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Lie Symmetry Analysis of a First‐Order Feedback Model of Option Pricing

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  • Winter Sinkala
  • Tembinkosi F. Nkalashe

Abstract

A first‐order feedback model of option pricing consisting of a coupled system of two PDEs, a nonliner generalised Black‐Scholes equation and the classical Black‐Scholes equation, is studied using Lie symmetry analysis. This model arises as an extension of the classical Black‐Scholes model when liquidity is incorporated into the market. We compute the admitted Lie point symmetries of the system and construct an optimal system of the associated one‐dimensional subalgebras. We also construct some invariant solutions of the model.

Suggested Citation

  • Winter Sinkala & Tembinkosi F. Nkalashe, 2015. "Lie Symmetry Analysis of a First‐Order Feedback Model of Option Pricing," Advances in Mathematical Physics, John Wiley & Sons, vol. 2015(1).
    • Handle: RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:361785
    DOI: 10.1155/2015/361785
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    References listed on IDEAS

    as
    1. Gerd Baumann, 2000. "Symmetry Analysis of Differential Equations with Mathematica®," Springer Books, Springer, number 978-1-4612-2110-4, March.
    2. 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.
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