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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
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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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    Paper provided by 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

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