Numerical Solution of Black-scholes Equation Using Bernstein Multi-scaling Functions

Volume 15, Issue 4, pp 272-280 http://dx.doi.org/10.22436/jmcs.015.04.03

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Authors

M. Moradipour - Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran S. A. Yousefi - Department of Mathematics, Shahid Beheshti University, G.C., Tehran, Iran

Abstract

A numerical method for solving Black-Scholes equation is presented. The method is based upon Bernstein multi-scaling basis approximations. The properties of Bernstein multi-scaling functions are first presented. These properties together with the forward Euler and Ritz-Galerkin method are then utilized to reduce the Black-Scholes equation to the solution of algebraic equations. Illustrative example is included to demonstrate the validity and applicability of the new technique.

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ISRP Style

M. Moradipour, S. A. Yousefi, Numerical Solution of Black-scholes Equation Using Bernstein Multi-scaling Functions, Journal of Mathematics and Computer Science, 15 (2015), no. 4, 272-280

AMA Style

Moradipour M., Yousefi S. A., Numerical Solution of Black-scholes Equation Using Bernstein Multi-scaling Functions. J Math Comput SCI-JM. (2015); 15(4):272-280

Chicago/Turabian Style

Moradipour, M., Yousefi, S. A.. "Numerical Solution of Black-scholes Equation Using Bernstein Multi-scaling Functions." Journal of Mathematics and Computer Science, 15, no. 4 (2015): 272-280

Keywords

Bernstein polynomial
Bernstein multi-scaling functions
Black-Scholes equation
Euler method
Ritz-Galerkin method.

MSC

91G60
65N06
35Q91

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