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

Juan He | Zendy; Wei Tu | Zendy; Aiqing Zhang | Zendy

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

Author(s) -

Juan He,

Wei Tu,

Aiqing Zhang

Publication year - 2022

Publication title -

mathematical problems in engineering

Language(s) - English

Resource type - Journals

SCImago Journal Rank - 0.262

H-Index - 62

eISSN - 1026-7077

pISSN - 1024-123X

DOI - 10.1155/2022/6563766

Subject(s) - mathematics , black–scholes model , rate of convergence , convergence (economics) , galerkin method , legendre polynomials , scheme (mathematics) , space (punctuation) , finite difference scheme , numerical analysis , order (exchange) , mathematical optimization , finite element method , mathematical analysis , computer science , econometrics , volatility (finance) , computer network , channel (broadcasting) , physics , finance , economics , thermodynamics , economic growth , operating system

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.

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