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

Abstract EN

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.