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

Winter Sinkala and Tembinkosi F. Nkalashe

Advances in Mathematical Physics, 2015, vol. 2015, issue 1

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.

Date: 2015
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https://doi.org/10.1155/2015/361785

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Persistent link: https://EconPapers.repec.org/RePEc:wly:jnlamp:v:2015:y:2015:i:1:n:361785

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