ANALYSIS OF OPTION PRICING MECHANISMS IN FINANCIAL MARKETS USING THE BLACK-SCHOLES MODEL AND SNEDECOR’S F-DISTRIBUTION
Abstract
The success of any investment largely depends on the valuation of options, which plays a pivotal role in shaping the financial strategies of investors. The Black-Scholes (B-S) equation remains a foundational mathematical tool for estimating stock option prices. This study examines the Black-Scholes model for European call options alongside Snedecor’s F-distribution to evaluate option pricing on the share prices of Fidelity and Access Banks. Closed-form solutions for call option prices were obtained for two distinct expiration dates. The variation in call option prices between these dates provides valuable insights into the market's expectations regarding future movements of the underlying securities.
Additionally, hypothesis testing was conducted and accepted for both banks, revealing statistically significant differences in the variances of call option prices across expiration dates. The analysis yielded variances of 0.8954 for Fidelity Bank and 0.9746 for Access Bank, indicating that higher variance implies greater potential for price fluctuation over time. Hence, Fidelity Bank, with the lower variance, offers better precision for informed investment decisions.
Furthermore, a theoretical proposition was formulated and validated to analyze prospective price changes and support strategic decision-making. The study also considered the means and standard deviations of projected future prices, offering practical implications for understanding investment returns within capital markets.
Downloads
References
Udom, A. U. (2015). Elements of Applied Mathematical Statistics, Second Edition
Published by University of Nigeria press Limited.
Amadi, I. U., Nmerukini, A, Ogbogolgbo, P. C., Aboko, S. I and Udoye, A. (2024). The
Analysis of Black-Scholes of Option Pricing with Time-Varying Parameters on Share
Prices for Capital Market. An International Journal Applied Mathematics and Information
Sciences. 18 (3), 673 - 678.
Kwok, Y. K. (2008). Mathematical Models of Financial Derivatives. Springer-varlag, Singapore.
Hull, J.C. (2003). Options, Futures and other Derivatives, (5 Edition). Prentice Hall International, London.
Babasola, O. L., Irakoze, I., & Onoja, A. A. (2008). Valuation of European Options within the Black-Scholes Framework using the Hermite Polynomial. J Sci Eng Res, 5(2), 200-13.
Shin, B. and Kim, H. (2016). The Solution of Black-Scholes Terminal Value Problem by means of Laplace Transform. Global Journal of Pure and Applied Mathematics. Vol.12, pp.4153 - 4158.
Rodrigo, M. R., and R. S. Mamon (2006). An Alternative Approach to Solving the Black Scholes Equation with Time-Varying Parameters. Applied Math. Lett., 19: 398-402. DO1:10. 1016/j.aml.2005.06.012.
Osu, B. O. (2010). A Stochastic Model of the Variation of the Capital Market Price. International Journal of Trade, Economics and Finance, Vol.1, No.3), pp.297 - 302.
Nwobi, F. N., Annorzie, M. N. and Amadi, I. U. (2019). Crank-Nicolson Finite Difference Method in Valuation of Options. Communications in Mathematical Finance, Vol,8, No1, pp.93-122.
Nwobi, F. N., Amorzie M. N. and Amadi, I. U. (2019). The Impact of Crank-Nicolson Finite Difference Method in Valuation of Options. Communications in Mathematical Finance, Vol 8, No 1 2019, 93-122.
Bollerslev, T. (1986) Generalized Autoregressive Conditional Heteroskedasticity.
Journal of Econometrics, 31, 307-327. https://doi.org/10.1016/0304-
(86)90063-1.
Wu, Q. (2016). Stability of Stochastic Differential Equation with respect to Time – Changed
Brownian Motion. Tuffs University, Department of Mathematics, 503 Boston Avenue, Medford,
M.A. 02155, USA.
. Lai, C. H. (2019). Modification Terms to the Black–Scholes Model in a realistic
Hedging Strategy with Discrete Temporal Steps. International Journal of Computer
and Mathematics, 96(11), 2201-2208.
Amadi, I. U., Nmerukini, A., Ogbogolgbo, P.C., Aboko, S. I. and Udoye, A. (2024).
Analysis of Black – Scholes of Option Pricing with Time- Varying Parameters on Share
Prices for Capital Market. I8 (18), 673 – 678. Applied Mathematics and Information
Sciences An International Journal.
Yueng, L. T. (2012). Crank-Nicolson Scheme For Asian Option. M.Sc. Thesis Department of Mathematical and Actuarial Science, Faculty of Engineering and Science, University of Tunku Abdul Rahman.
. Azor,. P.A.(2021). Statistics for Universities and Colleges. Bestene Publishers Nigeria. Port Harcourt, Rivers State. ISBN: 978-49863-3-9.
The authors and co-authors warrant that the article is their original work, does not infringe any copyright, and has not been published elsewhere. By submitting the article to GPH - International Journal of Mathematics, the authors agree that the journal has the right to retract or remove the article in case of proven ethical misconduct.
