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.

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

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