Numerical solution of fractional black-scholes equation by using the multivariate pade approximation

Abstract

In this study, a new application of multivariate Pade approximation method has been used for solving European vanilla call option pricing problem. Pade polynomials have occurred for the fractional Black-Scholes equation, according to the relations of "smaller than", or "greater than", between stock price and exercise price of the option. Using these polynomials, we have applied the multivariate Pade approximation method to our fractional equation and we have calculated numerical solutions of fractional Black-Scholes equation for both of two situations. The obtained results show that the multivariate Pade approximation is a very quick and accurate method for fractional Black-Scholes equation. The fractional derivative is understood in the Caputo sense.