Quotation Frey, Rüdiger, Bordag, Ljudmila. 2009. Pricing options in illiquid markets: symmetry reductions and exact solutions. In: Nonlinear Models in Mathematical Finance New Research Trends in Option Pricing, Hrsg. Matthias Ehrhardt, 103-129. New York: Nova Science Publishers.


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Abstract

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.

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Publication's profile

Status of publication Published
Affiliation WU
Type of publication Chapter in edited volume
Language English
Title Pricing options in illiquid markets: symmetry reductions and exact solutions
Title of whole publication Nonlinear Models in Mathematical Finance New Research Trends in Option Pricing
Editor Matthias Ehrhardt
Page from 103
Page to 129
Location New York
Publisher Nova Science Publishers
Year 2009
URL http://www.math.tu-berlin.de/~ehrhardt/Projects/black-scholes-book.html

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Frey, Rüdiger (Details)
External
Bordag, Ljudmila
Organization
Institute for Statistics and Mathematics IN (Details)
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