The Lie Algebraic Approach for Determining Pricing for Trade Account Options

Abstract

In recent years, many advanced techniques have been applied to financial problems; however, very few scholars have used the Lie theory. The purpose of this study was to examine the options for a trade account through Lie symmetry analysis. According to our results, it is effective for determining analytical solutions for pricing issues and solving other partial differential equations. The proposed solution can be used by further researchers or practitioners in option pricing problems for better performance compared with the classical Black–Scholes model.

Keywords

• Lie theory
• symmetry analysis
• options for a trade account
• Hamilton–Jacobi–Bellman equation