can be used to produce analytical option pricing formulas for certain volatility functions.

Suggested Citation

  • Wenqing Bao & ChunLi Chen & Jin E. Zhang, 2013. "Option Pricing with Lie Symmetry Analysis and Similarity Reduction Method," Papers 1311.4074, arXiv.org.
    • Handle: RePEc:arx:papers:1311.4074
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    File URL: http://arxiv.org/pdf/1311.4074
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