In recent decades, fractional differential equations draw an increasing interest of a lot of researchers and has been becoming a popular research area, because its nonlocal property provides convenience in modelling physical phenomena, chemical reaction, biological phenomena, financial derivatives, and so on. In this thesis, some fractional differential equations and related optimization models governing different kinds of options pricing problems including barrier option, American option, multi-state American option and multi-asset European option, are considered. Several finite difference schemes are proposed to discretize the fractional differential equations and models with related stability, convergence and monotonicity analysis. Some preconditioned iterative methods with different preconditioners are proposed to solve the corresponding tempered fractional differential equation, HJB equation, linear complementary problem and two-dimensional fractional differential equation, respectively, with convergence analysis. In addition, a fast direction method is also considered to solve the tempered fractional differential equation with Ο(N log N)operation cost, where N is the matrix size. Numerical experiments and related options pricing examples are given to demonstrate the accuracy and efficiency of the proposed fast algorithms.