Solution of time fractional Black-Scholes European option pricing equation arising in financial market

[摘要] In this paper, we present fractional differential transform method (FDTM) and modified fractional differential transform method (MFDTM) for the solution of time fractional Black-Scholes European option pricing equation. The method finds the solution without any discretization, transformation, or restrictive assumptions with the use of appropriate initial or boundary conditions. The efficiency and exactitude of the proposed methods are tested by means of three examples.

[关键词] Fractional Black-Scholes equation;Fractional differential transform method;Modified fractional differential transform method