Symmetry reductions of a nonlinear option pricing model

Abstract

The studied model was suggested to design a perfect hedging strategy for a large trader. In this case the implementation of a hedging strategy affects the price of the underlying security. The feedback-effect leads to a nonlinear version of the Black-Scholes partial differential equation. Using the Lie group theory we reduce the partial differential equation in special cases to ordinary differential equations. The found Lie group of the model equation gives rise to invariant solutions. Families of exact invariant solutions for special values of parameters are described.