GROUP CLASSIFICATION FOR A GENERAL NONLINEAR MODEL OF OPTIONS PRICING

Abstract

We consider a family of equations with two free functional parameters containing the classical Black–Scholes model, Schönbucher–Wilmott model, Sircar–Papanicolaou equation for option pricing as partial cases. A five-dimensional group of equivalence transformations is calculated for that family. That group is applied to a search for specifications' parameters specifications corresponding to additional symmetries of the equation. Seven pairs of specifications are found.

Keywords

• Nonlinear partial differential equation, Group analysis, Group of equivalency transformations, Group classification, Nonlinear Black–Scholes equation, Option pricing, Dynamic hedging, Feedback effects of hedging