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

2015 ◽  
Vol 2015 ◽  
pp. 1-9 ◽  
Author(s):  
Winter Sinkala ◽  
Tembinkosi F. Nkalashe
Keyword(s):  
Option Pricing ◽  
Coupled System ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
First Order ◽  
Feedback Model ◽  
Black Scholes Model ◽  
Black Scholes

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.

scholarly journals The Lie Algebraic Approach for Determining Pricing for Trade Account Options

Mathematics ◽  
2021 ◽  
Vol 9 (3) ◽  
pp. 279
Author(s):  
Shih-Hsien Tseng ◽  
Tien Son Nguyen ◽  
Ruei-Ci Wang
Keyword(s):  
Option Pricing ◽  
Analytical Solutions ◽  
Algebraic Approach ◽  
Lie Symmetry ◽  
Lie Theory ◽  
Lie Symmetry Analysis ◽  
Black Scholes Model ◽  
Black Scholes ◽  
Trade Account ◽  
Pricing Problems

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.

scholarly journals Lie Symmetry Analysis of the Black-Scholes-Merton Model for European Options with Stochastic Volatility

Mathematics ◽  
2016 ◽  
Vol 4 (2) ◽  
pp. 28 ◽  
Author(s):  
Andronikos Paliathanasis ◽  
K. Krishnakumar ◽  
K.M. Tamizhmani ◽  
Peter Leach
Keyword(s):  
Stochastic Volatility ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
European Options ◽  
Lie Symmetry Analysis ◽  
Merton Model ◽  
Black Scholes

scholarly journals Symmetry Analysis and Conservation Laws of a Generalized Two-Dimensional Nonlinear KP-MEW Equation

2015 ◽  
Vol 2015 ◽  
pp. 1-7 ◽  
Author(s):  
Khadijo Rashid Adem ◽  
Chaudry Masood Khalique
Keyword(s):  
Conservation Laws ◽  
Exact Solutions ◽  
Expansion Method ◽  
Lie Symmetry ◽  
Symmetry Analysis ◽  
Optimal System ◽  
Two Dimensional ◽  
Lie Symmetry Analysis ◽  
One Dimensional ◽  
Similarity Reductions

Lie symmetry analysis is performed on a generalized two-dimensional nonlinear Kadomtsev-Petviashvili-modified equal width equation. The symmetries and adjoint representations for this equation are given and an optimal system of one-dimensional subalgebras is derived. The similarity reductions and exact solutions with the aid ofG′/G-expansion method are obtained based on the optimal systems of one-dimensional subalgebras. Finally conservation laws are constructed by using the multiplier method.

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