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A weighted finite difference method for subdiffusive Black-Scholes model. (English) Zbl 1447.65024

Summary: In this paper we focus on the subdiffusive Black-Scholes (B-S) model. The main part of our work consists of the finite difference method as a numerical approach to the option pricing in the considered model. We find the governing fractional differential equation and the related weighted numerical scheme being a generalization of the classical Crank-Nicolson (C-N) scheme. The proposed method has \(2-\alpha\) order of accuracy with respect to time where \(\alpha\in(0,1)\) is the subdiffusion parameter, and 2 with respect to space. Further, we provide the stability and convergence analysis. Finally, we present some numerical results.

MSC:

65M06 Finite difference methods for initial value and initial-boundary value problems involving PDEs
65M12 Stability and convergence of numerical methods for initial value and initial-boundary value problems involving PDEs
35R11 Fractional partial differential equations
26A33 Fractional derivatives and integrals
91G60 Numerical methods (including Monte Carlo methods)
91G20 Derivative securities (option pricing, hedging, etc.)
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References:

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