Computing option pricing models under transaction costs. (English) Zbl 1189.91203

Summary: 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 \(\Psi \) solution of a nonlinear ordinary differential equation. In this paper we obtain relevant properties of the function \(\Psi \) 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.


91G20 Derivative securities (option pricing, hedging, etc.)
91G60 Numerical methods (including Monte Carlo methods)
65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
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