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Solving The Asian Option Pde Using Lie Symmetry Methods

Author

Listed:
  • NICOLETTE C. CAISTER

    (Department of Statistics and Actuarial Science, University of KwaZulu-Natal, Private Bag X54001, Durban 4001, South Africa)

  • JOHN G. O'HARA

    (Centre for Computational Finance and Economic Agents, University of Essex, Colchester CO4 3SQ, United Kingdom)

  • KESHLAN S. GOVINDER

    (Astrophysics and Cosmology Research Unit, School of Mathematical Sciences, University of KwaZulu-Natal, Private Bag X54001, Durban 4001, South Africa)

Abstract

Asian options incorporate the average stock price in the terminal payoff. Examination of the Asian option partial differential equation (PDE) has resulted in many equations of reduced order that in general can be mapped into each other, although this is not always shown. In the literature these reductions and mappings are typically acquired via inspection or ad hoc methods. In this paper, we evaluate the classical Lie point symmetries of the Asian option PDE. We subsequently use these symmetries with Lie's systematic and algorithmic methods to show that one can obtain the same aforementioned results. In fact we find a familiar analytical solution in terms of a Laplace transform. Thus, when coupled with their methodic virtues, the Lie techniques reduce the amount of intuition usually required when working with differential equations in finance.

Suggested Citation

  • Nicolette C. Caister & John G. O'Hara & Keshlan S. Govinder, 2010. "Solving The Asian Option Pde Using Lie Symmetry Methods," International Journal of Theoretical and Applied Finance (IJTAF), World Scientific Publishing Co. Pte. Ltd., vol. 13(08), pages 1265-1277.
    • Handle: RePEc:wsi:ijtafx:v:13:y:2010:i:08:n:s0219024910006194
    DOI: 10.1142/S0219024910006194
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    Citations

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    Cited by:

    1. Andronikos Paliathanasis & K. Krishnakumar & K.M. Tamizhmani & Peter G.L. Leach, 2016. "Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility," Mathematics, MDPI, vol. 4(2), pages 1-14, May.
    2. A. Paliathanasis & K. Krishnakumar & K. M. Tamizhmani & P. G. L. Leach, 2015. "Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility," Papers 1508.06797, arXiv.org, revised May 2016.
    3. Michael Okelola & Keshlan Govinder, 2015. "Symmetry structure and solution of evolution-type equations with time dependent parameters in financial Mathematics," Papers 1503.03194, arXiv.org.
    4. Shih-Hsien Tseng & Tien Son Nguyen & Ruei-Ci Wang, 2021. "The Lie Algebraic Approach for Determining Pricing for Trade Account Options," Mathematics, MDPI, vol. 9(3), pages 1-9, January.

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