Qualitative analysis of a nonlinear stock price model

摘要

Attention is focused on stock price models with no closed-form solution, the most likely occurrence, when realistic assumptions are made about the sources of dividends. It is argued that these models can supply valuable information for both financial analysis and financial management, provided that they are treated as dynamic systems and tackled accordingly by means of a qualitative analysis. As an example, the profitability of a firm is taken as a state variable within the celebrated model by Gordon and Shapiro. A one parameter bifurcation analysis is performed on the ensuing nonlinear dynamic system. Novel results about the price-earnings ratio are obtained and financially interpreted.