A hybrid method for solution of the fractional black-scholes equation

In this thesis, the solution of fractional derivative Black-Scholes (BS) option pricing equation with Conformable Laplace Decomposition Method (CLAY) is given. Black-Scholes equation is an important mathematical equation of financial modeling. The aim of Black-Scholes equation is to create a portfolio consisting of option and option underlying asset and to make this portfolio insensitive to the market price of the underlying asset in small time intervals. Conformable Laplace decomposition method combines conformable Laplace transform with Adomian decomposition method. In our study, first of all, a general algorithm is given for solving Black-Scholes equation with conformable Laplace decomposition method. Then; the proposed algorithm is applied to two different examples, the obtained results are analyzed and interpreted with the help of graphics. From the obtained results, it is seen that Conformable Laplace decomposition method is a powerful, reliable and easy to use method for solving fractional derivative Black-Scholes equation.