| A new finite difference/spectral method for numerical solution of the Black--Scholes equation for European put options |
| کد مقاله : 1083-FEMATH6 |
| نویسندگان |
|
یونس طالعی * دانشگاه تبریز -فارغ التحصیل
دانشگاه محقق اردبیلی- حق التدریس در حال حاضر |
| چکیده مقاله |
| The Black--Scholes equation was proposed by Fisher Black and Myron Scholes in 1973 to express the behavior of the option price in the European style market. It is regarded as one of the best ways of determining fair prices of options. The main purpose of this paper is to invetigate a new numerical method based on backward finite difference method and spectral Galerkin method for solving Black--Scholes equation for European put option. In this paper, by discretization in time for the Black-scholes equation we get the ordinary system of differential equations (ODEs) in the spatial domain. The obtained ODEs is solved by applying the spectral galerkin method based on the generalized Jacobi polynomials. Therefore, the problem is reduce to the solution of a system of algebraic equations. The convergence of the method in suitable spaces of functions, equipped with the weighted $L^2$- norm is discussed. Also, we provide numerical experiment to show the accuracy of method. |
| کلیدواژه ها |
| Black--Scholes equation, Generalized Jacobi polynomials, Backward-difference method, Convergence analysis |
| وضعیت: پذیرفته شده برای ارائه شفاهی |