Asian Journal of Economics, Finance and Management

This study presents an analytical investigation of capital market volatility and its implications for investment decision-making using a Frobenius-based solution framework. The classical Black-Scholes partial differential equation is transformed into a nonlinear ordinary differential equation through an appropriate variable substitution, with stock volatility (θ) incorporated as a key model parameter. The Frobenius method is then applied to obtain convergent series solutions for equilibrium asset prices, thereby enabling an examination of financial-variable behaviour under stochastic conditions. The study further evaluates the influence of volatility, stock-price levels and growth dynamics on equilibrium pricing, marginal rates of change and the acceleration of price adjustments. Numerical simulations, supported by tables and MATLAB-based graphical analyses from selected parameter values, show that increases in volatility amplify equilibrium asset values and strengthen market responsiveness, while also increasing nonlinear effects and price instability. The results indicate increasing marginal returns and accelerated price dynamics in highly volatile markets. The model provides an analytical framework for examining complex financial systems and offers insights into asset valuation and risk assessment. The findings contribute to mathematical finance by extending the traditional Black-Scholes modelling framework through a series-based solution, with practical relevance for investors and policymakers operating in volatile capital-market environments.