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Company, R.; Jódar, L.; Pintos, J.-R.; Roselló, M.-D.

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

Comput. Math. Appl. 59, No. 2, 651-662 (2010).
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.

Cited in 2 Documents

MSC:

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

Keywords:

nonlinear Black-Scholes equation; call option; numerical analysis; semidiscretization; transaction costs
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\textit{R. Company} et al., Comput. Math. Appl. 59, No. 2, 651--662 (2010; Zbl 1189.91203)
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References:

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