| Matrix forms of the Black-Scholes equation with boundary conditions |
| کد مقاله : 1082-SLAA10 |
| نویسندگان |
|
مهدی رضوی *1، عباس سالمی پاریزی2، محمد مهدی حسینی3 1دانشگاه شهید با هنر کرمان 2ریاضی محض، ریاضی و کامپیوتر، شهید باهنر کرمان، کرمان، ایران 3بخش ریاضی کاربردی - دانشگاه شهید باهنر کرمان - کرمان - ایران |
| چکیده مقاله |
| In mathematical finance, the Black-Scholes equation is a backward parabolic partial differential equation finding the price evolution of a European call/put options. There are numerous numerical and analytical methods to solve Black-Scholes equation, but most of these methods have computational complexity and so far these methods couldn’t present a general form to solve the Black-Scholes equation. In this paper by using the spectral method and special linear operators, we obtain matrix form of the Black-Scholes equation and matrix form of boundary conditions. Moreover, by using these matrix forms, we present a linear system of equations which approximate the solutions of the Black-Scholes equation. |
| کلیدواژه ها |
| Black-Scholes equation, Finance mathematic, Spectral methods, Chebyshev polynomials. |
| وضعیت: پذیرفته شده مشروط برای ارائه شفاهی |