Asymptotic Convergence Analysis and Error Estimate for Black-Scholes Model of Option Pricing

Juan He, Wei Tu, Aiqing Zhang and Binchang Wang

Mathematical Problems in Engineering, 2022, vol. 2022, 1-9

Abstract: In this work, we discuss the numerical method for the solution of the Black-Scholes model. First of all, the asymptotic convergence for the solution of Black-Scholes model is proved. Second, we develop a linear, unconditionally stable, and second-order time-accurate numerical scheme for this model. By using the finite difference method and Legendre-Galerkin spectral method, we construct a time and space discrete scheme. Finally, we prove that the scheme has second-order accuracy and spectral accuracy in time and space, respectively. Several numerical experiments further verify the convergence rate and effectiveness of the developed scheme.

Date: 2022
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Persistent link: https://EconPapers.repec.org/RePEc:hin:jnlmpe:6563766

DOI: 10.1155/2022/6563766

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