Using the Euler-Maruyama Method for Finding a Solution to Stochastic Financial Problems

The purpose of this paper is to survey stochastic differential equations and Euler-Maruyama method for approximating the solution to these equations in financial p roblems. It is not possible to get explicit solution and analytically answer for many of stochastic differential equations, but in the case of linear stochastic differential equations it may be possible to get an exp licit answer. We can approximate the solution with standard numerical methods, such as Euler-Maruyama method, Milstein method and Runge-Kutta method. We will use Euler-Maruyama method for simulat ion of stochastic differential equations for financial problems, such as asset pricing model, square-root asset pricing model, payoff for a European call option and estimating value of European call option and Asian option to buy the asset at the future time. We will d iscuss how to find the approximated solutions to stochastic differential equations for financial problems with examples . Index Iterms—Stochastic Differential Equations, EulerMaruyama method, Asset pricing model, Square-Root asset pricing model.