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Option Pricing with Lie Symmetry Analysis and Similarity Reduction Method

  • Wenqing Bao
  • ChunLi Chen
  • Jin E. Zhang
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    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.

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    File URL: http://arxiv.org/pdf/1311.4074
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    Paper provided by arXiv.org in its series Papers with number 1311.4074.

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    Date of creation: Nov 2013
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    Handle: RePEc:arx:papers:1311.4074
    Contact details of provider: Web page: http://arxiv.org/

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    1. Jin Zhang & Yi Xiang, 2008. "The implied volatility smirk," Quantitative Finance, Taylor & Francis Journals, vol. 8(3), pages 263-284.
    2. C. F. Lo & C. H. Hui, 2001. "Valuation of financial derivatives with time-dependent parameters: Lie-algebraic approach," Quantitative Finance, Taylor & Francis Journals, vol. 1(1), pages 73-78.
    3. Cox, John C. & Ross, Stephen A., 1976. "The valuation of options for alternative stochastic processes," Journal of Financial Economics, Elsevier, vol. 3(1-2), pages 145-166.
    4. Yishen Li & Jin Zhang, 2004. "Option pricing with Weyl-Titchmarsh theory," Quantitative Finance, Taylor & Francis Journals, vol. 4(4), pages 457-464.
    5. Peter Laurence & Tai-Ho Wang, 2005. "Closed Form Solutions For Quadratic And Inverse Quadratic Term Structure Models," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 8(08), pages 1059-1083.
    6. Schroder, Mark Douglas, 1989. " Computing the Constant Elasticity of Variance Option Pricing Formula," Journal of Finance, American Finance Association, vol. 44(1), pages 211-19, March.
    7. Black, Fischer & Scholes, Myron S, 1973. "The Pricing of Options and Corporate Liabilities," Journal of Political Economy, University of Chicago Press, vol. 81(3), pages 637-54, May-June.
    8. Robert C. Merton, 1973. "Theory of Rational Option Pricing," Bell Journal of Economics, The RAND Corporation, vol. 4(1), pages 141-183, Spring.
    9. Jin E. Zhang & Yishen Li, 2012. "New analytical option pricing models with Weyl--Titchmarsh theory," Quantitative Finance, Taylor & Francis Journals, vol. 12(7), pages 1003-1010, June.
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