The Analytical Examination of the Impacts of Time – Varying Parameters on Call Option Prices for Capital Market Using Black-Scholes Model

This study adopted the Black-Scholes option pricing framework as a comparative benchmark to capture forward-looking market expectations of bank risk while recognizing its backward-looking nature of accounting-based performance measures. The effects of variables whose values change over time were examined using the Black -Scholes framework as a benchmark pricing model to compare the market-implied risk and valuation of two banks; First City Monument Bank (FCMB) and Stanbic Investment Banking & Trust Company (IBTC) Bank across two years; 2019 and 2025. Daily opening and closing share prices of these two banks were obtained from Market Screener Website; spanning from 2019 to 2025. Visual inspection of the time plot in Fig. 1 showed that FCMB's shares exhibited no strong long – upward or downward trend. The share prices appeared relatively stable and rose up towards the end of 2025. The stability implied that the shares entered a phase of price consolidation. The 2025-time plot of STANBIC IBTC (Fig. 2) started the year at a relatively low level and increased steadily, indicating general upward movement and improved market valuation. The mean daily returns for these two banks were calculated alongside their annual volatilities for 2019 and 2025. The result revealed that FCMB outperformed Stanbic IBTC in 2019 due to its positive average return (0.00067) with a 53% annual volatility indicating a high but investors were compensated with higher returns while Stanbic IBTC recorded a negative average return (-0.0004098) indicating a decline in bank share price despite a lower volatility of 43% compared to FCMB. By the year 2025, Stanbic IBTC showed a superior performance achieving a higher average return (0.002428) with a lower volatility of 41%, indicating improved efficiency and stronger risk-adjusted performance. FCMB on the other hand had a lower but positive average daily return (0.0008) with a higher volatility of 43% indicating stability but not accompanied with much return. The Black-Scholes model provided a theoretical benchmark against which observed prices or risk measures were compared.