A new approach to using the cubic B-spline functions to solve the Black-Scholes equation

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Aminikhah Hossein; Alavi Seyyed Javad

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Journal: JOURNAL OF NEW RESEARCHES IN MATHEMATICS Year:2019 | Volume:5 | Issue:18 Page(s): 71-80

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Title

A new approach to using the cubic B-spline functions to solve the Black-Scholes equation

Author(s)

Aminikhah Hossein | Alavi Seyyed Javad | Issue Writer Certificate

Keywords

Black-Scholes equationQ1

European and American option difference schemesQ1

B-spline functionQ1

StabilityQ1

ConvergenceQ2

Abstract

Nowadays, options are common financial derivatives. For this reason, by increase of applications for these financial derivatives, the problem of options pricing is one of the most important economic issues. With the development of stochastic models, the need for randomly computational methods caused the generation of a new field called financial engineering. In the financial engineering the presentation of Black-Scholes model in 1973, attracted the attention of economists to the partial differential equations more than past. Therefore, we need a simple and precise solution for this kind of partial differential equations to determine the pricing option contracts. In this article the cubic B-spline collocation method has been used in the form of a difference method to solving Black-Scholes partial differential equation. Using this method as simplicity as finite difference method and does not have complex computation of traditional B-spline collocation method. The use of this method leads to a system of tridiagonal algebraic equations which is suitable for computer programming. The Stability and Convergence of this method is discussed and numerical results are presented for European and American options.

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APA: Copy

Aminikhah, Hossein, & Alavi, Seyyed Javad. (2019). A new approach to using the cubic B-spline functions to solve the Black-Scholes equation. JOURNAL OF NEW RESEARCHES IN MATHEMATICS, 5(18 ), 71-80. SID. https://sid.ir/paper/257317/en

Vancouver: Copy

Aminikhah Hossein, Alavi Seyyed Javad. A new approach to using the cubic B-spline functions to solve the Black-Scholes equation. JOURNAL OF NEW RESEARCHES IN MATHEMATICS[Internet]. 2019;5(18 ):71-80. Available from: https://sid.ir/paper/257317/en

IEEE: Copy

Hossein Aminikhah, and Seyyed Javad Alavi, “A new approach to using the cubic B-spline functions to solve the Black-Scholes equation,” JOURNAL OF NEW RESEARCHES IN MATHEMATICS, vol. 5, no. 18 , pp. 71–80, 2019, [Online]. Available: https://sid.ir/paper/257317/en

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