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ESAIM: M2AN 43 (2009) 1045-1061
DOI: 10.1051/m2an/2009014
Consistent stable difference schemes for nonlinear Black-Scholes equations modelling option pricing with transaction costs
Rafael Company, Lucas Jódar and José-Ramón PintosInstituto Universitario de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, piso 2, P.O. Box 46022, Valencia, Spain. rcompany@imm.upv.es; ljodar@imm.upv.es; jrpt60@gmail.com
Received August 1st, 2008. Revised February 25, 2009. Published online June 12, 2009.
Abstract
This paper deals with the numerical solution of nonlinear Black-Scholes equation modeling European vanilla call option pricing under transaction costs. Using an explicit finite difference scheme consistent with the partial differential equation valuation problem, a sufficient condition for the stability of the solution is given in terms of the stepsize discretization variables and the parameter measuring the transaction costs. This stability condition is linked to some properties of the numerical approximation of the Gamma of the option, previously obtained. Results are illustrated with numerical examples.
Mathematics Subject Classification. 35K55, 65M12, 39A10, 90A09
Key words: Nonlinear Black-Scholes equation, option pricing, numerical analysis, transaction costs.
© EDP Sciences, SMAI 2009
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