Stochastic Pricing of European Options Using the Black-scholes Model on the Analysis of Share Prices for Capital Markets

Financial instruments used in the capital market to finance long-term investments are stocks and shares, company bonds and government bonds. This involves the issue and market of shares, bonds and debentures using the services of brokers, dealers and underwriters. The capital market provides a means through which this is made possible. However, the paucity of long-term capital has posed the greatest challenge. This study is about option pricing and some of its dynamics in financial markets via valuation using the Black-Scholes (BS) model, as it explores the changes of option values as a function of security and time. The study is based on Stochastic Differential Equations and the Black-Scholes Model. The findings revealed that the Black-Scholes model of European options on the share price of Fidelity, Access and their future merged banks, which gave closed-form prices of Call and Put option prices with variations of maturity dates, average share prices, as well as their respective standard deviations affecting real-life changes for capital markets. From the share price analysis, the growth rates of each bank were considered, where Fidelity Bank had the largest growth rates, as this is informative to investors or management of the banks in terms of decision making. This paper offers a reflective consequence for future studies of option prices. However, the current study is on the European options case. Another study could be considered in the case of multiple options in one portfolio of investments.