Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange

Osei Antwi

doi:doi:10.11648/j.ijssam.20170206.12

| Peer-Reviewed

Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange

Osei Antwi

Published in International Journal of Systems Science and Applied Mathematics (Volume 2, Issue 6)

Received: 12 September 2017 Accepted: 27 September 2017 Published: 14 November 2017

Views: Downloads:

Download PDF

Share This Article

Twitter
Linked In
Facebook

Abstract

This paper analyzes stock price behaviour on Ghana Stock Exchange (GSE) and develops a stochastic model to predict the behaviour of stock prices on the exchange using Monte Carlo simulations. The first part looks at the various justifications and models that have been put forward to explain stock behaviour and its distribution elsewhere. It traces the foundations of the use of stochastic process as a means of predicting stock price behaviour from Louis Bachelier normality assumption to the works of Samuelson’s lognormal supposition through to the doctoral thesis of Fama French in which he premised the behaviour of stock price to the idea of a random walk. We subsequently apply the Geometric Brownian Motion formulation to simulate stock price behaviour for all listed stocks on the GSE for the coming year (2015) using historical volatility and mean returns of the previous year (2014). The results find increasing evidence that the stochastic model consistently predict the stock price behaviour on the exchange in more than 80% of the listed stocks.

Published in	International Journal of Systems Science and Applied Mathematics (Volume 2, Issue 6)
DOI	10.11648/j.ijssam.20170206.12
Page(s)	116-125
Creative Commons	This is an Open Access article, distributed under the terms of the Creative Commons Attribution 4.0 International License (http://creativecommons.org/licenses/by/4.0/), which permits unrestricted use, distribution and reproduction in any medium or format, provided the original work is properly cited.
Copyright	Copyright © The Author(s), 2017. Published by Science Publishing Group

Keywords

Stock Price, Geometric Brownian Motion, Stock return, Stock Volatility, Monte Carlo Simulation

References

[1]	Brown, R. (1828), A brief account of microscopical observations made on the particles contained in the pollen of plants, London and Edinburgh philosophical magazine and journal of science, 4, 161-173.
[2]	A. Einstein, (1905), On the movement of small particles suspended in stationary liquids required by the molecular-kinetic theory of heat, Annalen der Physik, 17, 549-560.
[3]	N. Wiener, (1921), The average of an analytic functional and the Brownian movement, Proc. Natl. Acad. Sci. USA 7, 294–298.
[4]	Bachelier, L. (1900), The´orie de la spe´culation, Annales Scientifiques de l’E´cole Normale Supe´rieure Se´r., 3(17), 21–86.
[5]	Kendall, M. G. (1953), The analysis of economic time-series. Part I: Prices. Journal of the Royal Statistical Society 116, 11-25.
[6]	Roberts, H. V. (1959), Stock-market patterns and financial analysis: methodological suggestions. Journal of Finance, 14. 1, 1-10.
[7]	Samuelson, P. A. (1965), Proof that properly anticipated prices fluctuate randomly, Industrial Management Review, 6(2), 41–49.
[8]	Fama, E. F. (1965), The behavior of stock-market prices. Journal of Business 38.1, 34-105.
[9]	Fama, E. F. (1970), Efficient Capital Markets: A review of theory and empirical work. Journal of Finance, 25. 2, 383-417.
[10]	Cootner, P. H. (1962), Stock prices: random vs. systematic changes. Industrial Management Review 3. 2, 24-45.
[11]	Beja, A. (1977), The limits of price information in market processes, Working paper 61, University of California, Berkeley, Berkeley.
[12]	Grossman, S. J., Stiglitz J. E. (1980), The impossibility of informationally efficient markets. American Economic Review, 70. 3, 393-407.
[13]	Summers, L. H. (1986), Does the stock market rationally reflect fundamental values? The Journal of Finance, 41(3), 591–601.
[14]	French, K. R. and Roll, R. (1986), Stock return variances: The arrival of information and the reaction of traders, Journal of Financial Economics 17(1), 5–26.
[15]	Lo and MacKinlay (1988), Stock market do not follow random walks: evidence from a simple specification test, the review of financial studies, Vol 1. No. 1 (spring 1988) 41-66.
[16]	Poterba and Summers, (1988), Mean reversion in stock prices, Journal of Financial Economics, Vol. 22, 27-59.
[17]	Harvey, S. K. et al., (2008), Effect of exchange rate volatility on the Ghana Stock Exchange, African Journal of Accounting, Economics, Finance and Banking Research. 3(3): 28 – 47.
[18]	Antwi S. et al., (2012), An empirical analysis of the performance of the Ghana stock exchange and treasury bills, International Journal of Business and Social Science Vol. 3 No. 23.
[19]	Osei V, (2005), Does the stock market matter in Ghana? A Granger-Causality Analysis (Research Dept.) Bank of Ghana.
[20]	Mantas Landauskas, (2011), Modelling of stock prices by the Markov chain Monte Carlo method, Intellectual Economics., Vol. 5, no. 2(10), 244–256.
[21]	Yoon, Y., Swales, G., (1991), Predicting stock price performance: A neural network approach. In: Proceedings of the 24th Hawaii International Conference on System Sciences., 4, 156–162.
[22]	Refenes, A. N., Zapranis, A., Francis, G., (1994). Stock performance modeling using neural networks: A comparative study with regression models. Neural Networks, 7 (2), 375–388.
[23]	Kryzanowski, L., Galler, M., Wright, D. W., (1993), Using artificial neural networks to pick stocks. Financial Analysts Journal, 21–27.
[24]	Azoff, E. M., (1994), Neural Network Time Series Forecasting of Financial Markets. John Wiley and Sons, Chichester.
[25]	Neenwi, S., Asagba, P. O., L. G. Kabari., (2013), Predicting the Nigerian stock market using artificial neural network European journal of computer science and information Vol. 1 No. 1, 30-39.
[26]	Rene D. Estember, Michael John R. Maraña (2016), Forecasting of stock prices using brownian motion –Monte Carlo Simulation, Proceedings of the 2016 International Conference on Industrial Engineering and Operations Management Kuala Lumpur, Malaysia,
[27]	Introduction to Stochastic Calculus with Applications (2005), Second Edition, Fima C. Klebener, Imperial College Press, 57 Shelton Street, Covent Garden, London WC2H 9HE.
[28]	Walter A. Rosenkrantz, (2003), Why stock prices have a lognormal distribution, Department of Mathematics and Statistics, University of Massachusetts at Amhers.
[29]	Hull John. C., (2006), Option, Futures and Other Derivatives, 6^th edition, Pearson Education Inc. Prentice Hall, Upper Sale River, New Jersey, 263-312.

