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.
Highlights
Both researchers and practitioners have studied option pricing for over a century [1,2,3].Many theoretical models have been proposed to help investors decide how to buy and sell an asset within a specified period [1,2,4,5,6,7], such as option pricing, which is affected by financial aspects including stock prices, interest rates and exchange rates [8]
Hyer, Lipton-Lifschitz and Pugachevsky [6] introduced the passport option based on the partial differential equation (PDE) method and solved it by using the Hamilton–Jacobi–Bellman (HJB) equation
Lie theory requires a massive number of algebraic trade account problem
Summary
Both researchers and practitioners have studied option pricing for over a century [1,2,3]. Black and Scholes [4] presented a general equilibrium of option pricing utilizing stochastic differential equations. Hyer, Lipton-Lifschitz and Pugachevsky [6] introduced the passport option based on the partial differential equation (PDE) method and solved it by using the Hamilton–Jacobi–Bellman (HJB) equation Their model was later extended by [9], who utilized both continuous and discrete switching. Developed a model, which can be used for both discrete and continuous partial differential equations to ascertain general analytic solutions and determine the most effective options for a trade account (OTA). The most effective strategy regarding option pricing can be found by solving a PDE using the Lie symmetry theory.
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