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

Full Text (PDF, 674KB), PP.48-55

##### Author(s)

1. Department of Mathematics, University of Science and Culture, Tehran, Iran

* Corresponding author.

Received: 11 Sep. 2015 / Revised: 20 Dec. 2015 / Accepted: 1 Feb. 2016 / Published: 8 Jun. 2016

##### Index Terms

Stochastic Differential Equations, Euler-Maruyama method, Asset pricing model, Square-Root asset pricing model

##### Abstract

The purpose of this paper is to survey stochastic differential equations and Euler-Maruyama method for approximating the solution to these equations in financial problems. 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 explicit 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 simulation 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 discuss how to find the approximated solutions to stochastic differential equations for financial problems with examples.

##### Cite This Paper

Hamid Reza Erfanian, Mahshid Hajimohammadi, Mohammad Javad Abdi, "Using the Euler-Maruyama Method for Finding a Solution to Stochastic Financial Problems", International Journal of Intelligent Systems and Applications (IJISA), Vol.8, No.6, pp.48-55, 2016. DOI:10.5815/ijisa.2016.06.06

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