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Pricing European Put Option in a Geometric Brownian Motion Stochastic Volatility Model
Applied and Computational Mathematics
Volume 6, Issue 5, October 2017, Pages: 215-221
Received: Jun. 9, 2017; Accepted: Jun. 26, 2017; Published: Sep. 7, 2017
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Kolawole Imole Oluwakemi, School of Mathematical and Computer Sciences, Heriot-Watt University, Edinburgh, Scotland
Mataramvura Sure, Department of Mathematical Sciences, University of Cape Town, Cape Town, South Africa
Ogunlade Temitope Olu, Department of Mathematics, Ekiti State University, Ado-Ekiti, Nigeria
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Stochastic volatility models were introduced because option prices have been mis-priced using Black-Scholes model. In this work, focus is made on pricing European put option in a Geometric Brownian Motion (GBM) stochastic volatility model with uncorrelated stock and volatility. The option is priced using two numerical methods (Crank-Nicolson and Alternating Direction Implicit (ADI) finite difference). Numerical schemes were considered because the closed form solution to the model could not be obtained. The change in option value due to changes in volatility, maturity time and market price of volatility risk are considered and comparison between the efficiency of the numerical methods by computing the CPU time was made.
Geometric Brownian Motion (GBM), Alternating Direction Implicit (ADI) Scheme Crank Nicolson Scheme, Black-Scholes Model, European Put Option
To cite this article
Kolawole Imole Oluwakemi, Mataramvura Sure, Ogunlade Temitope Olu, Pricing European Put Option in a Geometric Brownian Motion Stochastic Volatility Model, Applied and Computational Mathematics. Vol. 6, No. 5, 2017, pp. 215-221. doi: 10.11648/j.acm.20170605.11
Copyright © 2017 Authors retain the copyright of this article.
This article is an open access article distributed under the Creative Commons Attribution License ( which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.
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