A numerical method for European option pricing with transaction costs nonlinear equation. (English) Zbl 1185.91174

Summary: This paper deals with the construction of a finite difference scheme and the numerical analysis of its solution for a nonlinear Black-Scholes partial differential equation modelling stock option pricing in the realistic case when transaction costs arising in the hedging of portfolios are taken into account. The analysed model is the Barles-Soner one for which an appropriate fully nonlinear numerical method has not still applied. After construction of the numerical solution, consistency and stability are studied and some illustrative examples are included.


91G20 Derivative securities (option pricing, hedging, etc.)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
Full Text: DOI


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