Computing option pricing models under transaction costs

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