Computing option pricing models under transaction costs

Authors:
R. Company;L. Jódar;J. -R. Pintos;M. -D. Roselló
Affiliations:
Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, piso 2, P.O. Box 46022, Valencia, Spain;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, piso 2, P.O. Box 46022, Valencia, Spain;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, piso 2, P.O. Box 46022, Valencia, Spain;Instituto de Matemática Multidisciplinar, Universidad Politécnica de Valencia, Edificio 8G, piso 2, P.O. Box 46022, Valencia, Spain
Venue:
Computers & Mathematics with Applications
Year:
2010

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Abstract

This paper deals with the Barles-Soner model arising in the hedging of portfolios for option pricing with transaction costs. This model is based on a correction volatility function @J solution of a nonlinear ordinary differential equation. In this paper we obtain relevant properties of the function @J which are crucial in the numerical analysis and computing of the underlying nonlinear Black-Scholes equation. Consistency and stability of the proposed numerical method are detailed and illustrative examples are given.