Using Bernstein and Legendre Multi-Scaling Functions and Ritz Galerkin method to solve Black-Scholes equation

A numerical method for solving Black-Scholes equation based on Bernstein and Legendre multi-scaling approximation is proposed. We convert the European option prices under Black-Scholes model to heat equation by using the change of variables. By considering these properties and applying the forward Euler and Ritz Galerkin method, Black-Scholes equation is reduced to algebraic equations. Finally, the obtained results of two polynomials are presented and the comparison shows that both approximations are acceptable and accurate.

Keywords:

Black-Scholes equation , Eropean option price , Bernstein polynomial , Legendre polynomial , Euler method , Ritz Galerkin method