#TITLE_ALTERNATIVE# - BUDI NUGROHO (NIM 20106002), DIDIT
The Asian option is an option whose payoff depends on the average price of the underlying asset over certain time interval. When the Asian option is based on arithmetic average, with the asset price follows a geometric Brownian motion, up to now there is no explicit formula for Asian option pricing. The aim of this thesis is to investigate application of the finite element method (FEM) to problem of arithmetic averaging European-style Asian option pricing on non-dividend paying asset. It is considered arithmetic averaging Asian option as special case of an option on a traded account. Using risk neutral pricing theory, partial differential equation (PDE) for the price of Asian option is derived. The resulting PDE is two space dimension. Then, the PDE is reduced to a one space dimension PDE with applying the numeraire technique for easy to solve. In this article, in particular, we prove that maximum price for floating strike Asian call option is achieved at t = 0, while maximum price for floating strike Asian put option is achieved at same time t E (0, T), where T is expiry date of the option, for any asset price at t = 0. FEM is applied for solving variational formulation of PDE where space is approached by finite elements and time is proceeded by three finite difference scheme: explicit, implicit, and Crank-Nicolson. For the implementation of the finite element method, a type of finite elements: hat functions, is chosen. By applying the successive overrelaxation (SOR) iterative method with accurancy tolerance e = 10-s and relaxation factor w = 1.15, shown numerically that the FEM with explicit scheme is unconditionally stable. Using FEM, An accurate answer for option value can be obtained at some grid point UM) without an interpolation. It is shown that the FEM with Crank-Nicolson is a capable tool to compute the value of Asian options.