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 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.

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