Symmetry analysis of the parabolic system for european option pricing with liquidity shocks
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Date
2025
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National University of Lesotho
Abstract
We address the knowledge gap between financial theory and practice by developing a framework to analyse European option pricing under liquidity shocks, which reduce market completeness and challenge traditional models like Black–Scholes. To tackle this, we undertake a Lie symmetry analysis of a coupled system designed to model European options subject to liquidity shocks. The system consists of a degenerate parabolic equation and another is a first-order nonlinear ordinary differential equation (ODE) in time with no spatial derivatives. Our analysis has uncovered the parabolic system’s Lie symmetry group and infinitesimal generators. We have then proceeded to investigate the system dynamics by constructing commutative tables that illustrate the relationships between the vector fields under study and the one-dimensional optimal system of symmetry subalgebras associated with the initial equation. Employing similarity reductions, we have applied the Lie symmetry methodology to decompose the system into several nonlinear ordinary differential equations (ODEs) corresponding
to each symmetry subalgebra. Finally, we present obtained invariant solutions through simulations as 2D and 3D graphs.
Description
Master's degree thesis