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 Ψ solution of a nonlinear ordinary differential equation. In this paper we obtain relevant properties of the function Ψ 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.
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