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

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

Views: 0 Downloads: 0


Hamid Reza Erfanian 1,* Mahshid Hajimohammadi 1 Mohammad Javad Abdi 1

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


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


[1]Desmond J. Higham. An Algorithmic Introduction to Numerical Simulation of Stochastic Differential Equations. SIAM Rev. Volume 43, Issue 3, 2001, PP. 525-546.
[2]Timothy. Sauer. Numerical Solution of Stochastic Differential equations in finance. To appear, Handbook of Computational Finance, 2008, Springer.
[3]Matthew, Rajotte. Stochastic Differential Equations and Numerical Application. Virginia Commonwealth University. Theses and Dissertations. 2014.
[4]Peter E. Kloeden, Ekhard. Platen. A survey of numerical methods for stochastic differential equation, Stochastic Hydrology and Hydraulics. 1989, Springer.
[5]Alain C. Nsengiyumva. Numerical Simulation of Stochastic Differential Equations. Master’s thesis, Lappeenranta University of Technology. 2013.
[6]Bernt. Oksendal. Stochastic Differential Equations, 6th ed, Springer-Verlag. 2013.
[7]Mark. Richardson. Stochastic Differential Equations Case Study, 2009.
[8]Bernt. Oksendal. Stochastic Differential Equations. An Introduction with Applications. Book. Fifth ed, Corrected Printing. 2000, Springer-Verlag Heidelberg New York.
[9]Gilsing. Hagen. Shardlow, Tony. SDELab: stochastic differential equations with MATLAB. Manchester nstitute for Mathematical Science School of Mathematics. The University of Manchester. 2006.
[10]Chaminda H. Baduraliya, Xuerong Ma. The Euler–Maruyama approximation for the asset price in the mean-reverting-theta stochastic volatility model. 2012, ELSEVIER.
[11]Peter E. Kloeden, Ekhard. Numerical Solution of Stochastic Differential Equations. Book. 1995, Springer.
[12]Timothy. Sauer. Computational Solution of stochastic differential equations. Advanced Review, 2013, WIREs Comput Stat, 5:362-371.
[13]Sean. Fanning, Jay. parekh. Stochastic Processes and their Application to Mathematical Finance, 2004.
[14]Desmond J. Higham, Peter E. Kloeden.2002.MAPLE and MATLAB for stochastic differential equations in finance.
[15]John C. Hull. options, futures and other derivatives. Book.7th ed, 2008.
[16]Picchini. Umberto. Simulation and Estimation of Stochastic Differential Equations with MATLAB. SDE TOOLBOX. User’s Guide for version 1.4.1. 2007.