Track: Graduate Student Paper Competition

Abstract

The Black-Scholes model became popular and almost universally accepted by option traders to estimate and assess option prices over time. Black-Scholes model involves several assumptions that must be fulfilled, so sometimes the Black-Scholes model is difficult to apply to real life under certain conditions because of these assumptions. Therefore, several models were developed to approach these assumptions, one of them is fractional Black-Scholes model. The model used in this paper is time-fractional Black-Scholes model. This paper begins with a brief description of the history of the Black-Scholes model then followed by an explanation of time-fractional Black-Scholes obtained from ordinary Black-Scholes models. The main points highlighted in this paper are the methods of solving the fractional Black-Scholes model. This paper aims to review the methods that have been successfully used in previous studies. Like Laplace Homotopy Perturbation Method (LHPM), fractional variational iteration method, Block-Pulse operational matrix method, Homo-Separation of Variables method, and several other methods. In reviewing these methods, this paper presents summary of the contexts that are worked out using these methods, conclusions and the efficiency of the methods, so that differences among the methods can be seen clearly.