Cite This Article

Plain Text BibTeX RIS

APA Style

Osei Antwi. (2017). Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange. International Journal of Systems Science and Applied Mathematics, 2(6), 116-125. https://doi.org/10.11648/j.ijssam.20170206.12

Copy | Download

ACS Style

Osei Antwi. Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange. Int. J. Syst. Sci. Appl. Math. 2017, 2(6), 116-125. doi: 10.11648/j.ijssam.20170206.12

Copy | Download

AMA Style

Osei Antwi. Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange. Int J Syst Sci Appl Math. 2017;2(6):116-125. doi: 10.11648/j.ijssam.20170206.12

Copy | Download

@article{10.11648/j.ijssam.20170206.12,
  author = {Osei Antwi},
  title = {Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {116-125},
  doi = {10.11648/j.ijssam.20170206.12},
  url = {https://doi.org/10.11648/j.ijssam.20170206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20170206.12},
  abstract = {This paper analyzes stock price behaviour on Ghana Stock Exchange (GSE) and develops a stochastic model to predict the behaviour of stock prices on the exchange using Monte Carlo simulations. The first part looks at the various justifications and models that have been put forward to explain stock behaviour and its distribution elsewhere. It traces the foundations of the use of stochastic process as a means of predicting stock price behaviour from Louis Bachelier normality assumption to the works of Samuelson’s lognormal supposition through to the doctoral thesis of Fama French in which he premised the behaviour of stock price to the idea of a random walk. We subsequently apply the Geometric Brownian Motion formulation to simulate stock price behaviour for all listed stocks on the GSE for the coming year (2015) using historical volatility and mean returns of the previous year (2014). The results find increasing evidence that the stochastic model consistently predict the stock price behaviour on the exchange in more than 80% of the listed stocks.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange
AU  - Osei Antwi
Y1  - 2017/11/14
PY  - 2017
N1  - https://doi.org/10.11648/j.ijssam.20170206.12
DO  - 10.11648/j.ijssam.20170206.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 116
EP  - 125
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20170206.12
AB  - This paper analyzes stock price behaviour on Ghana Stock Exchange (GSE) and develops a stochastic model to predict the behaviour of stock prices on the exchange using Monte Carlo simulations. The first part looks at the various justifications and models that have been put forward to explain stock behaviour and its distribution elsewhere. It traces the foundations of the use of stochastic process as a means of predicting stock price behaviour from Louis Bachelier normality assumption to the works of Samuelson’s lognormal supposition through to the doctoral thesis of Fama French in which he premised the behaviour of stock price to the idea of a random walk. We subsequently apply the Geometric Brownian Motion formulation to simulate stock price behaviour for all listed stocks on the GSE for the coming year (2015) using historical volatility and mean returns of the previous year (2014). The results find increasing evidence that the stochastic model consistently predict the stock price behaviour on the exchange in more than 80% of the listed stocks.
VL  - 2
IS  - 6
ER  -

