Pricing options in illiquid markets: symmetry reductions and exact solutions

Rüdiger Frey, Ljudmila Bordag

Publication: Chapter in book/Conference proceedingChapter in edited volume


This chapter is concerned with nonlinear Black-Scholes equations arising in certain option pricing models with a large trader and/or transaction costs. In the first part we give an overview of existing option pricing models with frictions. While the financial setup differs between models, it turns out that in many of these models derivative prices can be characterized by fully nonlinear versions of the standard parabolic Black-Scholes PDE. In the second part of this chapter we study a typical nonlinear Black-Scholes equation using methods from Lie group analysis. The equation possesses a rich symmetry group. By introducing invariant variables, invariant solutions can therefore be characterized in terms of solutions to ordinary differential equations. Finally we discuss properties and applications of these solutions.
Original languageEnglish
Title of host publicationNonlinear Models in Mathematical Finance New Research Trends in Option Pricing
Editors Matthias Ehrhardt
Place of PublicationNew York
PublisherNova Science Publishers
Pages103 - 129
Publication statusPublished - 1 May 2009

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