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Pricing options in illiquid markets: symmetry reductions and exact solutions
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS), MPE-lab. (Financial Mathematics)
Leipzig University, Department of Mathematics. (Financial Mathematics)
2008 (English)In: Nonlinear Models in Mathematical Finance: New Research Trends in Option Pricing / [ed] Matthias Ehrhardt, New York: Nova Science Publishers, Inc., 2008, 103-130 p.Chapter in book (Other academic)
Abstract [en]

The present paper 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-ScholesPDE. In the second part of the paper 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.

Place, publisher, year, edition, pages
New York: Nova Science Publishers, Inc., 2008. 103-130 p.
Keyword [en]
Nonlinear Black Scholes equations, Option pricing models, Illiquid markets
National Category
Computational Mathematics
Identifiers
URN: urn:nbn:se:hh:diva-5531ISBN: 978-1-60456-931-5 OAI: oai:DiVA.org:hh-5531DiVA: diva2:346555
Available from: 2010-09-01 Created: 2010-09-01 Last updated: 2012-09-27Bibliographically approved

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Bordag, Ljudmila A.
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CiteExportLink to record
Permanent link

Direct link
Cite
Citation style
  • apa
  • harvard1
  • ieee
  • modern-language-association-8th-edition
  • vancouver
  • Other style
More styles
Language
  • de-DE
  • en-GB
  • en-US
  • fi-FI
  • nn-NO
  • nn-NB
  • sv-SE
  • Other locale
More languages
Output format
  • html
  • text
  • asciidoc
  • rtf