Lie symmetry reductions and exact solutions of an option-pricing equation for large agents
Lekalakala, Senkepeng Louisa
Khalique, Chaudry Masood
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In this paper, we study a nonlinear partial differential equation that models the one-factor term structure option-pricing for large agents from the Lie symmetry stand point. This equation was modelled by Jonsson and Keppo (Appl Math Financ 9:261-272, 2002) and is a nonlinear modified Black-Scholes partial differential equation. We first determine an optimal system of one-dimensional subalgebras. We then use it to obtain symmetry reductions and families of group-invariant solutions of the underlying equation.