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

Subject Areas : Statistics

Hossein Aminikhah ¹ , Seyyed Javad Alavi ²

1 - Associate Professor, Department of Applied Mathematics and Computer Science, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.
2 - PhD student, Department of Applied Mathematics, Faculty of Mathematical Sciences, University of Guilan, Rasht, Iran.

Received: 2017-08-05 Accepted : 2019-04-07 Published : 2019-05-01

Keywords: توابع بی-اسپلاین&rlm, , اختیار معامله اروپایی و آمریکایی, معادله بلک-شولز, همگرایی, پایداری, طرح تفاضلی,

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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