The Nexus Between Black-Scholes-Merton Option Pricing and Risk: A Case of Ghana Stock Exchange
DOI:
https://doi.org/10.14738/abr.105.12350Keywords:
Option Pricing, Black-Scholes-Merton Model, Volatility, Ghana Stock ExchangeAbstract
Even though option pricing and its market activities are not new, in Ghana the idea of trading options is yet to be realized. One popular method in pricing options is known as Black-Scholes-Merton option pricing model. Even though option pricing activities are not currently happening on the Ghana Stock Exchange, authors looked at the possibilities and preparedness of the GES to start trading such financial instrument. The main objective of this study therefore was to know how Black-Scholes-Merton model could be used to help in appropriate option value and undertake a risk assessment of stocks on the exchange. This study basically used the black-Scholes formula in calculating the call and put option prices for 28 companies listed GES. The results showed that the price of call option for 18 out of 28 listed stocks showed a value of zero. Again, only seven (7) companies had a value for both call and put options. This means stocks of 21 companies cannot be an underlying asset for trading financial derivatives. Reason for this performance of stock is due to low volatility. The study recommends that policies to increase volatility on the stock market should be put in place in other to make option pricing possible.
References
Antwi, O., & Oduro, F. T. (2018). Pricing Options on Ghanaian Stocks Using Black-Scholes Model. Science Journal of Applied Mathematics and Statistics, 6(1), 16.
Akrami, M. H., & Erjaee, G. H. (2015). Examples of analytical solutions by means of Mittag-Leffler function of fractional Black-Scholes option pricing equation. Fractional Calculus and Applied Analysis, 18(1), 38-47.
Alòs, E. (2012), A decomposition formula for option prices in the Heston model and applications to option pricing approximation. Finance and Stochastic, 16(3), 403-422.
Benninga, S., & Wiener, Z. (1997), The binomial option pricing model, Mathematica in Education and Research, 6, 27-34.
Burkovska, O., Haasdonk, B., Salomon, J., & Wohlmuth, B. (2015). Reduced basis methods for pricing options with the Black--Scholes and Heston models. SIAM Journal on Financial Mathematics, 6(1), 685-712.
Chesney, M., & Scott, L. (1989). Pricing European currency options: A comparison of the modified Black-Scholes model and a random variance model. Journal of Financial and Quantitative Analysis, 24(3), 267-284
Contreras, M., Pellicer, R., Villena, M., & Ruiz, A. (2010). A quantum model of option pricing: When Black–Scholes meets Schrödinger and its semi-classical limit. Physica A: Statistical Mechanics and its Applications, 389(23), 5447-5459
Cox, J. C., Ross, S. A., & Rubinstein, M. (1979), Option pricing: A simplified approach. Journal of financial Economics, 7(3), 229-263
Cedric Achille, M. M., Lamon, R., Sofiane, S., Max, M., Nontle, K., Yannis, A., & Bleming, N. (2013), Guidebook on African Commodity and Derivatives Exchanges. African Development Bank Group
Du Plooy, R., & Venter, P. J. (2021), Pricing vanilla options using artificial neural networks: Application to the South African market. Cogent Economics & Finance, 9(1), 1914285
Duan, J. C. (1995), The GARCH option pricing model. Mathematical finance, 5(1), 13-32
David W. (2020), Ghana Stock Exchange targets futures and options, Dual London listings to Deepen Market, The African Report
Flint, E., & Maré, E. (2017), Fractional Black–Scholes option pricing, volatility calibration and implied Hurst exponents in South African context, South African journal of economic and management sciences, 20(1), 1-11
Ghandehari, M. A. M., & Ranjbar, M. (2014), European option pricing of fractional Black-Scholes model with new Lagrange multipliers. Computational Methods for Differential Equations, 2(1), 1-10.
Hull, J. C. (2015). Options, futures and other derivatives Nineth Edition, Pearson Education, Inc
Holman, G., Van Breda, R., & Correia, C. (2011). The use of the Merton model to quantify the default probabilities of the top 42 non-financial South African firms. African Finance Journal, 13(si-1), 1-33.
Ivancevic, V. G. (2010), Adaptive-wave alternative for the Black-scholes option pricing model. Cognitive Computation, 2(1), 17-30.
Jena, R. M., & Chakraverty, S. (2019). A new iterative method based solution for fractional Black–Scholes option pricing equations (BSOPE). SN Applied Sciences, 1(1), 1-11.
Jordaan, F. Y., & Van Rooyen, J. H. (2010). An investigation into the reasons for the pricing differences betweeen a warrant and an option on the same stock in the South African derivatives market.
Kleinert, H., & Korbel, J. (2016). Option pricing beyond Black–Scholes based on double-fractional diffusion. Physica A: Statistical Mechanics and its Applications, 449, 200-214.
Kumar, S., Yildirim, A., Khan, Y., Jafari, H., Sayevand, K., & Wei, L. (2012), Analytical solution of fractional Black-Scholes European option pricing equation by using Laplace transform, Journal of fractional calculus and Applications, 2(8), 1-9
Lee, C. F., Tzeng, G. H., & Wang, S. Y. (2005). A new application of fuzzy set theory to the Black–Scholes option pricing model. Expert Systems with Applications, 29(2), 330-342.
Mpapalika, J. (2019). Alternative Financing Instruments for African Economies. Journal of Mathematical Finance, 10(1), 42-57
MacBeth, J. D., & Merville, L. J. (1979). An empirical examination of the Black-Scholes call option pricing model. The journal of finance, 34(5), 1173-1186.
Merton, R. C., & Scholes, M. S. (2013). Fischer Black. Annu. Rev. Financ. Econ., 5(1), 9-19.
Merton, R. C., & Scholes, M. S. (1995). Fischer Black. The Journal of Finance, 50(5), 1359-1370.
Mitra, S. K. (2012). An option pricing model that combines neural network approach and Black Scholes formula. Global Journal of Computer Science and Technology.
Okaro, C. S. O., Okeke, C. K., & Uzondu, C. S. (2018). Efficiency of the black-scholes option pricing model in the pricing of palm-oil futures in Nigeria’s Physical Market. International Journal of Academic Management Science, 2(9), 83-92.
Rouah, F. D. (2013), The Heston model and its extensions in Matlab and C. John Wiley & Sons.
Rubinstein, M. (2000), On the relation between binomial and trinomial option pricing models. The Journal of derivatives, 8(2), 47-50.
Song, L., & Wang, W. (2013), Solution of the fractional Black-Scholes option pricing model by finite difference method. In Abstract and applied analysis (Vol. 2013). Hindawi.
Venter, P. J., & Maré, E. (2020). GARCH option pricing models in a South African equity context. ORiON, 36(1), 1-17.
Wall Street Journal (2021), https://www.wsj.com/market-data?mod=nav_top_subsection
Weber, E. J. (2009), A short history of derivative security markets. In Vinzenz Bronzin’s option pricing models (pp. 431-466). Springer, Berlin, Heidelberg.
Yavuz, M., & Özdemir, N. (2018). A different approach to the European option pricing model with new fractional operator. Mathematical Modelling of Natural Phenomena, 13(1), 12.
Downloads
Published
How to Cite
Issue
Section
License
Copyright (c) 2022 Joseph Antwi Baafi
This work is licensed under a Creative Commons Attribution 4.0 International License.