Copy | Download

Author Information

Osei Antwi

Mathematics & Statistics Department, Accra Technical University, Accra, Ghana

Download PDF

Sections

Plain Text BibTeX RIS

APA Style

Osei Antwi. (2017). Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange. International Journal of Systems Science and Applied Mathematics, 2(6), 116-125. https://doi.org/10.11648/j.ijssam.20170206.12

Copy | Download

ACS Style

Osei Antwi. Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange. Int. J. Syst. Sci. Appl. Math. 2017, 2(6), 116-125. doi: 10.11648/j.ijssam.20170206.12

Copy | Download

AMA Style

Osei Antwi. Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange. Int J Syst Sci Appl Math. 2017;2(6):116-125. doi: 10.11648/j.ijssam.20170206.12

Copy | Download

@article{10.11648/j.ijssam.20170206.12,
  author = {Osei Antwi},
  title = {Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange},
  journal = {International Journal of Systems Science and Applied Mathematics},
  volume = {2},
  number = {6},
  pages = {116-125},
  doi = {10.11648/j.ijssam.20170206.12},
  url = {https://doi.org/10.11648/j.ijssam.20170206.12},
  eprint = {https://article.sciencepublishinggroup.com/pdf/10.11648.j.ijssam.20170206.12},
  abstract = {This paper analyzes stock price behaviour on Ghana Stock Exchange (GSE) and develops a stochastic model to predict the behaviour of stock prices on the exchange using Monte Carlo simulations. The first part looks at the various justifications and models that have been put forward to explain stock behaviour and its distribution elsewhere. It traces the foundations of the use of stochastic process as a means of predicting stock price behaviour from Louis Bachelier normality assumption to the works of Samuelson’s lognormal supposition through to the doctoral thesis of Fama French in which he premised the behaviour of stock price to the idea of a random walk. We subsequently apply the Geometric Brownian Motion formulation to simulate stock price behaviour for all listed stocks on the GSE for the coming year (2015) using historical volatility and mean returns of the previous year (2014). The results find increasing evidence that the stochastic model consistently predict the stock price behaviour on the exchange in more than 80% of the listed stocks.},
 year = {2017}
}

Copy | Download

TY  - JOUR
T1  - Stochastic Modeling of Stock Price Behavior on Ghana Stock Exchange
AU  - Osei Antwi
Y1  - 2017/11/14
PY  - 2017
N1  - https://doi.org/10.11648/j.ijssam.20170206.12
DO  - 10.11648/j.ijssam.20170206.12
T2  - International Journal of Systems Science and Applied Mathematics
JF  - International Journal of Systems Science and Applied Mathematics
JO  - International Journal of Systems Science and Applied Mathematics
SP  - 116
EP  - 125
PB  - Science Publishing Group
SN  - 2575-5803
UR  - https://doi.org/10.11648/j.ijssam.20170206.12
AB  - This paper analyzes stock price behaviour on Ghana Stock Exchange (GSE) and develops a stochastic model to predict the behaviour of stock prices on the exchange using Monte Carlo simulations. The first part looks at the various justifications and models that have been put forward to explain stock behaviour and its distribution elsewhere. It traces the foundations of the use of stochastic process as a means of predicting stock price behaviour from Louis Bachelier normality assumption to the works of Samuelson’s lognormal supposition through to the doctoral thesis of Fama French in which he premised the behaviour of stock price to the idea of a random walk. We subsequently apply the Geometric Brownian Motion formulation to simulate stock price behaviour for all listed stocks on the GSE for the coming year (2015) using historical volatility and mean returns of the previous year (2014). The results find increasing evidence that the stochastic model consistently predict the stock price behaviour on the exchange in more than 80% of the listed stocks.
VL  - 2
IS  - 6
ER  -

Copy | Download