Science Journal of Applied Mathematics and Statistics

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Pricing Options on Ghanaian Stocks Using Black-Scholes Model

Received: 13 September 2017    Accepted: 30 September 2017    Published: 01 February 2018
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Abstract

We present a succinct new approach to derive the Black-Scholes partial differential equation and subsequently the Black-Scholes formula. We proceed to use the formula to price options using stocks listed on Ghana stock exchange as underlying assets. From one year historical stock prices we obtain volatilities of the listed stocks which are subsequently used to compute prices of three month European call option. The results indicate that it is possible to use the Black Scholes formula to price options on the stocks listed on exchange. However, it was realised that most call option prices tend to zero either due to very low volatilities or very low stock prices. On the other hand put options were found to give positive prices even for stocks with very low volatilities or low stock prices.

DOI 10.11648/j.sjams.20180601.13
Published in Science Journal of Applied Mathematics and Statistics (Volume 6, Issue 1, February 2018)
Page(s) 16-27
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), 2024. Published by Science Publishing Group

Keywords

Option Price, Volatility, Stochastic Process, Brownian Motion, Geometric Brownian Motion, Black-Scholes Formula

References
[1] Bachelier, L. (1900), Theόrie de la spéculation, Annales Scientifiques de l’E´cole Normale Supe´rieure Se´r. 3(17), pp.21–86.
[2] Kendall, M. G. (1953), The Analysis of Economic Time-Series. Part I: Prices. Journal of the Royal Statistical Society pp.116, pp11-25.
[3] Roberts, H. V. (1959) Stock-Market Patterns and Financial Analysis: Methodological Suggestions, Journal of Finance 14, 1, pp.1-10.
[4] Osborne, M. F. M. (1959), Brownian motion in the stock market, Operations Research 7(2), pp145–73.
[5] Sprenkle C. (1964), Warrant Prices as indicator of expectation, Yale Economic Essays, 1 pp.412-74.
[6] Boness A. J., (1964), Elements of a theory of stock-option value, The Journal of Political Economy, 72, pp.163–175.
[7] Samuelson, P. A. (1965), Proof that properly anticipated prices fluctuate randomly, Industrial Management Review 6(2), pp.41–49.
[8] Black, F., Scholes, M., (1973). The Pricing of Options and Corporate Liabilities, Journal of Political Economics 81, pp.637–659.
[9] Merton, R., (1973), Rational Theory of Option Pricing, Bell Journal of Economics and Management Science 4, pp.141–183.
[10] Cox, J., Ross, S. & Rubinstein, M. (1979). Option Pricing: A Simplified Approach, Journal of Financial Economics 7: pp.229–263.
[11] Bally, V., L. Caramellino, and A. Zanette (2005). Pricing and Hedging American Options by Monte Carlo Methods using a Malliavin Calculus Approach, Monte Carlo Methods and Applications, 11, pp.97-133.
[12] Egloff, D. (2005), Monte Carlo Algorithms for Optimal Stopping and Statistical Learning. The Annals of Applied Probability, 15, 2 pp.1396-1432.
[13] Manuel Moreno and Javier F. Navas, (2003), On the robustness of least-squares Monte Carlo (LSM) for pricing American Derivatives, Review of Derivatives Research, 6(2): pp.107–128.
[14] Dagpunar, J. S., (2007), Simulation and Monte Carlo. John Wiley & Sons Ltd., Chichester West Sussex.
[15] Mehrdoust, F., S. Babaei & S. Fallah, (2017), Efficient Monte Carlo option pricing under CEV model Communications in Statistics, Vol. 46, Iss. 3.
[16] Fabio Bellini (2011) The Black-Scholes Model, Department of Statistics and Quantitative Methods, Via Bicocca degli Arcimboldi 8, 20126 Milano.
[17] Fima C. Klebener, (2005). Introduction to Stochastic Calculus with Applications, Second Edition, Imperial College Press, 57 Shelton Street, Covent Garden, London WC2H 9HE.
[18] Hull John. C., (2006), Option, Futures and Other Derivatives, 6th edition, Pearson Education Inc. Prentice Hall, Upper Sale River, New Jersey, pp.263-312.
Author Information
  • Mathematics & Statistics Department, Accra Technical University, Accra, Ghana

  • Department of Mathematics, Faculty of Physical and Computational Science, College of Science, Kwame Nkrumah University of Science & Technology, Kumasi, Ghana

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    Osei Antwi, Francis Tabi Oduro. (2018). Pricing Options on Ghanaian Stocks Using Black-Scholes Model. Science Journal of Applied Mathematics and Statistics, 6(1), 16-27. https://doi.org/10.11648/j.sjams.20180601.13

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    ACS Style

    Osei Antwi; Francis Tabi Oduro. Pricing Options on Ghanaian Stocks Using Black-Scholes Model. Sci. J. Appl. Math. Stat. 2018, 6(1), 16-27. doi: 10.11648/j.sjams.20180601.13

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    AMA Style

    Osei Antwi, Francis Tabi Oduro. Pricing Options on Ghanaian Stocks Using Black-Scholes Model. Sci J Appl Math Stat. 2018;6(1):16-27. doi: 10.11648/j.sjams.20180601.13

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  • @article{10.11648/j.sjams.20180601.13,
      author = {Osei Antwi and Francis Tabi Oduro},
      title = {Pricing Options on Ghanaian Stocks Using Black-Scholes Model},
      journal = {Science Journal of Applied Mathematics and Statistics},
      volume = {6},
      number = {1},
      pages = {16-27},
      doi = {10.11648/j.sjams.20180601.13},
      url = {https://doi.org/10.11648/j.sjams.20180601.13},
      eprint = {https://download.sciencepg.com/pdf/10.11648.j.sjams.20180601.13},
      abstract = {We present a succinct new approach to derive the Black-Scholes partial differential equation and subsequently the Black-Scholes formula. We proceed to use the formula to price options using stocks listed on Ghana stock exchange as underlying assets. From one year historical stock prices we obtain volatilities of the listed stocks which are subsequently used to compute prices of three month European call option. The results indicate that it is possible to use the Black Scholes formula to price options on the stocks listed on exchange. However, it was realised that most call option prices tend to zero either due to very low volatilities or very low stock prices. On the other hand put options were found to give positive prices even for stocks with very low volatilities or low stock prices.},
     year = {2018}
    }
    

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    T1  - Pricing Options on Ghanaian Stocks Using Black-Scholes Model
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    AB  - We present a succinct new approach to derive the Black-Scholes partial differential equation and subsequently the Black-Scholes formula. We proceed to use the formula to price options using stocks listed on Ghana stock exchange as underlying assets. From one year historical stock prices we obtain volatilities of the listed stocks which are subsequently used to compute prices of three month European call option. The results indicate that it is possible to use the Black Scholes formula to price options on the stocks listed on exchange. However, it was realised that most call option prices tend to zero either due to very low volatilities or very low stock prices. On the other hand put options were found to give positive prices even for stocks with very low volatilities or low stock prices.
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