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A high-order compact method for nonlinear Black-Scholes option pricing equations of American options
Halmstad University, School of Information Science, Computer and Electrical Engineering (IDE), Halmstad Embedded and Intelligent Systems Research (EIS).
Lehrstuhl für Angewandte Mathematik und Numerische Analysis, Fachbereich C Mathematik und Naturwissenschaften, Bergische Universität Wuppertal, Gaußstrasse 20, 42119 Wuppertal, Germany.
2011 (English)In: International Journal of Computer Mathematics, ISSN 0020-7160, E-ISSN 1029-0265, Vol. 88, no 13, 2782-2797 p.Article in journal (Refereed) Published
Abstract [en]

Due to transaction costs, illiquid markets, large investors or risks from an unprotected portfolio the assumptions in the classical Black-Scholes model become unrealistic and the model results in nonlinear, possibly degenerate, parabolic diffusion-convection equations. Since in general, a closed-form solution to the nonlinear Black-Scholes equation for American options does not exist (even in the linear case), these problems have to be solved numerically. We present from the literature different compact finite difference schemes to solve nonlinear Black-Scholes equations for American options with a nonlinear volatility function. As compact schemes cannot be directly applied to American type options, we use a fixed domain transformation proposed by Sevcovic and show how the accuracy of the method can be increased to order four in space and time.

Place, publisher, year, edition, pages
London: Gordon and Breach Publishers, 2011. Vol. 88, no 13, 2782-2797 p.
Keyword [en]
nonlinear Black-Scholes equation, compact finite difference scheme, American options, high-order methods, fixed domain transformation, transaction costs
National Category
Engineering and Technology
Identifiers
URN: urn:nbn:se:hh:diva-18882DOI: 10.1080/00207160.2011.558574ISI: 000293885100011Scopus ID: 2-s2.0-84860421134OAI: oai:DiVA.org:hh-18882DiVA: diva2:537603
Available from: 2012-06-27 Created: 2012-06-25 Last updated: 2012-12-12Bibliographically approved

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CiteExportLink to record
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Cite
Citation style
  • apa
  • 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
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  • asciidoc
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