Effect of Varying StepSizes in Numerical Approximation of Stochastic Differential Equations Using One Step Milstein Method
Applied and Computational Mathematics
Volume 4, Issue 5, October 2015, Pages: 351-362
Received: Aug. 13, 2015; Accepted: Aug. 28, 2015; Published: Sep. 9, 2015
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Authors
Sunday Jacob Kayode, Department of Mathematical Sciences, Federal University of Technology, Akure, Nigeria
Akeem Adebayo Ganiyu, Mathematics Department, Adeyemi College of Education, Ondo, Nigeria
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Abstract
This paper examines the effect of varying stepsizes in finding the approximate solution of stochastic differential equations (SDEs). One step Milstein method (MLSTM) for solution of general first order stochastic differential equations (SDEs) has been derived using Itô Lemma and Euler-Maruyama Method as supporting tools. Two problems in the form of first order SDEs have been considered. The method of solution used is one step Milstein method. The absolute errors were calculated using the exact solution and numerical solution. Comparison of varying the stepsizes was achieved using mean absolute error criterion. The results showed that the mean absolute error due to approximation decreases as the stepsizes decreases. The order of convergence is approximately 1, which indicates the accuracy of the method. Also, the effect of varying stepsizes can also be identified using graphical method constructed for various stepsizes.
Keywords
Stochastic Differential Equations, Itô Lemma, Euler-Maruyama Method, Milstein Method, Wiener Process, Wiener Increment, Black Scholes Option Price Model, StepSizes
To cite this article
Sunday Jacob Kayode, Akeem Adebayo Ganiyu, Effect of Varying StepSizes in Numerical Approximation of Stochastic Differential Equations Using One Step Milstein Method, Applied and Computational Mathematics. Vol. 4, No. 5, 2015, pp. 351-362. doi: 10.11648/j.acm.20150405.14
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