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Valuation of financial derivatives with time-dependent parameters: Lie-algebraic approach

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  • C. F. Lo
  • C. H. Hui

Abstract

Based upon the Wei-Norman theorem, this paper presents a Lie-algebraic technique for the pricing of financial derivatives with time-dependent parameters. By exploiting the dynamical symmetry of the pricing partial differential equations of the financial derivatives, the new method enables us to derive analytical closed-form pricing formulae very straightforwardly. We believe that this new approach will provide an efficient method for the valuation of financial derivatives.

Suggested Citation

  • 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.
    • Handle: RePEc:taf:quantf:v:1:y:2001:i:1:p:73-78
    DOI: 10.1080/713665552
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    Cited by:

    1. Melike Bildirici & Nilgun Guler Bayazit & Yasemen Ucan, 2021. "Modelling Oil Price with Lie Algebras and Long Short-Term Memory Networks," Mathematics, MDPI, vol. 9(14), pages 1-10, July.
    2. Philippe Jacquinot & Nikolay Sukhomlin, 2010. "A direct formulation of implied volatility in the Black-Scholes model," Post-Print hal-02533014, HAL.
    3. Ming Xi Huang, 2010. "Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 15, July-Dece.
    4. Hui, C.H. & Lo, C.F. & Wong, T.C. & Man, P.K., 2006. "Measuring provisions for collateralised retail lending," Journal of Economics and Business, Elsevier, vol. 58(4), pages 343-361.
    5. Ming Xi Huang, 2010. "Modelling Default Correlations in a Two-Firm Model with Dynamic Leverage Ratios," PhD Thesis, Finance Discipline Group, UTS Business School, University of Technology, Sydney, number 4-2010, January-A.
    6. Melike Bildirici & Yasemen Ucan & Sérgio Lousada, 2022. "Interest Rate Based on The Lie Group SO(3) in the Evidence of Chaos," Mathematics, MDPI, vol. 10(21), pages 1-9, October.
    7. Philippe Jacquinot & Nikolay Sukhomlin, 2010. "A direct formulation of implied volatility in the Black- Scholes model," Post-Print hal-02527822, HAL.
    8. Wenqing Bao & ChunLi Chen & Jin E. Zhang, 2013. "Option Pricing with Lie Symmetry Analysis and Similarity Reduction Method," Papers 1311.4074, arXiv.org.

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